id	sid	tid	token	lemma	pos
ajpdis-102	1	1	11	11	NUM
ajpdis-102	1	2	american	american	ADJ
ajpdis-102	1	3	journal	journal	PROPN
ajpdis-102	1	4	of	of	ADP
ajpdis-102	1	5	public	public	ADJ
ajpdis-102	1	6	diplomacy	diplomacy	NOUN
ajpdis-102	1	7	and	and	CCONJ
ajpdis-102	1	8	international	international	ADJ
ajpdis-102	1	9	studies	study	NOUN
ajpdis-102	1	10	www	www	PROPN
ajpdis-102	1	11	.	.	PROPN
ajpdis-102	2	1	grnjournal.us	grnjournal.us	PROPN
ajpdis-102	2	2	american	american	PROPN
ajpdis-102	2	3	journal	journal	PROPN
ajpdis-102	2	4	of	of	ADP
ajpdis-102	2	5	public	public	ADJ
ajpdis-102	2	6	diplomacy	diplomacy	NOUN
ajpdis-102	2	7	and	and	CCONJ
ajpdis-102	2	8	international	international	ADJ
ajpdis-102	2	9	studies	study	NOUN
ajpdis-102	2	10	volume	volume	NOUN
ajpdis-102	2	11	01	01	NUM
ajpdis-102	2	12	,	,	PUNCT
ajpdis-102	2	13	issue	issue	NOUN
ajpdis-102	2	14	02	02	NUM
ajpdis-102	2	15	,	,	PUNCT
ajpdis-102	2	16	2023	2023	NUM
ajpdis-102	2	17	issn	issn	X
ajpdis-102	2	18	(	(	PUNCT
ajpdis-102	2	19	e	e	NOUN
ajpdis-102	2	20	):	):	PUNCT
ajpdis-102	2	21	ххх	ххх	PROPN
ajpdis-102	2	22	-	-	PUNCT
ajpdis-102	2	23	ххх	ххх	NOUN
ajpdis-102	2	24	non	non	ADJ
ajpdis-102	2	25	-	-	ADJ
ajpdis-102	2	26	standard	standard	ADJ
ajpdis-102	2	27	methods	method	NOUN
ajpdis-102	2	28	for	for	ADP
ajpdis-102	2	29	solving	solve	VERB
ajpdis-102	2	30	trigonometric	trigonometric	ADJ
ajpdis-102	2	31	inequalities	inequality	NOUN
ajpdis-102	2	32	sh	sh	PROPN
ajpdis-102	2	33	.	.	PROPN
ajpdis-102	2	34	l.	l.	PROPN
ajpdis-102	2	35	ermatov	ermatov	PROPN
ajpdis-102	2	36	andijan	andijan	PROPN
ajpdis-102	2	37	state	state	PROPN
ajpdis-102	2	38	university	university	NOUN
ajpdis-102	2	39	abstract	abstract	NOUN
ajpdis-102	2	40	:	:	PUNCT
ajpdis-102	2	41	this	this	DET
ajpdis-102	2	42	article	article	NOUN
ajpdis-102	2	43	describes	describe	VERB
ajpdis-102	2	44	non	non	ADJ
ajpdis-102	2	45	-	-	ADJ
ajpdis-102	2	46	standard	standard	ADJ
ajpdis-102	2	47	ususes	ususe	NOUN
ajpdis-102	2	48	for	for	ADP
ajpdis-102	2	49	solving	solve	VERB
ajpdis-102	2	50	trigonometric	trigonometric	ADJ
ajpdis-102	2	51	equations	equation	NOUN
ajpdis-102	2	52	.	.	PUNCT
ajpdis-102	3	1	it	it	PRON
ajpdis-102	3	2	presents	present	VERB
ajpdis-102	3	3	the	the	DET
ajpdis-102	3	4	method	method	NOUN
ajpdis-102	3	5	of	of	ADP
ajpdis-102	3	6	sectors	sector	NOUN
ajpdis-102	3	7	and	and	CCONJ
ajpdis-102	3	8	the	the	DET
ajpdis-102	3	9	method	method	NOUN
ajpdis-102	3	10	of	of	ADP
ajpdis-102	3	11	concentric	concentric	ADJ
ajpdis-102	3	12	circles	circle	NOUN
ajpdis-102	3	13	from	from	ADP
ajpdis-102	3	14	non	non	ADJ
ajpdis-102	3	15	-	-	ADJ
ajpdis-102	3	16	standard	standard	ADJ
ajpdis-102	3	17	methods	method	NOUN
ajpdis-102	3	18	of	of	ADP
ajpdis-102	3	19	solving	solve	VERB
ajpdis-102	3	20	trigonometric	trigonometric	ADJ
ajpdis-102	3	21	inequalities	inequality	NOUN
ajpdis-102	3	22	based	base	VERB
ajpdis-102	3	23	on	on	ADP
ajpdis-102	3	24	the	the	DET
ajpdis-102	3	25	principle	principle	NOUN
ajpdis-102	3	26	of	of	ADP
ajpdis-102	3	27	the	the	DET
ajpdis-102	3	28	genetic	genetic	ADJ
ajpdis-102	3	29	approach	approach	NOUN
ajpdis-102	3	30	.	.	PUNCT
ajpdis-102	4	1	keywords	keyword	NOUN
ajpdis-102	4	2	:	:	PUNCT
ajpdis-102	4	3	trigonometric	trigonometric	ADJ
ajpdis-102	4	4	issue	issue	NOUN
ajpdis-102	4	5	,	,	PUNCT
ajpdis-102	4	6	method	method	NOUN
ajpdis-102	4	7	of	of	ADP
ajpdis-102	4	8	concentric	concentric	ADJ
ajpdis-102	4	9	circles	circle	NOUN
ajpdis-102	4	10	,	,	PUNCT
ajpdis-102	4	11	method	method	NOUN
ajpdis-102	4	12	of	of	ADP
ajpdis-102	4	13	sectors	sector	NOUN
ajpdis-102	4	14	,	,	PUNCT
ajpdis-102	4	15	genetic	genetic	ADJ
ajpdis-102	4	16	approach	approach	NOUN
ajpdis-102	4	17	.	.	PUNCT
ajpdis-102	5	1	introduction	introduction	NOUN
ajpdis-102	5	2	:	:	PUNCT
ajpdis-102	5	3	the	the	DET
ajpdis-102	5	4	purpose	purpose	NOUN
ajpdis-102	5	5	of	of	ADP
ajpdis-102	5	6	teaching	teaching	NOUN
ajpdis-102	5	7	trigonometry	trigonometry	NOUN
ajpdis-102	5	8	in	in	ADP
ajpdis-102	5	9	specialized	specialized	ADJ
ajpdis-102	5	10	schools	school	NOUN
ajpdis-102	5	11	(	(	PUNCT
ajpdis-102	5	12	educational	educational	ADJ
ajpdis-102	5	13	,	,	PUNCT
ajpdis-102	5	14	educational	educational	ADJ
ajpdis-102	5	15	,	,	PUNCT
ajpdis-102	5	16	practical	practical	ADJ
ajpdis-102	5	17	)	)	PUNCT
ajpdis-102	5	18	is	be	AUX
ajpdis-102	5	19	determined	determine	VERB
ajpdis-102	5	20	by	by	ADP
ajpdis-102	5	21	the	the	DET
ajpdis-102	5	22	implementation	implementation	NOUN
ajpdis-102	5	23	of	of	ADP
ajpdis-102	5	24	trigonometry	trigonometry	NOUN
ajpdis-102	5	25	in	in	ADP
ajpdis-102	5	26	solving	solve	VERB
ajpdis-102	5	27	practical	practical	ADJ
ajpdis-102	5	28	issues	issue	NOUN
ajpdis-102	5	29	related	relate	VERB
ajpdis-102	5	30	to	to	ADP
ajpdis-102	5	31	various	various	ADJ
ajpdis-102	5	32	fields	field	NOUN
ajpdis-102	5	33	and	and	CCONJ
ajpdis-102	5	34	disciplines	discipline	NOUN
ajpdis-102	5	35	,	,	PUNCT
ajpdis-102	5	36	as	as	ADV
ajpdis-102	5	37	well	well	ADV
ajpdis-102	5	38	as	as	ADP
ajpdis-102	5	39	the	the	DET
ajpdis-102	5	40	application	application	NOUN
ajpdis-102	5	41	of	of	ADP
ajpdis-102	5	42	trigonometric	trigonometric	ADJ
ajpdis-102	5	43	functions	function	NOUN
ajpdis-102	5	44	.	.	PUNCT
ajpdis-102	6	1	trigonometry	trigonometry	NOUN
ajpdis-102	6	2	is	be	AUX
ajpdis-102	6	3	distinguished	distinguish	VERB
ajpdis-102	6	4	by	by	ADP
ajpdis-102	6	5	great	great	ADJ
ajpdis-102	6	6	importance	importance	NOUN
ajpdis-102	6	7	in	in	ADP
ajpdis-102	6	8	theory	theory	NOUN
ajpdis-102	6	9	and	and	CCONJ
ajpdis-102	6	10	practice	practice	NOUN
ajpdis-102	6	11	,	,	PUNCT
ajpdis-102	6	12	in	in	ADP
ajpdis-102	6	13	particular	particular	ADJ
ajpdis-102	6	14	,	,	PUNCT
ajpdis-102	6	15	by	by	ADP
ajpdis-102	6	16	the	the	DET
ajpdis-102	6	17	fact	fact	NOUN
ajpdis-102	6	18	that	that	SCONJ
ajpdis-102	6	19	it	it	PRON
ajpdis-102	6	20	is	be	AUX
ajpdis-102	6	21	an	an	DET
ajpdis-102	6	22	excellent	excellent	ADJ
ajpdis-102	6	23	computational	computational	ADJ
ajpdis-102	6	24	apparatus	apparatus	NOUN
ajpdis-102	6	25	in	in	ADP
ajpdis-102	6	26	solving	solve	VERB
ajpdis-102	6	27	various	various	ADJ
ajpdis-102	6	28	problems	problem	NOUN
ajpdis-102	6	29	of	of	ADP
ajpdis-102	6	30	geometry	geometry	NOUN
ajpdis-102	6	31	,	,	PUNCT
ajpdis-102	6	32	by	by	ADP
ajpdis-102	6	33	the	the	DET
ajpdis-102	6	34	means	mean	NOUN
ajpdis-102	6	35	of	of	ADP
ajpdis-102	6	36	trigonometric	trigonometric	ADJ
ajpdis-102	6	37	functions	function	NOUN
ajpdis-102	6	38	it	it	PRON
ajpdis-102	6	39	is	be	AUX
ajpdis-102	6	40	convenient	convenient	ADJ
ajpdis-102	6	41	to	to	PART
ajpdis-102	6	42	express	express	VERB
ajpdis-102	6	43	mathematical	mathematical	ADJ
ajpdis-102	6	44	concepts	concept	NOUN
ajpdis-102	6	45	such	such	ADJ
ajpdis-102	6	46	as	as	ADP
ajpdis-102	6	47	periodicity	periodicity	NOUN
ajpdis-102	6	48	,	,	PUNCT
ajpdis-102	6	49	monotony	monotony	ADV
ajpdis-102	6	50	,	,	PUNCT
ajpdis-102	6	51	pointing	pointing	NOUN
ajpdis-102	6	52	accuracy	accuracy	NOUN
ajpdis-102	6	53	,	,	PUNCT
ajpdis-102	6	54	delimitation	delimitation	NOUN
ajpdis-102	6	55	,	,	PUNCT
ajpdis-102	6	56	pairwise	pairwise	NOUN
ajpdis-102	6	57	rigidity	rigidity	NOUN
ajpdis-102	6	58	,	,	PUNCT
ajpdis-102	6	59	bias	bias	NOUN
ajpdis-102	6	60	and	and	CCONJ
ajpdis-102	6	61	convex	convex	NOUN
ajpdis-102	6	62	,	,	PUNCT
ajpdis-102	6	63	continuity	continuity	NOUN
ajpdis-102	6	64	in	in	ADP
ajpdis-102	6	65	a	a	DET
ajpdis-102	6	66	clear	clear	ADJ
ajpdis-102	6	67	,	,	PUNCT
ajpdis-102	6	68	visual	visual	ADJ
ajpdis-102	6	69	and	and	CCONJ
ajpdis-102	6	70	understandable	understandable	ADJ
ajpdis-102	6	71	way	way	NOUN
ajpdis-102	7	1	[	[	X
ajpdis-102	7	2	2,3,4	2,3,4	NUM
ajpdis-102	7	3	]	]	X
ajpdis-102	7	4	.	.	PUNCT
ajpdis-102	8	1	in	in	ADP
ajpdis-102	8	2	particular	particular	ADJ
ajpdis-102	8	3	,	,	PUNCT
ajpdis-102	8	4	the	the	DET
ajpdis-102	8	5	use	use	NOUN
ajpdis-102	8	6	of	of	ADP
ajpdis-102	8	7	non	non	ADJ
ajpdis-102	8	8	-	-	ADJ
ajpdis-102	8	9	standard	standard	ADJ
ajpdis-102	8	10	methods	method	NOUN
ajpdis-102	8	11	in	in	ADP
ajpdis-102	8	12	solving	solve	VERB
ajpdis-102	8	13	inequalities	inequality	NOUN
ajpdis-102	8	14	of	of	ADP
ajpdis-102	8	15	the	the	DET
ajpdis-102	8	16	trigonometric	trigonometric	ADJ
ajpdis-102	8	17	equation	equation	NOUN
ajpdis-102	8	18	extends	extend	VERB
ajpdis-102	8	19	the	the	DET
ajpdis-102	8	20	field	field	NOUN
ajpdis-102	8	21	of	of	ADP
ajpdis-102	8	22	application	application	NOUN
ajpdis-102	8	23	of	of	ADP
ajpdis-102	8	24	trigonometry	trigonometry	NOUN
ajpdis-102	8	25	.	.	PUNCT
ajpdis-102	9	1	below	below	ADP
ajpdis-102	9	2	we	we	PRON
ajpdis-102	9	3	give	give	VERB
ajpdis-102	9	4	several	several	ADJ
ajpdis-102	9	5	non	non	ADJ
ajpdis-102	9	6	-	-	ADJ
ajpdis-102	9	7	standard	standard	ADJ
ajpdis-102	9	8	methods	method	NOUN
ajpdis-102	9	9	for	for	ADP
ajpdis-102	9	10	solving	solve	VERB
ajpdis-102	9	11	trigonometric	trigonometric	ADJ
ajpdis-102	9	12	inequalities	inequality	NOUN
ajpdis-102	9	13	.	.	PUNCT
ajpdis-102	10	1	research	research	NOUN
ajpdis-102	10	2	methodology	methodology	NOUN
ajpdis-102	10	3	:	:	PUNCT
ajpdis-102	10	4	a	a	X
ajpdis-102	10	5	)	)	PUNCT
ajpdis-102	10	6	sectors	sector	NOUN
ajpdis-102	10	7	method	method	NOUN
ajpdis-102	10	8	in	in	ADP
ajpdis-102	10	9	solving	solve	VERB
ajpdis-102	10	10	trigonometric	trigonometric	ADJ
ajpdis-102	10	11	inequalities	inequality	NOUN
ajpdis-102	10	12	.	.	PUNCT
ajpdis-102	11	1	let	let	VERB
ajpdis-102	11	2	's	us	PRON
ajpdis-102	11	3	consider	consider	VERB
ajpdis-102	11	4	the	the	DET
ajpdis-102	11	5	method	method	NOUN
ajpdis-102	11	6	of	of	ADP
ajpdis-102	11	7	sectors	sector	NOUN
ajpdis-102	11	8	when	when	SCONJ
ajpdis-102	11	9	solving	solve	VERB
ajpdis-102	11	10	trigonometric	trigonometric	ADJ
ajpdis-102	11	11	inequalities	inequality	NOUN
ajpdis-102	11	12	.	.	PUNCT
ajpdis-102	12	1	in	in	ADP
ajpdis-102	12	2	the	the	DET
ajpdis-102	12	3	form	form	NOUN
ajpdis-102	12	4	(	(	PUNCT
ajpdis-102	12	5	where	where	SCONJ
ajpdis-102	12	6	and	and	CCONJ
ajpdis-102	12	7	rationally	rationally	ADV
ajpdis-102	12	8	introduced	introduce	VERB
ajpdis-102	12	9	trigonometric	trigonometric	ADJ
ajpdis-102	12	10	functions	function	NOUN
ajpdis-102	12	11	)	)	PUNCT
ajpdis-102	12	12	the	the	DET
ajpdis-102	12	13	solution	solution	NOUN
ajpdis-102	12	14	of	of	ADP
ajpdis-102	12	15	rational	rational	ADJ
ajpdis-102	12	16	trigonometric	trigonometric	ADJ
ajpdis-102	12	17	inequalities	inequality	NOUN
ajpdis-102	12	18	is	be	AUX
ajpdis-102	12	19	almost	almost	ADV
ajpdis-102	12	20	identical	identical	ADJ
ajpdis-102	12	21	to	to	ADP
ajpdis-102	12	22	the	the	DET
ajpdis-102	12	23	solution	solution	NOUN
ajpdis-102	12	24	of	of	ADP
ajpdis-102	12	25	rational	rational	ADJ
ajpdis-102	12	26	inequalities	inequality	NOUN
ajpdis-102	12	27	.	.	PUNCT
ajpdis-102	13	1	it	it	PRON
ajpdis-102	13	2	is	be	AUX
ajpdis-102	13	3	convenient	convenient	ADJ
ajpdis-102	13	4	to	to	PART
ajpdis-102	13	5	solve	solve	VERB
ajpdis-102	13	6	rational	rational	ADJ
ajpdis-102	13	7	inequalities	inequality	NOUN
ajpdis-102	13	8	by	by	ADP
ajpdis-102	13	9	the	the	DET
ajpdis-102	13	10	method	method	NOUN
ajpdis-102	13	11	of	of	ADP
ajpdis-102	13	12	intervals	interval	NOUN
ajpdis-102	13	13	on	on	ADP
ajpdis-102	13	14	the	the	DET
ajpdis-102	13	15	number	number	NOUN
ajpdis-102	13	16	axis	axis	NOUN
ajpdis-102	13	17	.	.	PUNCT
ajpdis-102	14	1	as	as	ADP
ajpdis-102	14	2	its	its	PRON
ajpdis-102	14	3	analogue	analogue	NOUN
ajpdis-102	14	4	and	and	CCONJ
ajpdis-102	14	5	for	for	ADP
ajpdis-102	14	6	the	the	DET
ajpdis-102	14	7	trigonometric	trigonometric	ADJ
ajpdis-102	14	8	circle	circle	NOUN
ajpdis-102	14	9	,	,	PUNCT
ajpdis-102	14	10	and	and	CCONJ
ajpdis-102	14	11	for	for	ADP
ajpdis-102	14	12	the	the	DET
ajpdis-102	14	13	solution	solution	NOUN
ajpdis-102	14	14	of	of	ADP
ajpdis-102	14	15	the	the	DET
ajpdis-102	14	16	rational	rational	ADJ
ajpdis-102	14	17	trigonometric	trigonometric	ADJ
ajpdis-102	14	18	inequality	inequality	NOUN
ajpdis-102	14	19	in	in	ADP
ajpdis-102	14	20	the	the	DET
ajpdis-102	14	21	semicircle	semicircle	NOUN
ajpdis-102	14	22	,	,	PUNCT
ajpdis-102	14	23	the	the	DET
ajpdis-102	14	24	method	method	NOUN
ajpdis-102	14	25	of	of	ADP
ajpdis-102	14	26	sectors	sector	NOUN
ajpdis-102	14	27	is	be	AUX
ajpdis-102	14	28	considered	consider	VERB
ajpdis-102	15	1	[	[	PUNCT
ajpdis-102	15	2	5,6,7	5,6,7	NOUN
ajpdis-102	15	3	]	]	X
ajpdis-102	15	4	.	.	PUNCT
ajpdis-102	16	1	1	1	X
ajpdis-102	16	2	.	.	X
ajpdis-102	16	3	solving	solve	VERB
ajpdis-102	16	4	form	form	NOUN
ajpdis-102	16	5	inequalities	inequality	NOUN
ajpdis-102	16	6	.	.	PUNCT
ajpdis-102	17	1	(	(	PUNCT
ajpdis-102	17	2	)	)	PUNCT
ajpdis-102	17	3	0	0	NUM
ajpdis-102	17	4	,	,	PUNCT
ajpdis-102	17	5	(	(	PUNCT
ajpdis-102	17	6	0	0	NUM
ajpdis-102	17	7	,	,	PUNCT
ajpdis-102	17	8	0	0	NUM
ajpdis-102	17	9	,	,	PUNCT
ajpdis-102	17	10	0	0	NUM
ajpdis-102	17	11	)	)	PUNCT
ajpdis-102	17	12	(	(	PUNCT
ajpdis-102	17	13	)	)	PUNCT
ajpdis-102	18	1	p	p	X
ajpdis-102	18	2	x	x	X
ajpdis-102	18	3	q	q	PUNCT
ajpdis-102	18	4	x	x	SYM
ajpdis-102	18	5			PROPN
ajpdis-102	18	6			PROPN
ajpdis-102	18	7			NUM
ajpdis-102	18	8			PROPN
ajpdis-102	18	9	(	(	PUNCT
ajpdis-102	18	10	)	)	PUNCT
ajpdis-102	18	11	p	p	NOUN
ajpdis-102	18	12	x	x	X
ajpdis-102	18	13	(	(	PUNCT
ajpdis-102	18	14	)	)	PUNCT
ajpdis-102	18	15	q	q	NOUN
ajpdis-102	18	16	x	x	X
ajpdis-102	18	17	sin	sin	NOUN
ajpdis-102	18	18	x	x	X
ajpdis-102	18	19	cosx	cosx	X
ajpdis-102	18	20	(	(	PUNCT
ajpdis-102	18	21	2	2	NUM
ajpdis-102	18	22	)	)	PUNCT
ajpdis-102	18	23	t	t	NOUN
ajpdis-102	18	24			VERB
ajpdis-102	18	25	tgx	tgx	PROPN
ajpdis-102	18	26	ctgx	ctgx	PROPN
ajpdis-102	18	27	(	(	PUNCT
ajpdis-102	18	28	)	)	PUNCT
ajpdis-102	18	29	t	t	NOUN
ajpdis-102	18	30			PRON
ajpdis-102	18	31	(	(	PUNCT
ajpdis-102	18	32	sin	sin	NOUN
ajpdis-102	18	33	,	,	PUNCT
ajpdis-102	18	34	cos	cos	PROPN
ajpdis-102	18	35	)	)	PUNCT
ajpdis-102	18	36	0	0	NUM
ajpdis-102	19	1	(	(	PUNCT
ajpdis-102	19	2	0	0	NUM
ajpdis-102	19	3	,	,	PUNCT
ajpdis-102	19	4	0	0	NUM
ajpdis-102	19	5	,	,	PUNCT
ajpdis-102	19	6	0	0	NUM
ajpdis-102	19	7	)	)	PUNCT
ajpdis-102	19	8	(	(	PUNCT
ajpdis-102	19	9	sin	sin	NOUN
ajpdis-102	19	10	,	,	PUNCT
ajpdis-102	19	11	cos	cos	PROPN
ajpdis-102	19	12	)	)	PUNCT
ajpdis-102	19	13	p	p	X
ajpdis-102	19	14	x	x	X
ajpdis-102	19	15	x	x	X
ajpdis-102	19	16	q	q	PUNCT
ajpdis-102	19	17	x	x	PUNCT
ajpdis-102	19	18	x	x	SYM
ajpdis-102	19	19			PROPN
ajpdis-102	19	20			PROPN
ajpdis-102	19	21			PROPN
ajpdis-102	19	22			PROPN
ajpdis-102	19	23	12	12	NUM
ajpdis-102	19	24	american	american	ADJ
ajpdis-102	19	25	journal	journal	NOUN
ajpdis-102	19	26	of	of	ADP
ajpdis-102	19	27	public	public	ADJ
ajpdis-102	19	28	diplomacy	diplomacy	NOUN
ajpdis-102	19	29	and	and	CCONJ
ajpdis-102	19	30	international	international	ADJ
ajpdis-102	19	31	studies	study	NOUN
ajpdis-102	19	32	www	www	PROPN
ajpdis-102	19	33	.	.	PROPN
ajpdis-102	20	1	grnjournal.us	grnjournal.us	X
ajpdis-102	20	2	the	the	DET
ajpdis-102	20	3	numerator	numerator	NOUN
ajpdis-102	20	4	and	and	CCONJ
ajpdis-102	20	5	denominator	denominator	NOUN
ajpdis-102	20	6	of	of	ADP
ajpdis-102	20	7	an	an	DET
ajpdis-102	20	8	expression	expression	NOUN
ajpdis-102	20	9	given	give	VERB
ajpdis-102	20	10	in	in	ADP
ajpdis-102	20	11	the	the	DET
ajpdis-102	20	12	interval	interval	NOUN
ajpdis-102	20	13	method	method	NOUN
ajpdis-102	20	14	are	be	AUX
ajpdis-102	20	15	whose	whose	DET
ajpdis-102	20	16	factors	factor	NOUN
ajpdis-102	20	17	correspond	correspond	VERB
ajpdis-102	20	18	to	to	ADP
ajpdis-102	20	19	it	it	PRON
ajpdis-102	20	20	when	when	SCONJ
ajpdis-102	20	21	passing	pass	VERB
ajpdis-102	20	22	through	through	ADP
ajpdis-102	20	23	the	the	DET
ajpdis-102	20	24	point	point	NOUN
ajpdis-102	20	25	,	,	PUNCT
ajpdis-102	20	26	the	the	DET
ajpdis-102	20	27	exchange	exchange	NOUN
ajpdis-102	20	28	of	of	ADP
ajpdis-102	20	29	signals	signal	NOUN
ajpdis-102	20	30	is	be	AUX
ajpdis-102	20	31	determined	determine	VERB
ajpdis-102	20	32	,	,	PUNCT
ajpdis-102	20	33	and	and	CCONJ
ajpdis-102	20	34	the	the	DET
ajpdis-102	20	35	corresponding	corresponding	ADJ
ajpdis-102	20	36	intervals	interval	NOUN
ajpdis-102	20	37	are	be	AUX
ajpdis-102	20	38	obtained	obtain	VERB
ajpdis-102	20	39	depending	depend	VERB
ajpdis-102	20	40	on	on	ADP
ajpdis-102	20	41	the	the	DET
ajpdis-102	20	42	signal	signal	NOUN
ajpdis-102	20	43	of	of	ADP
ajpdis-102	20	44	the	the	DET
ajpdis-102	20	45	inequality	inequality	NOUN
ajpdis-102	20	46	.	.	PUNCT
ajpdis-102	21	1	in	in	ADP
ajpdis-102	21	2	the	the	DET
ajpdis-102	21	3	sectoral	sectoral	ADJ
ajpdis-102	21	4	method	method	NOUN
ajpdis-102	21	5	,	,	PUNCT
ajpdis-102	21	6	however	however	ADV
ajpdis-102	21	7	,	,	PUNCT
ajpdis-102	21	8	each	each	DET
ajpdis-102	21	9	factor	factor	NOUN
ajpdis-102	21	10	of	of	ADP
ajpdis-102	21	11	the	the	DET
ajpdis-102	21	12	numerator	numerator	NOUN
ajpdis-102	21	13	and	and	CCONJ
ajpdis-102	21	14	denominator	denominator	NOUN
ajpdis-102	21	15	of	of	ADP
ajpdis-102	21	16	a	a	DET
ajpdis-102	21	17	given	give	VERB
ajpdis-102	21	18	expression	expression	NOUN
ajpdis-102	21	19	is	be	AUX
ajpdis-102	21	20	in	in	ADP
ajpdis-102	21	21	form	form	NOUN
ajpdis-102	21	22	.	.	PUNCT
ajpdis-102	22	1	here	here	ADV
ajpdis-102	22	2	or	or	CCONJ
ajpdis-102	22	3	is	be	AUX
ajpdis-102	22	4	one	one	NUM
ajpdis-102	22	5	of	of	ADP
ajpdis-102	22	6	the	the	DET
ajpdis-102	22	7	functions	function	NOUN
ajpdis-102	22	8	,	,	PUNCT
ajpdis-102	22	9	in	in	ADP
ajpdis-102	22	10	the	the	DET
ajpdis-102	22	11	trigonometric	trigonometric	ADJ
ajpdis-102	22	12	circle	circle	NOUN
ajpdis-102	22	13	and	and	CCONJ
ajpdis-102	22	14	divides	divide	VERB
ajpdis-102	22	15	two	two	NUM
ajpdis-102	22	16	sectors	sector	NOUN
ajpdis-102	22	17	corresponding	correspond	VERB
ajpdis-102	22	18	to	to	ADP
ajpdis-102	22	19	the	the	DET
ajpdis-102	22	20	corners	corner	NOUN
ajpdis-102	22	21	.	.	PUNCT
ajpdis-102	23	1	these	these	DET
ajpdis-102	23	2	corners	corner	NOUN
ajpdis-102	23	3	are	be	AUX
ajpdis-102	23	4	is	be	AUX
ajpdis-102	23	5	equivalent	equivalent	ADJ
ajpdis-102	23	6	to	to	ADP
ajpdis-102	23	7	from	from	ADP
ajpdis-102	23	8	in	in	ADP
ajpdis-102	23	9	the	the	DET
ajpdis-102	23	10	transition	transition	NOUN
ajpdis-102	23	11	to	to	ADP
ajpdis-102	23	12	the	the	DET
ajpdis-102	23	13	signal	signal	NOUN
ajpdis-102	23	14	of	of	ADP
ajpdis-102	23	15	the	the	DET
ajpdis-102	23	16	expression	expression	NOUN
ajpdis-102	23	17	is	be	AUX
ajpdis-102	23	18	determined	determine	VERB
ajpdis-102	23	19	.	.	PUNCT
ajpdis-102	24	1	the	the	DET
ajpdis-102	24	2	following	follow	VERB
ajpdis-102	24	3	should	should	AUX
ajpdis-102	24	4	be	be	AUX
ajpdis-102	24	5	borne	bear	VERB
ajpdis-102	24	6	in	in	ADP
ajpdis-102	24	7	mind	mind	NOUN
ajpdis-102	24	8	:	:	PUNCT
ajpdis-102	24	9	a	a	X
ajpdis-102	24	10	)	)	PUNCT
ajpdis-102	24	11	and	and	CCONJ
ajpdis-102	24	12	form	form	NOUN
ajpdis-102	24	13	factors	factor	NOUN
ajpdis-102	24	14	while	while	SCONJ
ajpdis-102	24	15	does	do	AUX
ajpdis-102	24	16	not	not	PART
ajpdis-102	24	17	change	change	VERB
ajpdis-102	24	18	the	the	DET
ajpdis-102	24	19	signal	signal	NOUN
ajpdis-102	24	20	at	at	ADP
ajpdis-102	24	21	all	all	DET
ajpdis-102	24	22	values	value	NOUN
ajpdis-102	24	23	of	of	ADP
ajpdis-102	24	24	.	.	PUNCT
ajpdis-102	25	1	therefore	therefore	ADV
ajpdis-102	25	2	,	,	PUNCT
ajpdis-102	25	3	such	such	ADJ
ajpdis-102	25	4	multipliers	multiplier	NOUN
ajpdis-102	25	5	are	be	AUX
ajpdis-102	25	6	discarded	discard	VERB
ajpdis-102	25	7	.	.	PUNCT
ajpdis-102	26	1	if	if	SCONJ
ajpdis-102	26	2	if	if	SCONJ
ajpdis-102	26	3	,	,	PUNCT
ajpdis-102	26	4	by	by	ADP
ajpdis-102	26	5	changing	change	VERB
ajpdis-102	26	6	the	the	DET
ajpdis-102	26	7	inequality	inequality	NOUN
ajpdis-102	26	8	signal	signal	NOUN
ajpdis-102	26	9	to	to	ADP
ajpdis-102	26	10	the	the	DET
ajpdis-102	26	11	opposite	opposite	NOUN
ajpdis-102	26	12	,	,	PUNCT
ajpdis-102	26	13	the	the	DET
ajpdis-102	26	14	factors	factor	NOUN
ajpdis-102	26	15	are	be	AUX
ajpdis-102	26	16	discarded	discard	VERB
ajpdis-102	26	17	.	.	PUNCT
ajpdis-102	27	1	b	b	X
ajpdis-102	27	2	)	)	PUNCT
ajpdis-102	27	3	and	and	CCONJ
ajpdis-102	27	4	form	form	NOUN
ajpdis-102	27	5	factors	factor	NOUN
ajpdis-102	27	6	are	be	AUX
ajpdis-102	27	7	also	also	ADV
ajpdis-102	27	8	discarded	discard	VERB
ajpdis-102	27	9	.	.	PUNCT
ajpdis-102	28	1	moreover	moreover	ADV
ajpdis-102	28	2	,	,	PUNCT
ajpdis-102	28	3	if	if	SCONJ
ajpdis-102	28	4	these	these	PRON
ajpdis-102	28	5	are	be	AUX
ajpdis-102	28	6	multiples	multiple	NOUN
ajpdis-102	28	7	of	of	ADP
ajpdis-102	28	8	the	the	DET
ajpdis-102	28	9	denominator	denominator	NOUN
ajpdis-102	28	10	,	,	PUNCT
ajpdis-102	28	11	then	then	ADV
ajpdis-102	28	12	and	and	CCONJ
ajpdis-102	28	13	will	will	AUX
ajpdis-102	28	14	be	be	AUX
ajpdis-102	28	15	thrown	throw	VERB
ajpdis-102	28	16	under	under	ADP
ajpdis-102	28	17	the	the	DET
ajpdis-102	28	18	conditioni	conditioni	NOUN
ajpdis-102	28	19	.	.	PUNCT
ajpdis-102	29	1	or	or	CCONJ
ajpdis-102	29	2	when	when	SCONJ
ajpdis-102	29	3	form	form	NOUN
ajpdis-102	29	4	factors	factor	NOUN
ajpdis-102	29	5	are	be	AUX
ajpdis-102	29	6	discarded	discard	VERB
ajpdis-102	29	7	,	,	PUNCT
ajpdis-102	29	8	the	the	DET
ajpdis-102	29	9	inequality	inequality	NOUN
ajpdis-102	29	10	signal	signal	VERB
ajpdis-102	29	11	changes	change	NOUN
ajpdis-102	29	12	to	to	ADP
ajpdis-102	29	13	the	the	DET
ajpdis-102	29	14	opposite	opposite	NOUN
ajpdis-102	29	15	.	.	PUNCT
ajpdis-102	30	1	2	2	X
ajpdis-102	30	2	.	.	X
ajpdis-102	30	3	solving	solve	VERB
ajpdis-102	30	4	form	form	NOUN
ajpdis-102	30	5	inequalities	inequality	NOUN
ajpdis-102	30	6	.	.	PUNCT
ajpdis-102	31	1	or	or	CCONJ
ajpdis-102	31	2	was	be	AUX
ajpdis-102	31	3	one	one	NUM
ajpdis-102	31	4	of	of	ADP
ajpdis-102	31	5	the	the	DET
ajpdis-102	31	6	functions	function	NOUN
ajpdis-102	31	7	of	of	ADP
ajpdis-102	31	8	the	the	DET
ajpdis-102	31	9	function	function	NOUN
ajpdis-102	31	10	each	each	DET
ajpdis-102	31	11	factor	factor	NOUN
ajpdis-102	31	12	of	of	ADP
ajpdis-102	31	13	the	the	DET
ajpdis-102	31	14	form	form	NOUN
ajpdis-102	31	15	is	be	AUX
ajpdis-102	31	16	a	a	DET
ajpdis-102	31	17	trigonometric	trigonometric	ADJ
ajpdis-102	31	18	semicircle	semicircle	NOUN
ajpdis-102	31	19	(	(	PUNCT
ajpdis-102	31	20	or	or	CCONJ
ajpdis-102	31	21	)	)	PUNCT
ajpdis-102	31	22	at	at	ADP
ajpdis-102	31	23	one	one	NUM
ajpdis-102	31	24	fits	fit	VERB
ajpdis-102	31	25	the	the	DET
ajpdis-102	31	26	angle	angle	NOUN
ajpdis-102	31	27	,	,	PUNCT
ajpdis-102	31	28	or	or	CCONJ
ajpdis-102	31	29	.	.	PUNCT
ajpdis-102	32	1	this	this	PRON
ajpdis-102	32	2	when	when	SCONJ
ajpdis-102	32	3	passing	pass	VERB
ajpdis-102	32	4	a	a	DET
ajpdis-102	32	5	point	point	NOUN
ajpdis-102	32	6	the	the	DET
ajpdis-102	32	7	signal	signal	NOUN
ajpdis-102	32	8	of	of	ADP
ajpdis-102	32	9	the	the	DET
ajpdis-102	32	10	multiplier	multipli	ADJ
ajpdis-102	32	11	alternates	alternate	NOUN
ajpdis-102	32	12	.	.	PUNCT
ajpdis-102	33	1	in	in	ADP
ajpdis-102	33	2	addition	addition	NOUN
ajpdis-102	33	3	,	,	PUNCT
ajpdis-102	33	4	function	function	NOUN
ajpdis-102	33	5	is	be	AUX
ajpdis-102	33	6	not	not	PART
ajpdis-102	33	7	defined	define	VERB
ajpdis-102	33	8	at	at	ADP
ajpdis-102	33	9	,	,	PUNCT
ajpdis-102	33	10	and	and	CCONJ
ajpdis-102	33	11	will	will	AUX
ajpdis-102	33	12	have	have	VERB
ajpdis-102	33	13	a	a	DET
ajpdis-102	33	14	different	different	ADJ
ajpdis-102	33	15	signal	signal	NOUN
ajpdis-102	33	16	on	on	ADP
ajpdis-102	33	17	the	the	DET
ajpdis-102	33	18	left	left	NOUN
ajpdis-102	33	19	and	and	CCONJ
ajpdis-102	33	20	right	right	NOUN
ajpdis-102	33	21	of	of	ADP
ajpdis-102	33	22	these	these	DET
ajpdis-102	33	23	points	point	NOUN
ajpdis-102	33	24	.	.	PUNCT
ajpdis-102	34	1	similar	similar	ADJ
ajpdis-102	34	2	function	function	NOUN
ajpdis-102	34	3	va	va	NOUN
ajpdis-102	34	4	at	at	ADP
ajpdis-102	34	5	undefined	undefined	ADJ
ajpdis-102	34	6	and	and	CCONJ
ajpdis-102	34	7	to	to	ADP
ajpdis-102	34	8	the	the	DET
ajpdis-102	34	9	right	right	NOUN
ajpdis-102	34	10	of	of	ADP
ajpdis-102	34	11	these	these	DET
ajpdis-102	34	12	points	point	NOUN
ajpdis-102	34	13	there	there	PRON
ajpdis-102	34	14	are	be	VERB
ajpdis-102	34	15	different	different	ADJ
ajpdis-102	34	16	symbols	symbol	NOUN
ajpdis-102	34	17	.	.	PUNCT
ajpdis-102	35	1	1example	1example	X
ajpdis-102	35	2	.	.	PUNCT
ajpdis-102	36	1	solve	solve	VERB
ajpdis-102	36	2	the	the	DET
ajpdis-102	36	3	inequality	inequality	NOUN
ajpdis-102	36	4	:	:	PUNCT
ajpdis-102	36	5	.	.	PUNCT
ajpdis-102	37	1	solution	solution	NOUN
ajpdis-102	37	2	:	:	PUNCT
ajpdis-102	37	3	.	.	PUNCT
ajpdis-102	38	1	trigonometric	trigonometric	ADJ
ajpdis-102	38	2	half	half	NOUN
ajpdis-102	38	3	in	in	ADP
ajpdis-102	38	4	the	the	DET
ajpdis-102	38	5	circle	circle	NOUN
ajpdis-102	38	6	the	the	DET
ajpdis-102	38	7	equation	equation	NOUN
ajpdis-102	38	8	is	be	AUX
ajpdis-102	38	9	given	give	VERB
ajpdis-102	38	10	by	by	ADP
ajpdis-102	38	11	angle	angle	NOUN
ajpdis-102	38	12	,	,	PUNCT
ajpdis-102	38	13	the	the	DET
ajpdis-102	38	14	equation	equation	NOUN
ajpdis-102	38	15	is	be	AUX
ajpdis-102	38	16	given	give	VERB
ajpdis-102	38	17	by	by	ADP
ajpdis-102	38	18	the	the	DET
ajpdis-102	38	19	angle	angle	NOUN
ajpdis-102	38	20	is	be	AUX
ajpdis-102	38	21	suitable	suitable	ADJ
ajpdis-102	38	22	.	.	PUNCT
ajpdis-102	39	1	they	they	PRON
ajpdis-102	39	2	divide	divide	VERB
ajpdis-102	39	3	the	the	DET
ajpdis-102	39	4	semicircle	semicircle	NOUN
ajpdis-102	39	5	into	into	ADP
ajpdis-102	39	6	three	three	NUM
ajpdis-102	39	7	sectors	sector	NOUN
ajpdis-102	39	8	,	,	PUNCT
ajpdis-102	39	9	and	and	CCONJ
ajpdis-102	39	10	their	their	PRON
ajpdis-102	39	11	in	in	ADP
ajpdis-102	39	12	each	each	DET
ajpdis-102	39	13	the	the	DET
ajpdis-102	39	14	function	function	NOUN
ajpdis-102	39	15	saves	save	VERB
ajpdis-102	39	16	the	the	DET
ajpdis-102	39	17	signal	signal	NOUN
ajpdis-102	39	18	and	and	CCONJ
ajpdis-102	39	19	exchanges	exchange	NOUN
ajpdis-102	39	20	hints	hint	VERB
ajpdis-102	39	21	in	in	ADP
ajpdis-102	39	22	each	each	DET
ajpdis-102	39	23	sector	sector	NOUN
ajpdis-102	39	24	(	(	PUNCT
ajpdis-102	39	25	1	1	NUM
ajpdis-102	39	26	-	-	PUNCT
ajpdis-102	39	27	picture	picture	NOUN
ajpdis-102	39	28	)	)	PUNCT
ajpdis-102	39	29	.	.	PUNCT
ajpdis-102	40	1	1	1	NUM
ajpdis-102	40	2	-	-	PUNCT
ajpdis-102	40	3	picture	picture	NOUN
ajpdis-102	40	4	0	0	NUM
ajpdis-102	40	5	(	(	PUNCT
ajpdis-102	40	6	)	)	PUNCT
ajpdis-102	40	7	x	x	SYM
ajpdis-102	40	8	x	x	PROPN
ajpdis-102	40	9	0x	0x	NOUN
ajpdis-102	40	10	(	(	PUNCT
ajpdis-102	40	11	(	(	PUNCT
ajpdis-102	40	12	)	)	PUNCT
ajpdis-102	40	13	)	)	PUNCT
ajpdis-102	40	14	f	f	X
ajpdis-102	40	15	x	x	X
ajpdis-102	40	16	a	a	X
ajpdis-102	40	17	(	(	PUNCT
ajpdis-102	40	18	)	)	PUNCT
ajpdis-102	40	19	f	f	NOUN
ajpdis-102	40	20	x	x	PUNCT
ajpdis-102	40	21	sin	sin	VERB
ajpdis-102	40	22	x	x	PUNCT
ajpdis-102	40	23	cos	cos	PROPN
ajpdis-102	40	24	,	,	PUNCT
ajpdis-102	40	25	x	x	PROPN
ajpdis-102	40	26	1	1	NUM
ajpdis-102	40	27	1a	1a	NUM
ajpdis-102	40	28			PROPN
ajpdis-102	40	29			PROPN
ajpdis-102	40	30	1x	1x	NUM
ajpdis-102	41	1	2x	2x	NUM
ajpdis-102	41	2	1	1	NUM
ajpdis-102	41	3	2	2	NUM
ajpdis-102	41	4	(	(	PUNCT
ajpdis-102	41	5	(	(	PUNCT
ajpdis-102	41	6	)	)	PUNCT
ajpdis-102	41	7	(	(	PUNCT
ajpdis-102	41	8	)	)	PUNCT
ajpdis-102	41	9	)	)	PUNCT
ajpdis-102	42	1	f	f	X
ajpdis-102	43	1	x	x	PUNCT
ajpdis-102	43	2	f	f	NOUN
ajpdis-102	43	3	x	x	PUNCT
ajpdis-102	43	4	a	a	VERB
ajpdis-102	43	5			NUM
ajpdis-102	43	6	1x	1x	NUM
ajpdis-102	43	7	2x	2x	NUM
ajpdis-102	43	8	(	(	PUNCT
ajpdis-102	43	9	(	(	PUNCT
ajpdis-102	43	10	)	)	PUNCT
ajpdis-102	43	11	)	)	PUNCT
ajpdis-102	43	12	f	f	X
ajpdis-102	44	1	x	x	X
ajpdis-102	44	2	a	a	X
ajpdis-102	44	3	(	(	PUNCT
ajpdis-102	44	4	sin	sin	NOUN
ajpdis-102	44	5	)	)	PUNCT
ajpdis-102	44	6	x	x	SYM
ajpdis-102	44	7	a	a	X
ajpdis-102	44	8	(	(	PUNCT
ajpdis-102	44	9	cos	cos	PROPN
ajpdis-102	44	10	)	)	PUNCT
ajpdis-102	44	11	x	x	SYM
ajpdis-102	44	12	a	a	VERB
ajpdis-102	44	13	|	|	ADV
ajpdis-102	44	14	|	|	ADV
ajpdis-102	44	15	1a	1a	VERB
ajpdis-102	44	16			VERB
ajpdis-102	44	17	x	x	ADJ
ajpdis-102	44	18	1a	1a	X
ajpdis-102	44	19			INTJ
ajpdis-102	44	20	(	(	PUNCT
ajpdis-102	44	21	sin	sin	NOUN
ajpdis-102	44	22	1)x	1)x	NUM
ajpdis-102	44	23			PROPN
ajpdis-102	44	24	(	(	PUNCT
ajpdis-102	44	25	cos	cos	INTJ
ajpdis-102	44	26	1)x	1)x	PROPN
ajpdis-102	44	27			PROPN
ajpdis-102	44	28	sin	sin	VERB
ajpdis-102	44	29	1x	1x	NUM
ajpdis-102	44	30			PROPN
ajpdis-102	45	1			PROPN
ajpdis-102	45	2	cos	cos	PROPN
ajpdis-102	45	3	1x	1x	PROPN
ajpdis-102	45	4			PROPN
ajpdis-102	45	5			PROPN
ajpdis-102	45	6	(	(	PUNCT
ajpdis-102	45	7	sin	sin	NOUN
ajpdis-102	45	8	1)x	1)x	NUM
ajpdis-102	45	9			PROPN
ajpdis-102	45	10	(	(	PUNCT
ajpdis-102	45	11	cos	cos	PROPN
ajpdis-102	45	12	1)x	1)x	NUM
ajpdis-102	45	13			PROPN
ajpdis-102	45	14	(	(	PUNCT
ajpdis-102	45	15	,	,	PUNCT
ajpdis-102	45	16	)	)	PUNCT
ajpdis-102	45	17	0	0	NUM
ajpdis-102	46	1	(	(	PUNCT
ajpdis-102	46	2	0	0	NUM
ajpdis-102	46	3	,	,	PUNCT
ajpdis-102	46	4	0	0	NUM
ajpdis-102	46	5	,	,	PUNCT
ajpdis-102	46	6	0	0	NUM
ajpdis-102	46	7	)	)	PUNCT
ajpdis-102	46	8	(	(	PUNCT
ajpdis-102	46	9	,	,	PUNCT
ajpdis-102	46	10	)	)	PUNCT
ajpdis-102	47	1	p	p	PROPN
ajpdis-102	47	2	tgx	tgx	PROPN
ajpdis-102	47	3	ctgx	ctgx	VERB
ajpdis-102	47	4	q	q	PROPN
ajpdis-102	47	5	tgx	tgx	PROPN
ajpdis-102	47	6	ctgx	ctgx	NOUN
ajpdis-102	47	7			PROPN
ajpdis-102	47	8			PROPN
ajpdis-102	47	9			NUM
ajpdis-102	47	10			PROPN
ajpdis-102	47	11	tgx	tgx	NOUN
ajpdis-102	47	12	ctgx	ctgx	NOUN
ajpdis-102	47	13	(	(	PUNCT
ajpdis-102	47	14	)	)	PUNCT
ajpdis-102	47	15	f	f	X
ajpdis-102	47	16	x	x	X
ajpdis-102	47	17	(	(	PUNCT
ajpdis-102	47	18	(	(	PUNCT
ajpdis-102	47	19	)	)	PUNCT
ajpdis-102	47	20	)	)	PUNCT
ajpdis-102	48	1	f	f	X
ajpdis-102	48	2	x	x	PUNCT
ajpdis-102	48	3	a	a	VERB
ajpdis-102	48	4	2	2	NUM
ajpdis-102	48	5	2	2	NUM
ajpdis-102	48	6	x	x	SYM
ajpdis-102	48	7			PROPN
ajpdis-102	48	8			ADJ
ajpdis-102	48	9			NOUN
ajpdis-102	48	10			PROPN
ajpdis-102	48	11			PROPN
ajpdis-102	48	12	0	0	NUM
ajpdis-102	49	1	x	x	SYM
ajpdis-102	49	2			ADP
ajpdis-102	49	3			PROPN
ajpdis-102	49	4	0x	0x	NOUN
ajpdis-102	49	5	0	0	NUM
ajpdis-102	49	6	(	(	PUNCT
ajpdis-102	49	7	)	)	PUNCT
ajpdis-102	49	8	f	f	X
ajpdis-102	49	9	x	x	PUNCT
ajpdis-102	49	10	a	a	VERB
ajpdis-102	49	11	0x	0x	X
ajpdis-102	49	12	0	0	NUM
ajpdis-102	49	13	(	(	PUNCT
ajpdis-102	49	14	(	(	PUNCT
ajpdis-102	49	15	)	)	PUNCT
ajpdis-102	49	16	f	f	NOUN
ajpdis-102	49	17	x	x	X
ajpdis-102	49	18	a	a	VERB
ajpdis-102	49	19	tgx	tgx	PROPN
ajpdis-102	49	20	2	2	NUM
ajpdis-102	49	21	x	x	SYM
ajpdis-102	49	22			NOUN
ajpdis-102	49	23			PROPN
ajpdis-102	49	24			PROPN
ajpdis-102	49	25	ctgx	ctgx	VERB
ajpdis-102	49	26	0x	0x	NOUN
ajpdis-102	49	27			PROPN
ajpdis-102	49	28	x	x	PUNCT
ajpdis-102	49	29			VERB
ajpdis-102	49	30	2	2	NUM
ajpdis-102	49	31	0ctg	0ctg	NOUN
ajpdis-102	49	32	x	x	SYM
ajpdis-102	49	33	ctgx	ctgx	VERB
ajpdis-102	49	34			X
ajpdis-102	49	35	(	(	PUNCT
ajpdis-102	49	36	1	1	X
ajpdis-102	49	37	)	)	PUNCT
ajpdis-102	49	38	0ctgx	0ctgx	NOUN
ajpdis-102	49	39	ctgx	ctgx	VERB
ajpdis-102	49	40			VERB
ajpdis-102	50	1			PROPN
ajpdis-102	50	2	0	0	PUNCT
ajpdis-102	51	1	x	x	SYM
ajpdis-102	51	2			NUM
ajpdis-102	51	3			PROPN
ajpdis-102	51	4	0ctgx	0ctgx	NUM
ajpdis-102	52	1			NOUN
ajpdis-102	52	2	1	1	NUM
ajpdis-102	52	3	2	2	NUM
ajpdis-102	52	4	x	x	SYM
ajpdis-102	52	5			PROPN
ajpdis-102	52	6			NUM
ajpdis-102	52	7	1ctgx	1ctgx	NUM
ajpdis-102	52	8			NUM
ajpdis-102	52	9			NOUN
ajpdis-102	52	10	1	1	NUM
ajpdis-102	52	11	3	3	NUM
ajpdis-102	52	12	4	4	NUM
ajpdis-102	52	13	x	x	SYM
ajpdis-102	52	14			PROPN
ajpdis-102	52	15			PROPN
ajpdis-102	52	16	(	(	PUNCT
ajpdis-102	52	17	1)y	1)y	NUM
ajpdis-102	52	18	ctgx	ctgx	PROPN
ajpdis-102	52	19	ctgx	ctgx	NUM
ajpdis-102	52	20			ADJ
ajpdis-102	52	21	13	13	NUM
ajpdis-102	52	22	american	american	PROPN
ajpdis-102	52	23	journal	journal	PROPN
ajpdis-102	52	24	of	of	ADP
ajpdis-102	52	25	public	public	ADJ
ajpdis-102	52	26	diplomacy	diplomacy	NOUN
ajpdis-102	52	27	and	and	CCONJ
ajpdis-102	52	28	international	international	ADJ
ajpdis-102	52	29	studies	study	NOUN
ajpdis-102	52	30	www	www	PROPN
ajpdis-102	52	31	.	.	PUNCT
ajpdis-102	53	1	grnjournal.us	grnjournal.us	X
ajpdis-102	53	2	in	in	ADP
ajpdis-102	53	3	the	the	DET
ajpdis-102	53	4	sector	sector	NOUN
ajpdis-102	53	5	.	.	PUNCT
ajpdis-102	54	1	and	and	CCONJ
ajpdis-102	54	2	in	in	ADP
ajpdis-102	54	3	the	the	DET
ajpdis-102	54	4	rest	rest	NOUN
ajpdis-102	54	5	,	,	PUNCT
ajpdis-102	54	6	the	the	DET
ajpdis-102	54	7	hint	hint	NOUN
ajpdis-102	54	8	alternates	alternate	NOUN
ajpdis-102	54	9	.	.	PUNCT
ajpdis-102	55	1	period	period	NOUN
ajpdis-102	55	2	of	of	ADP
ajpdis-102	55	3	function	function	NOUN
ajpdis-102	55	4	.	.	PUNCT
ajpdis-102	56	1	since	since	SCONJ
ajpdis-102	56	2	it	it	PRON
ajpdis-102	56	3	is	be	AUX
ajpdis-102	56	4	positive	positive	ADJ
ajpdis-102	56	5	-	-	PUNCT
ajpdis-102	56	6	signal	signal	NOUN
ajpdis-102	56	7	sectors	sector	NOUN
ajpdis-102	56	8	we	we	PRON
ajpdis-102	56	9	choose	choose	VERB
ajpdis-102	56	10	.	.	PUNCT
ajpdis-102	57	1	answer	answer	NOUN
ajpdis-102	57	2	:	:	PUNCT
ajpdis-102	57	3	.	.	PUNCT
ajpdis-102	58	1	b	b	X
ajpdis-102	58	2	)	)	PUNCT
ajpdis-102	58	3	method	method	NOUN
ajpdis-102	58	4	of	of	ADP
ajpdis-102	58	5	concentric	concentric	ADJ
ajpdis-102	58	6	circles	circle	NOUN
ajpdis-102	58	7	solving	solve	VERB
ajpdis-102	58	8	a	a	DET
ajpdis-102	58	9	system	system	NOUN
ajpdis-102	58	10	of	of	ADP
ajpdis-102	58	11	trigonometric	trigonometric	ADJ
ajpdis-102	58	12	inequalities	inequality	NOUN
ajpdis-102	58	13	.	.	PUNCT
ajpdis-102	59	1	this	this	DET
ajpdis-102	59	2	method	method	NOUN
ajpdis-102	59	3	is	be	AUX
ajpdis-102	59	4	compared	compare	VERB
ajpdis-102	59	5	to	to	ADP
ajpdis-102	59	6	the	the	DET
ajpdis-102	59	7	parallel	parallel	ADJ
ajpdis-102	59	8	number	number	NOUN
ajpdis-102	59	9	axis	axis	NOUN
ajpdis-102	59	10	method	method	NOUN
ajpdis-102	59	11	when	when	SCONJ
ajpdis-102	59	12	solving	solve	VERB
ajpdis-102	59	13	a	a	DET
ajpdis-102	59	14	system	system	NOUN
ajpdis-102	59	15	of	of	ADP
ajpdis-102	59	16	rational	rational	ADJ
ajpdis-102	59	17	inequalities	inequality	NOUN
ajpdis-102	59	18	.	.	PUNCT
ajpdis-102	60	1	let	let	VERB
ajpdis-102	60	2	's	us	PRON
ajpdis-102	60	3	see	see	VERB
ajpdis-102	60	4	the	the	DET
ajpdis-102	60	5	following	follow	VERB
ajpdis-102	60	6	example	example	NOUN
ajpdis-102	60	7	.	.	PUNCT
ajpdis-102	61	1	if	if	SCONJ
ajpdis-102	61	2	the	the	DET
ajpdis-102	61	3	system	system	NOUN
ajpdis-102	61	4	of	of	ADP
ajpdis-102	61	5	inequalities	inequality	NOUN
ajpdis-102	61	6	is	be	AUX
ajpdis-102	61	7	solved	solve	VERB
ajpdis-102	61	8	on	on	ADP
ajpdis-102	61	9	a	a	DET
ajpdis-102	61	10	single	single	ADJ
ajpdis-102	61	11	number	number	NOUN
ajpdis-102	61	12	of	of	ADP
ajpdis-102	61	13	axes	axis	NOUN
ajpdis-102	61	14	,	,	PUNCT
ajpdis-102	61	15	the	the	DET
ajpdis-102	61	16	image	image	NOUN
ajpdis-102	61	17	presents	present	VERB
ajpdis-102	61	18	difficulties	difficulty	NOUN
ajpdis-102	61	19	in	in	ADP
ajpdis-102	61	20	isolating	isolate	VERB
ajpdis-102	61	21	the	the	DET
ajpdis-102	61	22	solution	solution	NOUN
ajpdis-102	61	23	,	,	PUNCT
ajpdis-102	61	24	it	it	PRON
ajpdis-102	61	25	is	be	AUX
ajpdis-102	61	26	much	much	ADV
ajpdis-102	61	27	easier	easy	ADJ
ajpdis-102	61	28	to	to	PART
ajpdis-102	61	29	isolate	isolate	VERB
ajpdis-102	61	30	the	the	DET
ajpdis-102	61	31	solution	solution	NOUN
ajpdis-102	61	32	if	if	SCONJ
ajpdis-102	61	33	solved	solve	VERB
ajpdis-102	61	34	on	on	ADP
ajpdis-102	61	35	the	the	DET
ajpdis-102	61	36	parallel	parallel	ADJ
ajpdis-102	61	37	number	number	NOUN
ajpdis-102	61	38	axis	axis	NOUN
ajpdis-102	61	39	(	(	PUNCT
ajpdis-102	61	40	2	2	NUM
ajpdis-102	61	41	-	-	PUNCT
ajpdis-102	61	42	picture	picture	NOUN
ajpdis-102	61	43	)	)	PUNCT
ajpdis-102	61	44	.	.	PUNCT
ajpdis-102	62	1	2	2	NUM
ajpdis-102	62	2	-	-	PUNCT
ajpdis-102	62	3	picture	picture	NOUN
ajpdis-102	62	4	.	.	PUNCT
ajpdis-102	63	1	solving	solve	VERB
ajpdis-102	63	2	inequalities	inequality	NOUN
ajpdis-102	63	3	on	on	ADP
ajpdis-102	63	4	the	the	DET
ajpdis-102	63	5	parallel	parallel	ADJ
ajpdis-102	63	6	number	number	NOUN
ajpdis-102	63	7	axis	axis	NOUN
ajpdis-102	63	8	.	.	PUNCT
ajpdis-102	64	1	answer	answer	NOUN
ajpdis-102	64	2	:	:	PUNCT
ajpdis-102	64	3	.	.	PUNCT
ajpdis-102	65	1	1example	1example	X
ajpdis-102	65	2	.	.	PUNCT
ajpdis-102	66	1	solve	solve	VERB
ajpdis-102	66	2	the	the	DET
ajpdis-102	66	3	system	system	NOUN
ajpdis-102	66	4	of	of	ADP
ajpdis-102	66	5	inequalities	inequality	NOUN
ajpdis-102	66	6	:	:	PUNCT
ajpdis-102	66	7	0	0	NUM
ajpdis-102	66	8	2	2	NUM
ajpdis-102	66	9	x	x	SYM
ajpdis-102	66	10			PROPN
ajpdis-102	66	11			PROPN
ajpdis-102	66	12			PROPN
ajpdis-102	66	13	(	(	PUNCT
ajpdis-102	66	14	1	1	X
ajpdis-102	66	15	)	)	PUNCT
ajpdis-102	66	16	0ctgx	0ctgx	NOUN
ajpdis-102	66	17	ctgx	ctgx	VERB
ajpdis-102	66	18			PROPN
ajpdis-102	66	19			PROPN
ajpdis-102	66	20	(	(	PUNCT
ajpdis-102	66	21	1)y	1)y	NUM
ajpdis-102	66	22	ctgx	ctgx	PROPN
ajpdis-102	66	23	ctgx	ctgx	NUM
ajpdis-102	66	24			PROPN
ajpdis-102	66	25	t	t	PROPN
ajpdis-102	66	26			VERB
ajpdis-102	66	27	2	2	NUM
ajpdis-102	66	28	0ctg	0ctg	NOUN
ajpdis-102	66	29	x	x	SYM
ajpdis-102	66	30	ctgx	ctgx	VERB
ajpdis-102	66	31			ADJ
ajpdis-102	66	32	2	2	NUM
ajpdis-102	66	33	,	,	PUNCT
ajpdis-102	66	34	3	3	NUM
ajpdis-102	66	35	4	4	NUM
ajpdis-102	66	36	n	n	NOUN
ajpdis-102	66	37	x	x	SYM
ajpdis-102	66	38	n	n	CCONJ
ajpdis-102	66	39	n	n	PROPN
ajpdis-102	66	40	z	z	NOUN
ajpdis-102	66	41	n	n	NOUN
ajpdis-102	66	42	x	x	SYM
ajpdis-102	66	43	n	n	PROPN
ajpdis-102	66	44			PROPN
ajpdis-102	66	45			PROPN
ajpdis-102	66	46			PROPN
ajpdis-102	66	47			PROPN
ajpdis-102	66	48			PROPN
ajpdis-102	66	49			PROPN
ajpdis-102	66	50			PROPN
ajpdis-102	66	51			PROPN
ajpdis-102	66	52			PROPN
ajpdis-102	66	53			PROPN
ajpdis-102	66	54			PROPN
ajpdis-102	66	55			PUNCT
ajpdis-102	66	56			VERB
ajpdis-102	66	57			PROPN
ajpdis-102	66	58			PROPN
ajpdis-102	66	59			PROPN
ajpdis-102	66	60			VERB
ajpdis-102	66	61			NOUN
ajpdis-102	66	62	3	3	NUM
ajpdis-102	66	63	2	2	NUM
ajpdis-102	66	64	(	(	PUNCT
ajpdis-102	66	65	2	2	NUM
ajpdis-102	66	66	)	)	PUNCT
ajpdis-102	66	67	(	(	PUNCT
ajpdis-102	66	68	1	1	NUM
ajpdis-102	66	69	)	)	PUNCT
ajpdis-102	66	70	(	(	PUNCT
ajpdis-102	66	71	4	4	NUM
ajpdis-102	66	72	)	)	PUNCT
ajpdis-102	66	73	0	0	NUM
ajpdis-102	66	74	,	,	PUNCT
ajpdis-102	66	75	(	(	PUNCT
ajpdis-102	66	76	4	4	NUM
ajpdis-102	66	77	)	)	PUNCT
ajpdis-102	66	78	(	(	PUNCT
ajpdis-102	66	79	2	2	NUM
ajpdis-102	66	80	)	)	PUNCT
ajpdis-102	66	81	0	0	NUM
ajpdis-102	66	82	,	,	PUNCT
ajpdis-102	66	83	(	(	PUNCT
ajpdis-102	66	84	3	3	X
ajpdis-102	66	85	)	)	PUNCT
ajpdis-102	66	86	(	(	PUNCT
ajpdis-102	66	87	3	3	X
ajpdis-102	66	88	)	)	PUNCT
ajpdis-102	66	89	(	(	PUNCT
ajpdis-102	66	90	1	1	X
ajpdis-102	66	91	)	)	PUNCT
ajpdis-102	66	92	(	(	PUNCT
ajpdis-102	66	93	2	2	NUM
ajpdis-102	66	94	)	)	PUNCT
ajpdis-102	66	95	0	0	NUM
ajpdis-102	66	96	.	.	PUNCT
ajpdis-102	67	1	(	(	PUNCT
ajpdis-102	67	2	5	5	NUM
ajpdis-102	67	3	)	)	PUNCT
ajpdis-102	67	4	(	(	PUNCT
ajpdis-102	67	5	4	4	NUM
ajpdis-102	67	6	)	)	PUNCT
ajpdis-102	67	7	x	x	X
ajpdis-102	68	1	x	x	PUNCT
ajpdis-102	68	2	x	x	PUNCT
ajpdis-102	68	3	x	x	PUNCT
ajpdis-102	68	4	x	x	PUNCT
ajpdis-102	68	5	x	x	PUNCT
ajpdis-102	68	6	x	x	PUNCT
ajpdis-102	68	7	x	x	PUNCT
ajpdis-102	68	8	x	x	PUNCT
ajpdis-102	68	9	x	x	PUNCT
ajpdis-102	68	10	x	x	PUNCT
ajpdis-102	68	11	x	x	PUNCT
ajpdis-102	68	12	x	x	SYM
ajpdis-102	68	13			NOUN
ajpdis-102	68	14			ADV
ajpdis-102	68	15			PUNCT
ajpdis-102	68	16			PROPN
ajpdis-102	68	17			PROPN
ajpdis-102	68	18			PUNCT
ajpdis-102	68	19			NOUN
ajpdis-102	68	20			NUM
ajpdis-102	68	21			DET
ajpdis-102	68	22			NOUN
ajpdis-102	68	23			ADV
ajpdis-102	68	24			NOUN
ajpdis-102	68	25			SYM
ajpdis-102	68	26			PROPN
ajpdis-102	68	27			ADP
ajpdis-102	68	28			PROPN
ajpdis-102	68	29			PUNCT
ajpdis-102	68	30			CCONJ
ajpdis-102	68	31	{	{	PUNCT
ajpdis-102	68	32	2	2	NUM
ajpdis-102	68	33	}	}	PUNCT
ajpdis-102	68	34	[	[	PUNCT
ajpdis-102	68	35	1;0	1;0	NUM
ajpdis-102	68	36	)	)	PUNCT
ajpdis-102	68	37	(	(	PUNCT
ajpdis-102	68	38	4	4	NUM
ajpdis-102	68	39	;	;	PUNCT
ajpdis-102	68	40	)	)	PUNCT
ajpdis-102	68	41			PROPN
ajpdis-102	68	42			PROPN
ajpdis-102	68	43			ADJ
ajpdis-102	68	44	14	14	NUM
ajpdis-102	68	45	american	american	ADJ
ajpdis-102	68	46	journal	journal	NOUN
ajpdis-102	68	47	of	of	ADP
ajpdis-102	68	48	public	public	ADJ
ajpdis-102	68	49	diplomacy	diplomacy	NOUN
ajpdis-102	68	50	and	and	CCONJ
ajpdis-102	68	51	international	international	ADJ
ajpdis-102	68	52	studies	study	NOUN
ajpdis-102	68	53	www	www	PROPN
ajpdis-102	68	54	.	.	PUNCT
ajpdis-102	68	55	grnjournal.us	grnjournal.us	X
ajpdis-102	68	56	solution	solution	NOUN
ajpdis-102	68	57	.	.	PUNCT
ajpdis-102	69	1	we	we	PRON
ajpdis-102	69	2	solve	solve	VERB
ajpdis-102	69	3	each	each	DET
ajpdis-102	69	4	inequality	inequality	NOUN
ajpdis-102	69	5	separately	separately	ADV
ajpdis-102	69	6	in	in	ADP
ajpdis-102	69	7	the	the	DET
ajpdis-102	69	8	unit	unit	NOUN
ajpdis-102	69	9	circle	circle	NOUN
ajpdis-102	69	10	.	.	PUNCT
ajpdis-102	70	1	1	1	NUM
ajpdis-102	70	2	)	)	PUNCT
ajpdis-102	70	3	argument	argument	NOUN
ajpdis-102	70	4	is	be	AUX
ajpdis-102	70	5	solving	solve	VERB
ajpdis-102	70	6	the	the	DET
ajpdis-102	70	7	inequality	inequality	NOUN
ajpdis-102	70	8	(	(	PUNCT
ajpdis-102	70	9	3	3	NUM
ajpdis-102	70	10	-	-	NOUN
ajpdis-102	70	11	picture	picture	NOUN
ajpdis-102	70	12	)	)	PUNCT
ajpdis-102	70	13	.	.	PUNCT
ajpdis-102	71	1	3	3	NUM
ajpdis-102	71	2	-	-	PUNCT
ajpdis-102	71	3	picture	picture	NOUN
ajpdis-102	71	4	.	.	PUNCT
ajpdis-102	72	1	2	2	NUM
ajpdis-102	72	2	)	)	PUNCT
ajpdis-102	72	3	and	and	CCONJ
ajpdis-102	72	4	we	we	PRON
ajpdis-102	72	5	solve	solve	VERB
ajpdis-102	72	6	for	for	ADP
ajpdis-102	72	7	inequalities	inequality	NOUN
ajpdis-102	72	8	(	(	PUNCT
ajpdis-102	72	9	4	4	NUM
ajpdis-102	72	10	-	-	NUM
ajpdis-102	72	11	picture	picture	NOUN
ajpdis-102	72	12	)	)	PUNCT
ajpdis-102	72	13	.	.	PUNCT
ajpdis-102	73	1	4	4	NUM
ajpdis-102	73	2	-	-	NUM
ajpdis-102	73	3	picture	picture	NOUN
ajpdis-102	73	4	.	.	PUNCT
ajpdis-102	74	1	now	now	ADV
ajpdis-102	74	2	for	for	ADP
ajpdis-102	74	3	arguments	argument	NOUN
ajpdis-102	74	4	,	,	PUNCT
ajpdis-102	74	5	we	we	PRON
ajpdis-102	74	6	draw	draw	VERB
ajpdis-102	74	7	concentric	concentric	ADJ
ajpdis-102	74	8	circles	circle	NOUN
ajpdis-102	74	9	.	.	PUNCT
ajpdis-102	75	1	we	we	PRON
ajpdis-102	75	2	draw	draw	VERB
ajpdis-102	75	3	a	a	DET
ajpdis-102	75	4	circle	circle	NOUN
ajpdis-102	75	5	corresponding	correspond	VERB
ajpdis-102	75	6	to	to	ADP
ajpdis-102	75	7	the	the	DET
ajpdis-102	75	8	solution	solution	NOUN
ajpdis-102	75	9	of	of	ADP
ajpdis-102	75	10	the	the	DET
ajpdis-102	75	11	first	first	ADJ
ajpdis-102	75	12	inequality	inequality	NOUN
ajpdis-102	75	13	and	and	CCONJ
ajpdis-102	75	14	we	we	PRON
ajpdis-102	75	15	are	be	AUX
ajpdis-102	75	16	the	the	DET
ajpdis-102	75	17	shitrich	shitrich	NOUN
ajpdis-102	75	18	,	,	PUNCT
ajpdis-102	75	19	then	then	ADV
ajpdis-102	75	20	we	we	PRON
ajpdis-102	75	21	draw	draw	VERB
ajpdis-102	75	22	a	a	DET
ajpdis-102	75	23	circle	circle	NOUN
ajpdis-102	75	24	with	with	ADP
ajpdis-102	75	25	a	a	DET
ajpdis-102	75	26	larger	large	ADJ
ajpdis-102	75	27	radius	radius	NOUN
ajpdis-102	75	28	and	and	CCONJ
ajpdis-102	75	29	we	we	PRON
ajpdis-102	75	30	are	be	AUX
ajpdis-102	75	31	the	the	DET
ajpdis-102	75	32	shitrich	shitrich	NOUN
ajpdis-102	75	33	according	accord	VERB
ajpdis-102	75	34	to	to	ADP
ajpdis-102	75	35	the	the	DET
ajpdis-102	75	36	solution	solution	NOUN
ajpdis-102	75	37	of	of	ADP
ajpdis-102	75	38	the	the	DET
ajpdis-102	75	39	second	second	NOUN
ajpdis-102	75	40	,	,	PUNCT
ajpdis-102	75	41	then	then	ADV
ajpdis-102	75	42	we	we	PRON
ajpdis-102	75	43	draw	draw	VERB
ajpdis-102	75	44	a	a	DET
ajpdis-102	75	45	circle	circle	NOUN
ajpdis-102	75	46	and	and	CCONJ
ajpdis-102	75	47	a	a	DET
ajpdis-102	75	48	base	base	NOUN
ajpdis-102	75	49	circle	circle	NOUN
ajpdis-102	75	50	for	for	ADP
ajpdis-102	75	51	the	the	DET
ajpdis-102	75	52	third	third	ADJ
ajpdis-102	75	53	inequality	inequality	NOUN
ajpdis-102	75	54	.	.	PUNCT
ajpdis-102	76	1	from	from	ADP
ajpdis-102	76	2	the	the	DET
ajpdis-102	76	3	center	center	NOUN
ajpdis-102	76	4	of	of	ADP
ajpdis-102	76	5	the	the	DET
ajpdis-102	76	6	circle	circle	NOUN
ajpdis-102	76	7	,	,	PUNCT
ajpdis-102	76	8	we	we	PRON
ajpdis-102	76	9	pass	pass	VERB
ajpdis-102	76	10	rays	ray	NOUN
ajpdis-102	76	11	through	through	ADP
ajpdis-102	76	12	the	the	DET
ajpdis-102	76	13	ends	end	NOUN
ajpdis-102	76	14	of	of	ADP
ajpdis-102	76	15	the	the	DET
ajpdis-102	76	16	arcs	arc	NOUN
ajpdis-102	76	17	so	so	SCONJ
ajpdis-102	76	18	that	that	SCONJ
ajpdis-102	76	19	they	they	PRON
ajpdis-102	76	20	cross	cross	VERB
ajpdis-102	76	21	all	all	DET
ajpdis-102	76	22	circles	circle	NOUN
ajpdis-102	76	23	.	.	PUNCT
ajpdis-102	77	1	the	the	DET
ajpdis-102	77	2	result	result	NOUN
ajpdis-102	77	3	is	be	AUX
ajpdis-102	77	4	a	a	DET
ajpdis-102	77	5	solution	solution	NOUN
ajpdis-102	77	6	in	in	ADP
ajpdis-102	77	7	the	the	DET
ajpdis-102	77	8	base	base	NOUN
ajpdis-102	77	9	circle	circle	NOUN
ajpdis-102	77	10	(	(	PUNCT
ajpdis-102	77	11	5	5	NUM
ajpdis-102	77	12	-	-	PUNCT
ajpdis-102	77	13	picture	picture	NOUN
ajpdis-102	77	14	)	)	PUNCT
ajpdis-102	77	15	.	.	PUNCT
ajpdis-102	78	1	1	1	NUM
ajpdis-102	78	2	cos	cos	NOUN
ajpdis-102	78	3	,	,	PUNCT
ajpdis-102	78	4	2	2	NUM
ajpdis-102	78	5	3	3	NUM
ajpdis-102	78	6	sin	sin	NOUN
ajpdis-102	78	7	2	2	NUM
ajpdis-102	78	8	,	,	PUNCT
ajpdis-102	78	9	2	2	NUM
ajpdis-102	78	10	1	1	NUM
ajpdis-102	78	11	x	x	SYM
ajpdis-102	78	12	x	x	SYM
ajpdis-102	78	13	tgx	tgx	NOUN
ajpdis-102	78	14			ADV
ajpdis-102	78	15			PROPN
ajpdis-102	78	16			NOUN
ajpdis-102	78	17			NUM
ajpdis-102	78	18			NOUN
ajpdis-102	78	19			ADJ
ajpdis-102	78	20			NUM
ajpdis-102	78	21			NUM
ajpdis-102	78	22			PROPN
ajpdis-102	78	23			NUM
ajpdis-102	78	24			PROPN
ajpdis-102	78	25	2x	2x	NUM
ajpdis-102	78	26	3	3	NUM
ajpdis-102	78	27	sin	sin	NOUN
ajpdis-102	78	28	2	2	NUM
ajpdis-102	78	29	2	2	NUM
ajpdis-102	78	30	x	x	SYM
ajpdis-102	78	31			PROPN
ajpdis-102	78	32	1	1	NUM
ajpdis-102	78	33	cos	cos	ADP
ajpdis-102	78	34	2	2	NUM
ajpdis-102	78	35	x	x	SYM
ajpdis-102	78	36			PROPN
ajpdis-102	78	37			PROPN
ajpdis-102	78	38	1tgx	1tgx	PROPN
ajpdis-102	78	39			NUM
ajpdis-102	78	40			PROPN
ajpdis-102	78	41	x	x	SYM
ajpdis-102	78	42	15	15	NUM
ajpdis-102	78	43	american	american	ADJ
ajpdis-102	78	44	journal	journal	NOUN
ajpdis-102	78	45	of	of	ADP
ajpdis-102	78	46	public	public	ADJ
ajpdis-102	78	47	diplomacy	diplomacy	NOUN
ajpdis-102	78	48	and	and	CCONJ
ajpdis-102	78	49	international	international	ADJ
ajpdis-102	78	50	studies	study	NOUN
ajpdis-102	78	51	www	www	PROPN
ajpdis-102	78	52	.	.	PROPN
ajpdis-102	79	1	grnjournal.us	grnjournal.us	X
ajpdis-102	79	2	5	5	NUM
ajpdis-102	79	3	-	-	PUNCT
ajpdis-102	79	4	picture	picture	NOUN
ajpdis-102	79	5	.	.	PUNCT
ajpdis-102	80	1	answer	answer	NOUN
ajpdis-102	80	2	:	:	PUNCT
ajpdis-102	80	3	.	.	PUNCT
ajpdis-102	81	1	example	example	NOUN
ajpdis-102	82	1	2	2	NUM
ajpdis-102	82	2	.	.	X
ajpdis-102	82	3	solve	solve	VERB
ajpdis-102	82	4	the	the	DET
ajpdis-102	82	5	inequality	inequality	NOUN
ajpdis-102	82	6	:	:	PUNCT
ajpdis-102	82	7	.	.	PUNCT
ajpdis-102	83	1	solution	solution	NOUN
ajpdis-102	83	2	.	.	PUNCT
ajpdis-102	84	1	using	use	VERB
ajpdis-102	84	2	the	the	DET
ajpdis-102	84	3	formula	formula	NOUN
ajpdis-102	84	4	,	,	PUNCT
ajpdis-102	84	5	we	we	PRON
ajpdis-102	84	6	substitute	substitute	VERB
ajpdis-102	84	7	the	the	DET
ajpdis-102	84	8	form	form	NOUN
ajpdis-102	84	9	:	:	PUNCT
ajpdis-102	84	10	,	,	PUNCT
ajpdis-102	84	11	,	,	PUNCT
ajpdis-102	84	12	.	.	PUNCT
ajpdis-102	85	1	we	we	PRON
ajpdis-102	85	2	solve	solve	VERB
ajpdis-102	85	3	for	for	ADP
ajpdis-102	85	4	the	the	DET
ajpdis-102	85	5	last	last	ADJ
ajpdis-102	85	6	inequality	inequality	NOUN
ajpdis-102	85	7	.	.	PUNCT
ajpdis-102	86	1	let	let	VERB
ajpdis-102	86	2	's	us	PRON
ajpdis-102	86	3	enter	enter	VERB
ajpdis-102	86	4	a	a	DET
ajpdis-102	86	5	mark	mark	NOUN
ajpdis-102	86	6	,	,	PUNCT
ajpdis-102	86	7	as	as	ADP
ajpdis-102	86	8	a	a	DET
ajpdis-102	86	9	result	result	NOUN
ajpdis-102	86	10	:	:	PUNCT
ajpdis-102	86	11	.	.	PUNCT
ajpdis-102	87	1	we	we	PRON
ajpdis-102	87	2	describe	describe	VERB
ajpdis-102	87	3	the	the	DET
ajpdis-102	87	4	solution	solution	NOUN
ajpdis-102	87	5	in	in	ADP
ajpdis-102	87	6	the	the	DET
ajpdis-102	87	7	unit	unit	NOUN
ajpdis-102	87	8	circle	circle	NOUN
ajpdis-102	87	9	(	(	PUNCT
ajpdis-102	87	10	6	6	NUM
ajpdis-102	87	11	-	-	PUNCT
ajpdis-102	87	12	picture	picture	NOUN
ajpdis-102	87	13	):	):	PUNCT
ajpdis-102	87	14	.	.	PUNCT
ajpdis-102	88	1	let	let	VERB
ajpdis-102	88	2	's	us	PRON
ajpdis-102	88	3	go	go	VERB
ajpdis-102	88	4	back	back	ADV
ajpdis-102	88	5	to	to	ADP
ajpdis-102	88	6	the	the	DET
ajpdis-102	88	7	variable	variable	NOUN
ajpdis-102	88	8	:	:	PUNCT
ajpdis-102	88	9	.	.	PUNCT
ajpdis-102	89	1	3	3	NUM
ajpdis-102	89	2	7	7	NUM
ajpdis-102	89	3	2	2	NUM
ajpdis-102	89	4	;	;	PUNCT
ajpdis-102	89	5	2	2	NUM
ajpdis-102	89	6	,	,	PUNCT
ajpdis-102	89	7	4	4	NUM
ajpdis-102	89	8	6	6	NUM
ajpdis-102	89	9	k	k	NOUN
ajpdis-102	89	10	k	k	PROPN
ajpdis-102	90	1	k	k	PROPN
ajpdis-102	90	2	z	z	PROPN
ajpdis-102	90	3			PROPN
ajpdis-102	90	4			PROPN
ajpdis-102	90	5			PROPN
ajpdis-102	90	6			PROPN
ajpdis-102	90	7			PROPN
ajpdis-102	90	8			NOUN
ajpdis-102	90	9			PROPN
ajpdis-102	90	10			PUNCT
ajpdis-102	90	11			PUNCT
ajpdis-102	90	12			NOUN
ajpdis-102	90	13			NOUN
ajpdis-102	90	14			PROPN
ajpdis-102	90	15	22sin	22sin	NOUN
ajpdis-102	90	16	3cos2	3cos2	NUM
ajpdis-102	90	17	0	0	NUM
ajpdis-102	90	18	4	4	NUM
ajpdis-102	90	19	x	x	SYM
ajpdis-102	90	20	x	x	SYM
ajpdis-102	90	21			PUNCT
ajpdis-102	90	22			PROPN
ajpdis-102	90	23			VERB
ajpdis-102	90	24			PROPN
ajpdis-102	90	25			X
ajpdis-102	90	26			PROPN
ajpdis-102	91	1			PROPN
ajpdis-102	91	2			NUM
ajpdis-102	91	3	21	21	NUM
ajpdis-102	91	4	cos2	cos2	NOUN
ajpdis-102	91	5	2sin	2sin	NUM
ajpdis-102	92	1			NOUN
ajpdis-102	93	1			NUM
ajpdis-102	93	2	1	1	NUM
ajpdis-102	93	3	cos	cos	PROPN
ajpdis-102	93	4	2	2	NUM
ajpdis-102	93	5	3cos2	3cos2	NUM
ajpdis-102	93	6	0	0	NUM
ajpdis-102	93	7	2	2	NUM
ajpdis-102	93	8	x	x	SYM
ajpdis-102	93	9	x	x	SYM
ajpdis-102	93	10			NUM
ajpdis-102	93	11			PROPN
ajpdis-102	93	12			PROPN
ajpdis-102	93	13			ADV
ajpdis-102	93	14			ADJ
ajpdis-102	93	15			X
ajpdis-102	93	16			PROPN
ajpdis-102	93	17			PROPN
ajpdis-102	93	18			PROPN
ajpdis-102	93	19	cos	cos	ADP
ajpdis-102	93	20	2	2	NUM
ajpdis-102	93	21	3cos2	3cos2	NUM
ajpdis-102	93	22	1	1	NUM
ajpdis-102	93	23	,	,	PUNCT
ajpdis-102	93	24	2	2	NUM
ajpdis-102	93	25	x	x	SYM
ajpdis-102	93	26	x	x	SYM
ajpdis-102	93	27			NUM
ajpdis-102	93	28			PROPN
ajpdis-102	93	29			PROPN
ajpdis-102	93	30			ADV
ajpdis-102	93	31			VERB
ajpdis-102	94	1			PROPN
ajpdis-102	95	1			PROPN
ajpdis-102	95	2			PROPN
ajpdis-102	96	1			ADJ
ajpdis-102	96	2			PROPN
ajpdis-102	96	3	sin2	sin2	NOUN
ajpdis-102	96	4	3cos2	3cos2	NUM
ajpdis-102	96	5	1x	1x	NUM
ajpdis-102	96	6	x	x	NOUN
ajpdis-102	96	7			PROPN
ajpdis-102	96	8			NOUN
ajpdis-102	96	9	1	1	NUM
ajpdis-102	96	10	3	3	NUM
ajpdis-102	96	11	1	1	NUM
ajpdis-102	96	12	sin	sin	NOUN
ajpdis-102	96	13	2	2	NUM
ajpdis-102	96	14	cos2	cos2	NOUN
ajpdis-102	96	15	,	,	PUNCT
ajpdis-102	96	16	2	2	NUM
ajpdis-102	96	17	2	2	NUM
ajpdis-102	96	18	2	2	NUM
ajpdis-102	96	19	x	x	SYM
ajpdis-102	96	20	x	x	NOUN
ajpdis-102	96	21			PRON
ajpdis-102	96	22			PROPN
ajpdis-102	96	23	1	1	NUM
ajpdis-102	96	24	sin	sin	NOUN
ajpdis-102	96	25	sin2	sin2	NOUN
ajpdis-102	96	26	cos	cos	PROPN
ajpdis-102	96	27	cos2	cos2	PROPN
ajpdis-102	96	28	,	,	PUNCT
ajpdis-102	96	29	6	6	NUM
ajpdis-102	96	30	6	6	NUM
ajpdis-102	96	31	2	2	NUM
ajpdis-102	96	32	x	x	SYM
ajpdis-102	96	33	x	x	SYM
ajpdis-102	96	34			PROPN
ajpdis-102	96	35			ADJ
ajpdis-102	96	36			ADJ
ajpdis-102	96	37			PROPN
ajpdis-102	96	38			PROPN
ajpdis-102	96	39	1	1	NUM
ajpdis-102	96	40	cos	cos	PROPN
ajpdis-102	96	41	2	2	NUM
ajpdis-102	96	42	6	6	NUM
ajpdis-102	96	43	2	2	NUM
ajpdis-102	96	44	x	x	SYM
ajpdis-102	96	45			PUNCT
ajpdis-102	96	46			PROPN
ajpdis-102	96	47			PROPN
ajpdis-102	96	48			PROPN
ajpdis-102	97	1			PROPN
ajpdis-102	97	2			PROPN
ajpdis-102	98	1			ADJ
ajpdis-102	98	2			NOUN
ajpdis-102	98	3	2	2	NUM
ajpdis-102	98	4	6	6	NUM
ajpdis-102	98	5	t	t	NOUN
ajpdis-102	98	6	x	x	SYM
ajpdis-102	98	7			PROPN
ajpdis-102	98	8			PROPN
ajpdis-102	98	9			NOUN
ajpdis-102	98	10	1	1	NUM
ajpdis-102	98	11	cos	cos	ADP
ajpdis-102	98	12	2	2	NUM
ajpdis-102	98	13	t	t	NOUN
ajpdis-102	98	14			VERB
ajpdis-102	98	15			NOUN
ajpdis-102	98	16	2	2	NUM
ajpdis-102	98	17	2	2	NUM
ajpdis-102	98	18	2	2	NUM
ajpdis-102	98	19	2	2	NUM
ajpdis-102	98	20	3	3	NUM
ajpdis-102	98	21	3	3	NUM
ajpdis-102	98	22	k	k	NOUN
ajpdis-102	98	23	t	t	PROPN
ajpdis-102	99	1	k	k	PROPN
ajpdis-102	99	2			PROPN
ajpdis-102	99	3			PROPN
ajpdis-102	99	4			PROPN
ajpdis-102	99	5			NOUN
ajpdis-102	99	6			ADV
ajpdis-102	99	7			PROPN
ajpdis-102	99	8			PROPN
ajpdis-102	99	9			ADV
ajpdis-102	99	10	x	x	PUNCT
ajpdis-102	99	11	2	2	NUM
ajpdis-102	99	12	2	2	NUM
ajpdis-102	99	13	2	2	NUM
ajpdis-102	99	14	2	2	NUM
ajpdis-102	99	15	2	2	NUM
ajpdis-102	99	16	3	3	NUM
ajpdis-102	99	17	6	6	NUM
ajpdis-102	99	18	3	3	NUM
ajpdis-102	99	19	k	k	NOUN
ajpdis-102	99	20	x	x	X
ajpdis-102	100	1	k	k	PROPN
ajpdis-102	100	2			PROPN
ajpdis-102	100	3			PROPN
ajpdis-102	100	4			PROPN
ajpdis-102	100	5			PROPN
ajpdis-102	100	6			NOUN
ajpdis-102	100	7			ADV
ajpdis-102	100	8			PROPN
ajpdis-102	100	9			PROPN
ajpdis-102	100	10			PROPN
ajpdis-102	100	11			ADV
ajpdis-102	100	12			NOUN
ajpdis-102	100	13	5	5	NUM
ajpdis-102	100	14	,	,	PUNCT
ajpdis-102	100	15	4	4	NUM
ajpdis-102	100	16	12	12	NUM
ajpdis-102	101	1	k	k	NOUN
ajpdis-102	101	2	x	x	X
ajpdis-102	102	1	k	k	PROPN
ajpdis-102	102	2	k	k	PROPN
ajpdis-102	102	3	z	z	PROPN
ajpdis-102	102	4			PROPN
ajpdis-102	102	5			PROPN
ajpdis-102	102	6			PROPN
ajpdis-102	102	7			NOUN
ajpdis-102	102	8			ADV
ajpdis-102	102	9			PROPN
ajpdis-102	102	10			PROPN
ajpdis-102	102	11			PUNCT
ajpdis-102	102	12			NOUN
ajpdis-102	102	13	16	16	NUM
ajpdis-102	102	14	american	american	PROPN
ajpdis-102	102	15	journal	journal	PROPN
ajpdis-102	102	16	of	of	ADP
ajpdis-102	102	17	public	public	ADJ
ajpdis-102	102	18	diplomacy	diplomacy	NOUN
ajpdis-102	102	19	and	and	CCONJ
ajpdis-102	102	20	international	international	ADJ
ajpdis-102	102	21	studies	study	NOUN
ajpdis-102	102	22	www	www	PROPN
ajpdis-102	102	23	.	.	PROPN
ajpdis-102	103	1	grnjournal.us	grnjournal.us	X
ajpdis-102	103	2	6	6	NUM
ajpdis-102	103	3	-	-	PUNCT
ajpdis-102	103	4	picture	picture	NOUN
ajpdis-102	103	5	.	.	PUNCT
ajpdis-102	104	1	conclusion	conclusion	NOUN
ajpdis-102	104	2	/	/	SYM
ajpdis-102	104	3	recommendations	recommendation	NOUN
ajpdis-102	104	4	:	:	PUNCT
ajpdis-102	104	5	in	in	ADP
ajpdis-102	104	6	conclusion	conclusion	NOUN
ajpdis-102	104	7	,	,	PUNCT
ajpdis-102	104	8	high	high	ADJ
ajpdis-102	104	9	requirements	requirement	NOUN
ajpdis-102	104	10	are	be	AUX
ajpdis-102	104	11	imposed	impose	VERB
ajpdis-102	104	12	on	on	ADP
ajpdis-102	104	13	the	the	DET
ajpdis-102	104	14	knowledge	knowledge	NOUN
ajpdis-102	104	15	,	,	PUNCT
ajpdis-102	104	16	skills	skill	NOUN
ajpdis-102	104	17	and	and	CCONJ
ajpdis-102	104	18	qualifications	qualification	NOUN
ajpdis-102	104	19	of	of	ADP
ajpdis-102	104	20	students	student	NOUN
ajpdis-102	104	21	of	of	ADP
ajpdis-102	104	22	a	a	DET
ajpdis-102	104	23	specialized	specialized	ADJ
ajpdis-102	104	24	school	school	NOUN
ajpdis-102	104	25	,	,	PUNCT
ajpdis-102	104	26	of	of	ADP
ajpdis-102	104	27	which	which	PRON
ajpdis-102	104	28	,	,	PUNCT
ajpdis-102	104	29	first	first	ADV
ajpdis-102	104	30	of	of	ADP
ajpdis-102	104	31	all	all	PRON
ajpdis-102	104	32	,	,	PUNCT
ajpdis-102	104	33	it	it	PRON
ajpdis-102	104	34	is	be	AUX
ajpdis-102	104	35	required	require	VERB
ajpdis-102	104	36	to	to	PART
ajpdis-102	104	37	have	have	VERB
ajpdis-102	104	38	a	a	DET
ajpdis-102	104	39	high	high	ADJ
ajpdis-102	104	40	level	level	NOUN
ajpdis-102	104	41	of	of	ADP
ajpdis-102	104	42	admission	admission	NOUN
ajpdis-102	104	43	indicators	indicator	NOUN
ajpdis-102	104	44	to	to	ADP
ajpdis-102	104	45	higher	high	ADJ
ajpdis-102	104	46	educational	educational	ADJ
ajpdis-102	104	47	institutions	institution	NOUN
ajpdis-102	104	48	,	,	PUNCT
ajpdis-102	104	49	while	while	SCONJ
ajpdis-102	104	50	maintaining	maintain	VERB
ajpdis-102	104	51	a	a	DET
ajpdis-102	104	52	deep	deep	ADJ
ajpdis-102	104	53	and	and	CCONJ
ajpdis-102	104	54	fluent	fluent	ADJ
ajpdis-102	104	55	mastery	mastery	NOUN
ajpdis-102	104	56	of	of	ADP
ajpdis-102	104	57	educational	educational	ADJ
ajpdis-102	104	58	material	material	NOUN
ajpdis-102	104	59	in	in	ADP
ajpdis-102	104	60	order	order	NOUN
ajpdis-102	104	61	to	to	PART
ajpdis-102	104	62	achieve	achieve	VERB
ajpdis-102	104	63	positive	positive	ADJ
ajpdis-102	104	64	results	result	NOUN
ajpdis-102	104	65	in	in	ADP
ajpdis-102	104	66	olympiads	olympiad	NOUN
ajpdis-102	104	67	conducted	conduct	VERB
ajpdis-102	104	68	in	in	ADP
ajpdis-102	104	69	different	different	ADJ
ajpdis-102	104	70	disciplines	discipline	NOUN
ajpdis-102	104	71	.	.	PUNCT
ajpdis-102	105	1	in	in	ADP
ajpdis-102	105	2	this	this	DET
ajpdis-102	105	3	case	case	NOUN
ajpdis-102	105	4	,	,	PUNCT
ajpdis-102	105	5	the	the	DET
ajpdis-102	105	6	application	application	NOUN
ajpdis-102	105	7	of	of	ADP
ajpdis-102	105	8	non	non	ADJ
ajpdis-102	105	9	-	-	ADJ
ajpdis-102	105	10	standard	standard	ADJ
ajpdis-102	105	11	methods	method	NOUN
ajpdis-102	105	12	opens	open	VERB
ajpdis-102	105	13	the	the	DET
ajpdis-102	105	14	way	way	NOUN
ajpdis-102	105	15	for	for	ADP
ajpdis-102	105	16	the	the	DET
ajpdis-102	105	17	development	development	NOUN
ajpdis-102	105	18	of	of	ADP
ajpdis-102	105	19	methodological	methodological	ADJ
ajpdis-102	105	20	issues	issue	NOUN
ajpdis-102	105	21	of	of	ADP
ajpdis-102	105	22	teaching	teach	VERB
ajpdis-102	105	23	mathematics	mathematic	NOUN
ajpdis-102	105	24	and	and	CCONJ
ajpdis-102	105	25	the	the	DET
ajpdis-102	105	26	solution	solution	NOUN
ajpdis-102	105	27	of	of	ADP
ajpdis-102	105	28	problems	problem	NOUN
ajpdis-102	105	29	in	in	ADP
ajpdis-102	105	30	its	its	PRON
ajpdis-102	105	31	teaching	teaching	NOUN
ajpdis-102	105	32	.	.	PUNCT
ajpdis-102	106	1	references	reference	NOUN
ajpdis-102	106	2	:	:	PUNCT
ajpdis-102	106	3	1	1	X
ajpdis-102	106	4	.	.	X
ajpdis-102	106	5	sh.l	sh.l	NOUN
ajpdis-102	106	6	.	.	PUNCT
ajpdis-102	107	1	ermatov	ermatov	PROPN
ajpdis-102	107	2	.	.	PUNCT
ajpdis-102	108	1	trigonometrik	trigonometrik	PROPN
ajpdis-102	108	2	tenglamalar	tenglamalar	ADJ
ajpdis-102	108	3	yechimlari	yechimlari	PROPN
ajpdis-102	108	4	to’plamini	to’plamini	PUNCT
ajpdis-102	108	5	umumlashtirishning	umumlashtirishne	VERB
ajpdis-102	108	6	bir	bir	NOUN
ajpdis-102	108	7	usuli	usuli	PROPN
ajpdis-102	108	8	.	.	PUNCT
ajpdis-102	109	1	наманган	наманган	PROPN
ajpdis-102	109	2	давлат	давлат	PROPN
ajpdis-102	109	3	университети	университети	PROPN
ajpdis-102	109	4	илмий	илмий	VERB
ajpdis-102	109	5	ахборотномаси	ахборотномаси	NOUN
ajpdis-102	109	6	.	.	PUNCT
ajpdis-102	110	1	-наманган	-наманган	PROPN
ajpdis-102	110	2	,	,	PUNCT
ajpdis-102	110	3	2021	2021	NUM
ajpdis-102	110	4	.	.	PUNCT
ajpdis-102	111	1	-	-	PUNCT
ajpdis-102	111	2	№	№	NOUN
ajpdis-102	111	3	10	10	NUM
ajpdis-102	111	4	.	.	PUNCT
ajpdis-102	111	5	б.445	б.445	NOUN
ajpdis-102	111	6	-	-	SYM
ajpdis-102	111	7	450	450	NUM
ajpdis-102	111	8	.	.	NOUN
ajpdis-102	112	1	2	2	NUM
ajpdis-102	112	2	.	.	X
ajpdis-102	112	3	khankulov	khankulov	PROPN
ajpdis-102	112	4	,	,	PUNCT
ajpdis-102	112	5	u.	u.	PROPN
ajpdis-102	112	6	k.	k.	PROPN
ajpdis-102	112	7	(	(	PUNCT
ajpdis-102	112	8	2017	2017	NUM
ajpdis-102	112	9	)	)	PUNCT
ajpdis-102	112	10	.	.	PUNCT
ajpdis-102	113	1	description	description	NOUN
ajpdis-102	113	2	of	of	ADP
ajpdis-102	113	3	methodical	methodical	ADJ
ajpdis-102	113	4	system	system	NOUN
ajpdis-102	113	5	of	of	ADP
ajpdis-102	113	6	teaching	teach	VERB
ajpdis-102	113	7	elements	element	NOUN
ajpdis-102	113	8	of	of	ADP
ajpdis-102	113	9	stochastics	stochastic	NOUN
ajpdis-102	113	10	line	line	NOUN
ajpdis-102	113	11	mathematics	mathematic	NOUN
ajpdis-102	113	12	using	use	VERB
ajpdis-102	113	13	computer	computer	NOUN
ajpdis-102	113	14	technologies	technology	NOUN
ajpdis-102	113	15	.	.	PUNCT
ajpdis-102	114	1	eastern	eastern	ADJ
ajpdis-102	114	2	european	european	PROPN
ajpdis-102	114	3	scientific	scientific	ADJ
ajpdis-102	114	4	journal	journal	NOUN
ajpdis-102	114	5	,	,	PUNCT
ajpdis-102	114	6	(	(	PUNCT
ajpdis-102	114	7	6	6	NUM
ajpdis-102	114	8	)	)	PUNCT
ajpdis-102	114	9	.	.	PUNCT
ajpdis-102	115	1	3	3	X
ajpdis-102	115	2	.	.	X
ajpdis-102	115	3	хонкулов	хонкулов	PROPN
ajpdis-102	115	4	,	,	PUNCT
ajpdis-102	115	5	у	у	X
ajpdis-102	115	6	.	.	PUNCT
ajpdis-102	116	1	х	х	X
ajpdis-102	116	2	.	.	PUNCT
ajpdis-102	117	1	(	(	PUNCT
ajpdis-102	117	2	2018	2018	NUM
ajpdis-102	117	3	)	)	PUNCT
ajpdis-102	117	4	.	.	PUNCT
ajpdis-102	118	1	on	on	ADP
ajpdis-102	118	2	the	the	DET
ajpdis-102	118	3	selection	selection	NOUN
ajpdis-102	118	4	principles	principle	NOUN
ajpdis-102	118	5	of	of	ADP
ajpdis-102	118	6	educational	educational	ADJ
ajpdis-102	118	7	content	content	NOUN
ajpdis-102	118	8	of	of	ADP
ajpdis-102	118	9	stochastic	stochastic	ADJ
ajpdis-102	118	10	elements	element	NOUN
ajpdis-102	118	11	оf	оf	ADP
ajpdis-102	118	12	mathematics	mathematic	NOUN
ajpdis-102	118	13	.	.	PUNCT
ajpdis-102	119	1	наука	наука	PROPN
ajpdis-102	119	2	и	и	PROPN
ajpdis-102	119	3	мир	мир	NOUN
ajpdis-102	119	4	,	,	PUNCT
ajpdis-102	119	5	2(4	2(4	NUM
ajpdis-102	119	6	)	)	PUNCT
ajpdis-102	119	7	,	,	PUNCT
ajpdis-102	119	8	5657	5657	NUM
ajpdis-102	119	9	.	.	PUNCT
ajpdis-102	120	1	4	4	X
ajpdis-102	120	2	.	.	X
ajpdis-102	120	3	хонкулов	хонкулов	PROPN
ajpdis-102	120	4	,	,	PUNCT
ajpdis-102	120	5	у	у	X
ajpdis-102	120	6	.	.	PUNCT
ajpdis-102	121	1	х	х	X
ajpdis-102	121	2	.	.	PUNCT
ajpdis-102	122	1	(	(	PUNCT
ajpdis-102	122	2	2015	2015	NUM
ajpdis-102	122	3	)	)	PUNCT
ajpdis-102	122	4	.	.	PUNCT
ajpdis-102	123	1	о	о	PROPN
ajpdis-102	123	2	применениях	применениях	ADJ
ajpdis-102	123	3	компьютерных	компьютерных	PROPN
ajpdis-102	123	4	технологий	технологий	PROPN
ajpdis-102	123	5	в	в	PROPN
ajpdis-102	123	6	обучении	обучении	AUX
ajpdis-102	123	7	элементов	элементов	PROPN
ajpdis-102	123	8	стохастики	стохастики	NOUN
ajpdis-102	123	9	.	.	PUNCT
ajpdis-102	124	1	региональные	региональные	NOUN
ajpdis-102	124	2	проблемы	проблемы	PROPN
ajpdis-102	124	3	преобразования	преобразования	PROPN
ajpdis-102	124	4	экономики	экономики	NOUN
ajpdis-102	124	5	,	,	PUNCT
ajpdis-102	124	6	(	(	PUNCT
ajpdis-102	124	7	8	8	NUM
ajpdis-102	124	8	(	(	PUNCT
ajpdis-102	124	9	58	58	NUM
ajpdis-102	124	10	)	)	PUNCT
ajpdis-102	124	11	)	)	PUNCT
ajpdis-102	124	12	,	,	PUNCT
ajpdis-102	124	13	7682	7682	NUM
ajpdis-102	124	14	.	.	PUNCT
ajpdis-102	125	1	5	5	X
ajpdis-102	125	2	.	.	X
ajpdis-102	126	1	zharov	zharov	PROPN
ajpdis-102	126	2	,	,	PUNCT
ajpdis-102	126	3	v.	v.	PROPN
ajpdis-102	126	4	k.	k.	PROPN
ajpdis-102	126	5	(	(	PUNCT
ajpdis-102	126	6	2012	2012	NUM
ajpdis-102	126	7	)	)	PUNCT
ajpdis-102	126	8	.	.	PUNCT
ajpdis-102	127	1	formanov	formanov	PROPN
ajpdis-102	127	2	sh	sh	PROPN
ajpdis-102	127	3	.	.	PROPN
ajpdis-102	127	4	k.	k.	PROPN
ajpdis-102	127	5	,	,	PUNCT
ajpdis-102	127	6	honkulov	honkulov	VERB
ajpdis-102	127	7	yu	yu	PROPN
ajpdis-102	127	8	.	.	PUNCT
ajpdis-102	128	1	kh	kh	PROPN
ajpdis-102	128	2	.	.	PUNCT
ajpdis-102	129	1	on	on	ADP
ajpdis-102	129	2	the	the	DET
ajpdis-102	129	3	statistical	statistical	ADJ
ajpdis-102	129	4	method	method	NOUN
ajpdis-102	129	5	in	in	ADP
ajpdis-102	129	6	a	a	DET
ajpdis-102	129	7	pedagogical	pedagogical	ADJ
ajpdis-102	129	8	experiment	experiment	NOUN
ajpdis-102	129	9	in	in	ADP
ajpdis-102	129	10	the	the	DET
ajpdis-102	129	11	context	context	NOUN
ajpdis-102	129	12	of	of	ADP
ajpdis-102	129	13	a	a	DET
ajpdis-102	129	14	modern	modern	ADJ
ajpdis-102	129	15	educational	educational	ADJ
ajpdis-102	129	16	process	process	NOUN
ajpdis-102	129	17	.	.	PUNCT
ajpdis-102	130	1	bulletin	bulletin	NOUN
ajpdis-102	130	2	of	of	ADP
ajpdis-102	130	3	the	the	DET
ajpdis-102	130	4	moscow	moscow	PROPN
ajpdis-102	130	5	state	state	PROPN
ajpdis-102	130	6	regional	regional	PROPN
ajpdis-102	130	7	university	university	PROPN
ajpdis-102	130	8	.	.	PUNCT
ajpdis-102	131	1	series	series	PROPN
ajpdis-102	131	2	pedagogy	pedagogy	PROPN
ajpdis-102	131	3	,	,	PUNCT
ajpdis-102	131	4	(	(	PUNCT
ajpdis-102	131	5	3	3	NUM
ajpdis-102	131	6	)	)	PUNCT
ajpdis-102	131	7	,	,	PUNCT
ajpdis-102	131	8	104	104	NUM
ajpdis-102	131	9	-	-	SYM
ajpdis-102	131	10	110	110	NUM
ajpdis-102	131	11	.	.	PUNCT
ajpdis-102	132	1	6	6	NUM
ajpdis-102	132	2	.	.	X
ajpdis-102	132	3	drawing	drawing	NOUN
ajpdis-102	132	4	and	and	CCONJ
ajpdis-102	132	5	image	image	NOUN
ajpdis-102	132	6	models	model	NOUN
ajpdis-102	132	7	tool	tool	VERB
ajpdis-102	132	8	math	math	NOUN
ajpdis-102	132	9	learning	learning	NOUN
ajpdis-102	132	10	options	option	NOUN
ajpdis-102	132	11	.	.	PUNCT
ajpdis-102	133	1	k.u	k.u	PROPN
ajpdis-102	133	2	khursanalievich	khursanalievich	ADJ
ajpdis-102	133	3	,	,	PUNCT
ajpdis-102	133	4	t.t.s	t.t.s	NOUN
ajpdis-102	133	5	ugli	ugli	ADJ
ajpdis-102	133	6	,	,	PUNCT
ajpdis-102	133	7	m.	m.	NOUN
ajpdis-102	133	8	askarali	askarali	PROPN
ajpdis-102	133	9	.	.	PUNCT
ajpdis-102	134	1	american	american	PROPN
ajpdis-102	134	2	journal	journal	PROPN
ajpdis-102	134	3	of	of	ADP
ajpdis-102	134	4	applied	apply	VERB
ajpdis-102	134	5	science	science	NOUN
ajpdis-102	134	6	and	and	CCONJ
ajpdis-102	134	7	technology	technology	NOUN
ajpdis-102	134	8	2	2	NUM
ajpdis-102	134	9	(	(	PUNCT
ajpdis-102	134	10	09	09	NUM
ajpdis-102	134	11	)	)	PUNCT
ajpdis-102	134	12	,	,	PUNCT
ajpdis-102	134	13	26	26	NUM
ajpdis-102	134	14	-	-	SYM
ajpdis-102	134	15	34	34	NUM
ajpdis-102	134	16	.	.	NOUN
ajpdis-102	135	1	7	7	NUM
ajpdis-102	135	2	.	.	X
ajpdis-102	135	3	хонкулов	хонкулов	PROPN
ajpdis-102	135	4	,	,	PUNCT
ajpdis-102	135	5	у	у	X
ajpdis-102	135	6	.	.	PUNCT
ajpdis-102	136	1	х	х	X
ajpdis-102	136	2	.	.	PUNCT
ajpdis-102	137	1	(	(	PUNCT
ajpdis-102	137	2	2015	2015	NUM
ajpdis-102	137	3	)	)	PUNCT
ajpdis-102	137	4	.	.	PUNCT
ajpdis-102	138	1	о	о	PROPN
ajpdis-102	138	2	применениях	применениях	ADJ
ajpdis-102	138	3	компьютерных	компьютерных	PROPN
ajpdis-102	138	4	технологий	технологий	PROPN
ajpdis-102	138	5	в	в	PROPN
ajpdis-102	138	6	обучении	обучении	AUX
ajpdis-102	138	7	элементов	элементов	PROPN
ajpdis-102	138	8	стохастики	стохастики	NOUN
ajpdis-102	138	9	.	.	PUNCT
ajpdis-102	139	1	региональные	региональные	NOUN
ajpdis-102	139	2	проблемы	проблемы	PROPN
ajpdis-102	139	3	преобразования	преобразования	PROPN
ajpdis-102	139	4	экономики	экономики	NOUN
ajpdis-102	139	5	,	,	PUNCT
ajpdis-102	139	6	(	(	PUNCT
ajpdis-102	139	7	8	8	NUM
ajpdis-102	139	8	(	(	PUNCT
ajpdis-102	139	9	58	58	NUM
ajpdis-102	139	10	)	)	PUNCT
ajpdis-102	139	11	)	)	PUNCT
ajpdis-102	139	12	,	,	PUNCT
ajpdis-102	139	13	7682	7682	NUM
ajpdis-102	139	14	.	.	PUNCT
ajpdis-102	140	1	https://scholar.google.com/citations?view_op=view_citation&hl=ru&user=arvdlawaaaaj&citation_for_view=arvdlawaaaaj:eqolee2rzwmc	https://scholar.google.com/citations?view_op=view_citation&hl=ru&user=arvdlawaaaaj&citation_for_view=arvdlawaaaaj:eqolee2rzwmc	PROPN