id	sid	tid	token	lemma	pos
ajtas-1767	1	1	american	american	PROPN
ajtas-1767	1	2	journal	journal	PROPN
ajtas-1767	1	3	of	of	ADP
ajtas-1767	1	4	technology	technology	NOUN
ajtas-1767	1	5	and	and	CCONJ
ajtas-1767	1	6	applied	apply	VERB
ajtas-1767	1	7	sciences	sciences	PROPN
ajtas-1767	1	8	issn	issn	X
ajtas-1767	1	9	(	(	PUNCT
ajtas-1767	1	10	e	e	NOUN
ajtas-1767	1	11	):	):	PUNCT
ajtas-1767	1	12	2832	2832	NUM
ajtas-1767	1	13	-	-	SYM
ajtas-1767	1	14	1766|	1766|	NUM
ajtas-1767	1	15	volume	volume	NOUN
ajtas-1767	1	16	20	20	NUM
ajtas-1767	1	17	,	,	PUNCT
ajtas-1767	1	18	january	january	PROPN
ajtas-1767	1	19	,	,	PUNCT
ajtas-1767	1	20	2024	2024	NUM
ajtas-1767	1	21	p	p	NOUN
ajtas-1767	1	22	a	a	DET
ajtas-1767	1	23	g	g	NOUN
ajtas-1767	1	24	e	e	NOUN
ajtas-1767	1	25	|	|	ADV
ajtas-1767	1	26	52	52	NUM
ajtas-1767	1	27	www.americanjournal.org	www.americanjournal.org	NOUN
ajtas-1767	1	28	trigonometry	trigonometry	NOUN
ajtas-1767	1	29	abdullayev	abdullayev	PROPN
ajtas-1767	1	30	nurbek	nurbek	PROPN
ajtas-1767	1	31	shuhrat	shuhrat	PROPN
ajtas-1767	1	32	og'li	og'li	PROPN
ajtas-1767	1	33	ro'ziqulov	ro'ziqulov	PROPN
ajtas-1767	1	34	sa'dulla	sa'dulla	PROPN
ajtas-1767	1	35	egamnazar	egamnazar	PROPN
ajtas-1767	1	36	o‘g‘li	o‘g‘li	NOUN
ajtas-1767	1	37	yoʻldoshev	yoʻldoshev	NOUN
ajtas-1767	1	38	bekmirza	bekmirza	NOUN
ajtas-1767	1	39	shuxrat	shuxrat	PROPN
ajtas-1767	1	40	oʻgʻli	oʻgʻli	VERB
ajtas-1767	1	41	a	a	DET
ajtas-1767	1	42	b	b	PROPN
ajtas-1767	1	43	s	s	ADP
ajtas-1767	1	44	t	t	PROPN
ajtas-1767	1	45	r	r	NOUN
ajtas-1767	1	46	a	a	DET
ajtas-1767	1	47	c	c	NOUN
ajtas-1767	1	48	t	t	NOUN
ajtas-1767	1	49	k	k	X
ajtas-1767	1	50	e	e	PROPN
ajtas-1767	1	51	y	y	PROPN
ajtas-1767	1	52	w	w	NOUN
ajtas-1767	1	53	o	o	NOUN
ajtas-1767	1	54	r	r	NOUN
ajtas-1767	1	55	d	d	PROPN
ajtas-1767	1	56	s	s	VERB
ajtas-1767	1	57	this	this	DET
ajtas-1767	1	58	article	article	NOUN
ajtas-1767	1	59	will	will	AUX
ajtas-1767	1	60	talk	talk	VERB
ajtas-1767	1	61	about	about	ADP
ajtas-1767	1	62	what	what	PRON
ajtas-1767	1	63	scientific	scientific	ADJ
ajtas-1767	1	64	research	research	NOUN
ajtas-1767	1	65	scientists	scientist	NOUN
ajtas-1767	1	66	have	have	AUX
ajtas-1767	1	67	done	do	VERB
ajtas-1767	1	68	in	in	ADP
ajtas-1767	1	69	ancient	ancient	ADJ
ajtas-1767	1	70	times	time	NOUN
ajtas-1767	1	71	in	in	ADP
ajtas-1767	1	72	the	the	DET
ajtas-1767	1	73	formation	formation	NOUN
ajtas-1767	1	74	of	of	ADP
ajtas-1767	1	75	trigonometry	trigonometry	NOUN
ajtas-1767	1	76	.	.	PUNCT
ajtas-1767	2	1	trigonometry	trigonometry	NOUN
ajtas-1767	2	2	,	,	PUNCT
ajtas-1767	2	3	triangle	triangle	NOUN
ajtas-1767	2	4	,	,	PUNCT
ajtas-1767	2	5	diameter	diameter	NOUN
ajtas-1767	2	6	,	,	PUNCT
ajtas-1767	2	7	segment	segment	NOUN
ajtas-1767	2	8	,	,	PUNCT
ajtas-1767	2	9	sine	sine	NOUN
ajtas-1767	2	10	,	,	PUNCT
ajtas-1767	2	11	cosine	cosine	NOUN
ajtas-1767	2	12	,	,	PUNCT
ajtas-1767	2	13	radian	radian	PROPN
ajtas-1767	2	14	.	.	PROPN
ajtas-1767	2	15	introduction	introduction	NOUN
ajtas-1767	2	16	the	the	DET
ajtas-1767	2	17	term	term	NOUN
ajtas-1767	2	18	"	"	PUNCT
ajtas-1767	2	19	trigonometry	trigonometry	NOUN
ajtas-1767	2	20	“	"	PUNCT
ajtas-1767	2	21	is	be	AUX
ajtas-1767	2	22	derived	derive	VERB
ajtas-1767	2	23	from	from	ADP
ajtas-1767	2	24	the	the	DET
ajtas-1767	2	25	greek	greek	NOUN
ajtas-1767	2	26	words	word	NOUN
ajtas-1767	2	27	”	"	PUNCT
ajtas-1767	2	28	trigonon	trigonon	NOUN
ajtas-1767	2	29	“	"	PUNCT
ajtas-1767	2	30	—	—	PUNCT
ajtas-1767	2	31	triangle	triangle	NOUN
ajtas-1767	2	32	and	and	CCONJ
ajtas-1767	2	33	”	"	PUNCT
ajtas-1767	2	34	metrio	metrio	NOUN
ajtas-1767	2	35	“	"	PUNCT
ajtas-1767	2	36	—	—	PUNCT
ajtas-1767	2	37	measure	measure	NOUN
ajtas-1767	2	38	,	,	PUNCT
ajtas-1767	2	39	and	and	CCONJ
ajtas-1767	2	40	together	together	ADV
ajtas-1767	2	41	means	mean	VERB
ajtas-1767	2	42	”	"	PUNCT
ajtas-1767	2	43	triangle	triangle	NOUN
ajtas-1767	2	44	measurement	measurement	NOUN
ajtas-1767	2	45	"	"	PUNCT
ajtas-1767	2	46	.	.	PUNCT
ajtas-1767	3	1	the	the	DET
ajtas-1767	3	2	demand	demand	NOUN
ajtas-1767	3	3	for	for	ADP
ajtas-1767	3	4	measuring	measure	VERB
ajtas-1767	3	5	angles	angle	NOUN
ajtas-1767	3	6	has	have	AUX
ajtas-1767	3	7	emerged	emerge	VERB
ajtas-1767	3	8	from	from	ADP
ajtas-1767	3	9	a	a	DET
ajtas-1767	3	10	very	very	ADV
ajtas-1767	3	11	long	long	ADJ
ajtas-1767	3	12	time	time	NOUN
ajtas-1767	3	13	,	,	PUNCT
ajtas-1767	3	14	as	as	SCONJ
ajtas-1767	3	15	has	have	VERB
ajtas-1767	3	16	the	the	DET
ajtas-1767	3	17	need	need	NOUN
ajtas-1767	3	18	to	to	PART
ajtas-1767	3	19	measure	measure	VERB
ajtas-1767	3	20	distances	distance	NOUN
ajtas-1767	3	21	.	.	PUNCT
ajtas-1767	4	1	one	one	NUM
ajtas-1767	4	2	of	of	ADP
ajtas-1767	4	3	the	the	DET
ajtas-1767	4	4	development	development	NOUN
ajtas-1767	4	5	factors	factor	NOUN
ajtas-1767	4	6	of	of	ADP
ajtas-1767	4	7	trigonometry	trigonometry	NOUN
ajtas-1767	4	8	came	come	VERB
ajtas-1767	4	9	from	from	ADP
ajtas-1767	4	10	the	the	DET
ajtas-1767	4	11	need	need	NOUN
ajtas-1767	4	12	to	to	PART
ajtas-1767	4	13	determine	determine	VERB
ajtas-1767	4	14	the	the	DET
ajtas-1767	4	15	timing	timing	NOUN
ajtas-1767	4	16	,	,	PUNCT
ajtas-1767	4	17	the	the	DET
ajtas-1767	4	18	position	position	NOUN
ajtas-1767	4	19	of	of	ADP
ajtas-1767	4	20	a	a	DET
ajtas-1767	4	21	ship	ship	NOUN
ajtas-1767	4	22	in	in	ADP
ajtas-1767	4	23	the	the	DET
ajtas-1767	4	24	high	high	ADJ
ajtas-1767	4	25	seas	sea	NOUN
ajtas-1767	4	26	or	or	CCONJ
ajtas-1767	4	27	a	a	DET
ajtas-1767	4	28	caravan	caravan	NOUN
ajtas-1767	4	29	in	in	ADP
ajtas-1767	4	30	the	the	DET
ajtas-1767	4	31	desert	desert	NOUN
ajtas-1767	4	32	.	.	PUNCT
ajtas-1767	5	1	having	having	AUX
ajtas-1767	5	2	studied	study	VERB
ajtas-1767	5	3	the	the	DET
ajtas-1767	5	4	connection	connection	NOUN
ajtas-1767	5	5	between	between	ADP
ajtas-1767	5	6	the	the	DET
ajtas-1767	5	7	sides	side	NOUN
ajtas-1767	5	8	and	and	CCONJ
ajtas-1767	5	9	corners	corner	NOUN
ajtas-1767	5	10	of	of	ADP
ajtas-1767	5	11	the	the	DET
ajtas-1767	5	12	triangle	triangle	NOUN
ajtas-1767	5	13	,	,	PUNCT
ajtas-1767	5	14	ancient	ancient	ADJ
ajtas-1767	5	15	people	people	NOUN
ajtas-1767	5	16	found	find	VERB
ajtas-1767	5	17	ways	way	NOUN
ajtas-1767	5	18	to	to	PART
ajtas-1767	5	19	calculate	calculate	VERB
ajtas-1767	5	20	various	various	ADJ
ajtas-1767	5	21	elements	element	NOUN
ajtas-1767	5	22	of	of	ADP
ajtas-1767	5	23	the	the	DET
ajtas-1767	5	24	triangle	triangle	NOUN
ajtas-1767	5	25	.	.	PUNCT
ajtas-1767	6	1	ancient	ancient	ADJ
ajtas-1767	6	2	vavilon	vavilon	NOUN
ajtas-1767	6	3	scientists	scientist	NOUN
ajtas-1767	6	4	had	have	VERB
ajtas-1767	6	5	some	some	DET
ajtas-1767	6	6	knowledge	knowledge	NOUN
ajtas-1767	6	7	of	of	ADP
ajtas-1767	6	8	trigonometry	trigonometry	NOUN
ajtas-1767	6	9	.	.	PUNCT
ajtas-1767	7	1	this	this	PRON
ajtas-1767	7	2	is	be	AUX
ajtas-1767	7	3	evidenced	evidence	VERB
ajtas-1767	7	4	by	by	ADP
ajtas-1767	7	5	the	the	DET
ajtas-1767	7	6	fact	fact	NOUN
ajtas-1767	7	7	that	that	SCONJ
ajtas-1767	7	8	the	the	DET
ajtas-1767	7	9	vavilonians	vavilonian	NOUN
ajtas-1767	7	10	know	know	VERB
ajtas-1767	7	11	about	about	ADP
ajtas-1767	7	12	solar	solar	ADJ
ajtas-1767	7	13	and	and	CCONJ
ajtas-1767	7	14	lunar	lunar	ADJ
ajtas-1767	7	15	eclipses	eclipse	NOUN
ajtas-1767	7	16	.	.	PUNCT
ajtas-1767	8	1	in	in	ADP
ajtas-1767	8	2	one	one	NUM
ajtas-1767	8	3	of	of	ADP
ajtas-1767	8	4	the	the	DET
ajtas-1767	8	5	clay	clay	NOUN
ajtas-1767	8	6	tables	table	NOUN
ajtas-1767	8	7	of	of	ADP
ajtas-1767	8	8	ancient	ancient	ADJ
ajtas-1767	8	9	vavilon	vavilon	NOUN
ajtas-1767	8	10	(	(	PUNCT
ajtas-1767	8	11	2	2	NUM
ajtas-1767	8	12	thousand	thousand	NUM
ajtas-1767	8	13	years	year	NOUN
ajtas-1767	8	14	ago	ago	ADV
ajtas-1767	8	15	bc	bc	PROPN
ajtas-1767	8	16	)	)	PUNCT
ajtas-1767	8	17	,	,	PUNCT
ajtas-1767	8	18	an	an	DET
ajtas-1767	8	19	issue	issue	NOUN
ajtas-1767	8	20	is	be	AUX
ajtas-1767	8	21	solved	solve	VERB
ajtas-1767	8	22	:	:	PUNCT
ajtas-1767	8	23	in	in	ADP
ajtas-1767	8	24	it	it	PRON
ajtas-1767	8	25	,	,	PUNCT
ajtas-1767	8	26	according	accord	VERB
ajtas-1767	8	27	to	to	ADP
ajtas-1767	8	28	the	the	DET
ajtas-1767	8	29	known	know	VERB
ajtas-1767	8	30	diameter	diameter	NOUN
ajtas-1767	8	31	of	of	ADP
ajtas-1767	8	32	the	the	DET
ajtas-1767	8	33	circle	circle	NOUN
ajtas-1767	8	34	and	and	CCONJ
ajtas-1767	8	35	the	the	DET
ajtas-1767	8	36	height	height	NOUN
ajtas-1767	8	37	of	of	ADP
ajtas-1767	8	38	the	the	DET
ajtas-1767	8	39	segment	segment	NOUN
ajtas-1767	8	40	,	,	PUNCT
ajtas-1767	8	41	the	the	DET
ajtas-1767	8	42	length	length	NOUN
ajtas-1767	8	43	of	of	ADP
ajtas-1767	8	44	the	the	DET
ajtas-1767	8	45	vatar	vatar	NOUN
ajtas-1767	8	46	is	be	AUX
ajtas-1767	8	47	calculated	calculate	VERB
ajtas-1767	8	48	,	,	PUNCT
ajtas-1767	8	49	which	which	PRON
ajtas-1767	8	50	corresponds	correspond	VERB
ajtas-1767	8	51	to	to	ADP
ajtas-1767	8	52	the	the	DET
ajtas-1767	8	53	establishment	establishment	NOUN
ajtas-1767	8	54	of	of	ADP
ajtas-1767	8	55	a	a	DET
ajtas-1767	8	56	connection	connection	NOUN
ajtas-1767	8	57	between	between	ADP
ajtas-1767	8	58	the	the	DET
ajtas-1767	8	59	sine	sine	NOUN
ajtas-1767	8	60	and	and	CCONJ
ajtas-1767	8	61	the	the	DET
ajtas-1767	8	62	cosine	cosine	NOUN
ajtas-1767	8	63	.	.	PUNCT
ajtas-1767	9	1	ancient	ancient	ADJ
ajtas-1767	9	2	greek	greek	ADJ
ajtas-1767	9	3	scholars	scholar	NOUN
ajtas-1767	9	4	knew	know	VERB
ajtas-1767	9	5	the	the	DET
ajtas-1767	9	6	methods	method	NOUN
ajtas-1767	9	7	of	of	ADP
ajtas-1767	9	8	solving	solve	VERB
ajtas-1767	9	9	right	right	ADJ
ajtas-1767	9	10	-	-	PUNCT
ajtas-1767	9	11	angled	angle	VERB
ajtas-1767	9	12	triangles	triangle	NOUN
ajtas-1767	9	13	.	.	PUNCT
ajtas-1767	10	1	the	the	DET
ajtas-1767	10	2	astronomer	astronomer	NOUN
ajtas-1767	10	3	and	and	CCONJ
ajtas-1767	10	4	mathematician	mathematician	ADJ
ajtas-1767	10	5	hipparchus	hipparchus	NOUN
ajtas-1767	10	6	(	(	PUNCT
ajtas-1767	10	7	until	until	ADP
ajtas-1767	10	8	2nd	2nd	ADJ
ajtas-1767	10	9	century	century	NOUN
ajtas-1767	10	10	ad	ad	NOUN
ajtas-1767	10	11	)	)	PUNCT
ajtas-1767	10	12	compiled	compile	VERB
ajtas-1767	10	13	a	a	DET
ajtas-1767	10	14	table	table	NOUN
ajtas-1767	10	15	of	of	ADP
ajtas-1767	10	16	vatars	vatar	NOUN
ajtas-1767	10	17	—	—	PUNCT
ajtas-1767	10	18	the	the	DET
ajtas-1767	10	19	first	first	ADJ
ajtas-1767	10	20	trigonometric	trigonometric	ADJ
ajtas-1767	10	21	tables	table	NOUN
ajtas-1767	10	22	.	.	PUNCT
ajtas-1767	11	1	one	one	NUM
ajtas-1767	11	2	of	of	ADP
ajtas-1767	11	3	the	the	DET
ajtas-1767	11	4	great	great	ADJ
ajtas-1767	11	5	successes	success	NOUN
ajtas-1767	11	6	in	in	ADP
ajtas-1767	11	7	the	the	DET
ajtas-1767	11	8	construction	construction	NOUN
ajtas-1767	11	9	of	of	ADP
ajtas-1767	11	10	trigonometric	trigonometric	ADJ
ajtas-1767	11	11	tables	table	NOUN
ajtas-1767	11	12	is	be	AUX
ajtas-1767	11	13	k.rolemey	k.rolemey	PRON
ajtas-1767	11	14	's	's	PART
ajtas-1767	11	15	(	(	PUNCT
ajtas-1767	11	16	2nd	2nd	ADJ
ajtas-1767	11	17	century	century	NOUN
ajtas-1767	11	18	)	)	PUNCT
ajtas-1767	11	19	“	"	PUNCT
ajtas-1767	11	20	almagest	almag	ADJ
ajtas-1767	11	21	”	"	PUNCT
ajtas-1767	11	22	became	become	VERB
ajtas-1767	11	23	a	a	DET
ajtas-1767	11	24	work	work	NOUN
ajtas-1767	11	25	.	.	PUNCT
ajtas-1767	12	1	the	the	DET
ajtas-1767	12	2	work	work	NOUN
ajtas-1767	12	3	collects	collect	VERB
ajtas-1767	12	4	and	and	CCONJ
ajtas-1767	12	5	summarizes	summarize	VERB
ajtas-1767	12	6	various	various	ADJ
ajtas-1767	12	7	data	datum	NOUN
ajtas-1767	12	8	from	from	ADP
ajtas-1767	12	9	astronomy	astronomy	NOUN
ajtas-1767	12	10	and	and	CCONJ
ajtas-1767	12	11	related	related	ADJ
ajtas-1767	12	12	sciences	science	NOUN
ajtas-1767	12	13	known	know	VERB
ajtas-1767	12	14	at	at	ADP
ajtas-1767	12	15	the	the	DET
ajtas-1767	12	16	time	time	NOUN
ajtas-1767	12	17	.	.	PUNCT
ajtas-1767	13	1	here	here	ADV
ajtas-1767	13	2	is	be	AUX
ajtas-1767	13	3	a	a	DET
ajtas-1767	13	4	table	table	NOUN
ajtas-1767	13	5	of	of	ADP
ajtas-1767	13	6	vatars	vatar	NOUN
ajtas-1767	13	7	compiled	compile	VERB
ajtas-1767	13	8	in	in	ADP
ajtas-1767	13	9	the	the	DET
ajtas-1767	13	10	hexadecimal	hexadecimal	ADJ
ajtas-1767	13	11	count	count	NOUN
ajtas-1767	13	12	system	system	NOUN
ajtas-1767	13	13	,	,	PUNCT
ajtas-1767	13	14	with	with	ADP
ajtas-1767	13	15	a	a	DET
ajtas-1767	13	16	half	half	ADJ
ajtas-1767	13	17	-	-	PUNCT
ajtas-1767	13	18	degree	degree	NOUN
ajtas-1767	13	19	interval	interval	NOUN
ajtas-1767	13	20	from	from	ADP
ajtas-1767	13	21	0	0	NUM
ajtas-1767	13	22	to	to	ADP
ajtas-1767	13	23	180	180	NUM
ajtas-1767	13	24	°	°	NOUN
ajtas-1767	13	25	.	.	PUNCT
ajtas-1767	14	1	in	in	ADP
ajtas-1767	14	2	fact	fact	NOUN
ajtas-1767	14	3	,	,	PUNCT
ajtas-1767	14	4	the	the	DET
ajtas-1767	14	5	vatars	vatar	NOUN
ajtas-1767	14	6	table	table	NOUN
ajtas-1767	14	7	is	be	AUX
ajtas-1767	14	8	the	the	DET
ajtas-1767	14	9	table	table	NOUN
ajtas-1767	14	10	of	of	ADP
ajtas-1767	14	11	sines	sine	NOUN
ajtas-1767	14	12	from	from	ADP
ajtas-1767	14	13	0	0	NUM
ajtas-1767	14	14	to	to	PART
ajtas-1767	14	15	90	90	NUM
ajtas-1767	14	16	degrees	degree	NOUN
ajtas-1767	14	17	itself	itself	PRON
ajtas-1767	14	18	.	.	PUNCT
ajtas-1767	15	1	ptolemy	ptolemy	PROPN
ajtas-1767	15	2	also	also	ADV
ajtas-1767	15	3	gives	give	VERB
ajtas-1767	15	4	rise	rise	NOUN
ajtas-1767	15	5	to	to	ADP
ajtas-1767	15	6	formulas	formula	NOUN
ajtas-1767	15	7	that	that	PRON
ajtas-1767	15	8	appear	appear	VERB
ajtas-1767	15	9	in	in	ADP
ajtas-1767	15	10	modern	modern	ADJ
ajtas-1767	15	11	designations	designation	NOUN
ajtas-1767	15	12	as	as	SCONJ
ajtas-1767	15	13	follows	follow	VERB
ajtas-1767	15	14	.	.	PUNCT
ajtas-1767	16	1	it	it	PRON
ajtas-1767	16	2	was	be	AUX
ajtas-1767	16	3	used	use	VERB
ajtas-1767	16	4	to	to	PART
ajtas-1767	16	5	determine	determine	VERB
ajtas-1767	16	6	distances	distance	NOUN
ajtas-1767	16	7	to	to	ADP
ajtas-1767	16	8	inaccessible	inaccessible	ADJ
ajtas-1767	16	9	places	place	NOUN
ajtas-1767	16	10	,	,	PUNCT
ajtas-1767	16	11	primarily	primarily	ADV
ajtas-1767	16	12	to	to	PART
ajtas-1767	16	13	address	address	VERB
ajtas-1767	16	14	practical	practical	ADJ
ajtas-1767	16	15	astronomy	astronomy	NOUN
ajtas-1767	16	16	issues	issue	NOUN
ajtas-1767	16	17	.	.	PUNCT
ajtas-1767	17	1	american	american	ADJ
ajtas-1767	17	2	journal	journal	PROPN
ajtas-1767	17	3	of	of	ADP
ajtas-1767	17	4	technology	technology	NOUN
ajtas-1767	17	5	and	and	CCONJ
ajtas-1767	17	6	applied	apply	VERB
ajtas-1767	17	7	sciences	science	NOUN
ajtas-1767	17	8	volume	volume	NOUN
ajtas-1767	17	9	20	20	NUM
ajtas-1767	17	10	,	,	PUNCT
ajtas-1767	17	11	january	january	PROPN
ajtas-1767	17	12	2024	2024	NUM
ajtas-1767	17	13	p	p	NOUN
ajtas-1767	17	14	a	a	DET
ajtas-1767	17	15	g	g	NOUN
ajtas-1767	17	16	e	e	NOUN
ajtas-1767	17	17	|	|	ADV
ajtas-1767	17	18	53	53	NUM
ajtas-1767	17	19	www.americanjournal.org	www.americanjournal.org	NOUN
ajtas-1767	17	20	trigonometry	trigonometry	NOUN
ajtas-1767	17	21	was	be	AUX
ajtas-1767	17	22	developed	develop	VERB
ajtas-1767	17	23	after	after	ADP
ajtas-1767	17	24	him	he	PRON
ajtas-1767	17	25	by	by	ADP
ajtas-1767	17	26	scientists	scientist	NOUN
ajtas-1767	17	27	from	from	ADP
ajtas-1767	17	28	india	india	PROPN
ajtas-1767	17	29	,	,	PUNCT
ajtas-1767	17	30	the	the	DET
ajtas-1767	17	31	middle	middle	ADJ
ajtas-1767	17	32	and	and	CCONJ
ajtas-1767	17	33	middle	middle	PROPN
ajtas-1767	17	34	east	east	PROPN
ajtas-1767	17	35	.	.	PUNCT
ajtas-1767	18	1	they	they	PRON
ajtas-1767	18	2	introduced	introduce	VERB
ajtas-1767	18	3	sine	sine	NOUN
ajtas-1767	18	4	,	,	PUNCT
ajtas-1767	18	5	cosine	cosine	NOUN
ajtas-1767	18	6	,	,	PUNCT
ajtas-1767	18	7	tangent	tangent	NOUN
ajtas-1767	18	8	,	,	PUNCT
ajtas-1767	18	9	cotangens	cotangen	NOUN
ajtas-1767	18	10	,	,	PUNCT
ajtas-1767	18	11	based	base	VERB
ajtas-1767	18	12	on	on	ADP
ajtas-1767	18	13	the	the	DET
ajtas-1767	18	14	radian	radian	ADJ
ajtas-1767	18	15	measure	measure	NOUN
ajtas-1767	18	16	of	of	ADP
ajtas-1767	18	17	the	the	DET
ajtas-1767	18	18	angle	angle	NOUN
ajtas-1767	18	19	.	.	PUNCT
ajtas-1767	19	1	trigonometry	trigonometry	NOUN
ajtas-1767	19	2	is	be	AUX
ajtas-1767	19	3	a	a	DET
ajtas-1767	19	4	branch	branch	NOUN
ajtas-1767	19	5	of	of	ADP
ajtas-1767	19	6	mathematics	mathematic	NOUN
ajtas-1767	19	7	that	that	PRON
ajtas-1767	19	8	deals	deal	VERB
ajtas-1767	19	9	with	with	ADP
ajtas-1767	19	10	the	the	DET
ajtas-1767	19	11	relationship	relationship	NOUN
ajtas-1767	19	12	between	between	ADP
ajtas-1767	19	13	the	the	DET
ajtas-1767	19	14	angles	angle	NOUN
ajtas-1767	19	15	and	and	CCONJ
ajtas-1767	19	16	sides	side	NOUN
ajtas-1767	19	17	of	of	ADP
ajtas-1767	19	18	triangles	triangle	NOUN
ajtas-1767	19	19	.	.	PUNCT
ajtas-1767	20	1	it	it	PRON
ajtas-1767	20	2	focuses	focus	VERB
ajtas-1767	20	3	on	on	ADP
ajtas-1767	20	4	the	the	DET
ajtas-1767	20	5	study	study	NOUN
ajtas-1767	20	6	of	of	ADP
ajtas-1767	20	7	trigonometric	trigonometric	ADJ
ajtas-1767	20	8	functions	function	NOUN
ajtas-1767	20	9	,	,	PUNCT
ajtas-1767	20	10	which	which	PRON
ajtas-1767	20	11	are	be	AUX
ajtas-1767	20	12	the	the	DET
ajtas-1767	20	13	ratios	ratio	NOUN
ajtas-1767	20	14	of	of	ADP
ajtas-1767	20	15	the	the	DET
ajtas-1767	20	16	sides	side	NOUN
ajtas-1767	20	17	of	of	ADP
ajtas-1767	20	18	the	the	DET
ajtas-1767	20	19	right	right	ADJ
ajtas-1767	20	20	triangle	triangle	NOUN
ajtas-1767	20	21	.	.	PUNCT
ajtas-1767	21	1	the	the	DET
ajtas-1767	21	2	primary	primary	ADJ
ajtas-1767	21	3	trigonometric	trigonometric	NOUN
ajtas-1767	21	4	functions	function	NOUN
ajtas-1767	21	5	are	be	AUX
ajtas-1767	21	6	:	:	PUNCT
ajtas-1767	21	7	sine	sine	ADJ
ajtas-1767	21	8	(	(	PUNCT
ajtas-1767	21	9	sin	sin	NOUN
ajtas-1767	21	10	)	)	PUNCT
ajtas-1767	21	11	,	,	PUNCT
ajtas-1767	21	12	cosine	cosine	NOUN
ajtas-1767	21	13	(	(	PUNCT
ajtas-1767	21	14	kos	kos	PROPN
ajtas-1767	21	15	)	)	PUNCT
ajtas-1767	21	16	,	,	PUNCT
ajtas-1767	21	17	and	and	CCONJ
ajtas-1767	21	18	tangent	tangent	NOUN
ajtas-1767	21	19	(	(	PUNCT
ajtas-1767	21	20	tan	tan	PROPN
ajtas-1767	21	21	)	)	PUNCT
ajtas-1767	21	22	.	.	PUNCT
ajtas-1767	22	1	these	these	DET
ajtas-1767	22	2	functions	function	NOUN
ajtas-1767	22	3	connect	connect	VERB
ajtas-1767	22	4	the	the	DET
ajtas-1767	22	5	angles	angle	NOUN
ajtas-1767	22	6	of	of	ADP
ajtas-1767	22	7	the	the	DET
ajtas-1767	22	8	right	right	ADJ
ajtas-1767	22	9	triangle	triangle	NOUN
ajtas-1767	22	10	with	with	ADP
ajtas-1767	22	11	the	the	DET
ajtas-1767	22	12	proportions	proportion	NOUN
ajtas-1767	22	13	of	of	ADP
ajtas-1767	22	14	its	its	PRON
ajtas-1767	22	15	sides	side	NOUN
ajtas-1767	22	16	.	.	PUNCT
ajtas-1767	23	1	the	the	DET
ajtas-1767	23	2	sine	sine	ADJ
ajtas-1767	23	3	function	function	NOUN
ajtas-1767	23	4	represents	represent	VERB
ajtas-1767	23	5	the	the	DET
ajtas-1767	23	6	ratio	ratio	NOUN
ajtas-1767	23	7	of	of	ADP
ajtas-1767	23	8	the	the	DET
ajtas-1767	23	9	length	length	NOUN
ajtas-1767	23	10	of	of	ADP
ajtas-1767	23	11	the	the	DET
ajtas-1767	23	12	side	side	NOUN
ajtas-1767	23	13	opposite	opposite	ADP
ajtas-1767	23	14	the	the	DET
ajtas-1767	23	15	angle	angle	NOUN
ajtas-1767	23	16	to	to	ADP
ajtas-1767	23	17	the	the	DET
ajtas-1767	23	18	length	length	NOUN
ajtas-1767	23	19	of	of	ADP
ajtas-1767	23	20	the	the	DET
ajtas-1767	23	21	hypotenuse	hypotenuse	NOUN
ajtas-1767	23	22	.	.	PUNCT
ajtas-1767	24	1	the	the	DET
ajtas-1767	24	2	cosine	cosine	NOUN
ajtas-1767	24	3	function	function	NOUN
ajtas-1767	24	4	represents	represent	VERB
ajtas-1767	24	5	the	the	DET
ajtas-1767	24	6	ratio	ratio	NOUN
ajtas-1767	24	7	of	of	ADP
ajtas-1767	24	8	the	the	DET
ajtas-1767	24	9	length	length	NOUN
ajtas-1767	24	10	of	of	ADP
ajtas-1767	24	11	the	the	DET
ajtas-1767	24	12	adjacent	adjacent	ADJ
ajtas-1767	24	13	side	side	NOUN
ajtas-1767	24	14	to	to	ADP
ajtas-1767	24	15	the	the	DET
ajtas-1767	24	16	angle	angle	NOUN
ajtas-1767	24	17	to	to	ADP
ajtas-1767	24	18	the	the	DET
ajtas-1767	24	19	length	length	NOUN
ajtas-1767	24	20	of	of	ADP
ajtas-1767	24	21	the	the	DET
ajtas-1767	24	22	hypotenuse	hypotenuse	NOUN
ajtas-1767	24	23	.	.	PUNCT
ajtas-1767	25	1	the	the	DET
ajtas-1767	25	2	tangent	tangent	NOUN
ajtas-1767	25	3	function	function	NOUN
ajtas-1767	25	4	represents	represent	VERB
ajtas-1767	25	5	the	the	DET
ajtas-1767	25	6	ratio	ratio	NOUN
ajtas-1767	25	7	of	of	ADP
ajtas-1767	25	8	the	the	DET
ajtas-1767	25	9	length	length	NOUN
ajtas-1767	25	10	of	of	ADP
ajtas-1767	25	11	the	the	DET
ajtas-1767	25	12	side	side	NOUN
ajtas-1767	25	13	opposite	opposite	ADP
ajtas-1767	25	14	the	the	DET
ajtas-1767	25	15	angle	angle	NOUN
ajtas-1767	25	16	to	to	ADP
ajtas-1767	25	17	the	the	DET
ajtas-1767	25	18	length	length	NOUN
ajtas-1767	25	19	of	of	ADP
ajtas-1767	25	20	the	the	DET
ajtas-1767	25	21	side	side	NOUN
ajtas-1767	25	22	adjacent	adjacent	ADJ
ajtas-1767	25	23	to	to	ADP
ajtas-1767	25	24	that	that	DET
ajtas-1767	25	25	angle	angle	NOUN
ajtas-1767	25	26	.	.	PUNCT
ajtas-1767	26	1	trigonometry	trigonometry	NOUN
ajtas-1767	26	2	is	be	AUX
ajtas-1767	26	3	used	use	VERB
ajtas-1767	26	4	in	in	ADP
ajtas-1767	26	5	various	various	ADJ
ajtas-1767	26	6	fields	field	NOUN
ajtas-1767	26	7	such	such	ADJ
ajtas-1767	26	8	as	as	ADP
ajtas-1767	26	9	physics	physics	NOUN
ajtas-1767	26	10	,	,	PUNCT
ajtas-1767	26	11	engineering	engineering	NOUN
ajtas-1767	26	12	,	,	PUNCT
ajtas-1767	26	13	architecture	architecture	NOUN
ajtas-1767	26	14	,	,	PUNCT
ajtas-1767	26	15	computer	computer	NOUN
ajtas-1767	26	16	graphics	graphic	NOUN
ajtas-1767	26	17	.	.	PUNCT
ajtas-1767	27	1	it	it	PRON
ajtas-1767	27	2	plays	play	VERB
ajtas-1767	27	3	a	a	DET
ajtas-1767	27	4	very	very	ADV
ajtas-1767	27	5	important	important	ADJ
ajtas-1767	27	6	role	role	NOUN
ajtas-1767	27	7	in	in	ADP
ajtas-1767	27	8	calculating	calculate	VERB
ajtas-1767	27	9	distances	distance	NOUN
ajtas-1767	27	10	,	,	PUNCT
ajtas-1767	27	11	heights	height	NOUN
ajtas-1767	27	12	,	,	PUNCT
ajtas-1767	27	13	trajectories	trajectory	NOUN
ajtas-1767	27	14	and	and	CCONJ
ajtas-1767	27	15	angles	angle	NOUN
ajtas-1767	27	16	in	in	ADP
ajtas-1767	27	17	real	real	ADJ
ajtas-1767	27	18	-	-	PUNCT
ajtas-1767	27	19	world	world	NOUN
ajtas-1767	27	20	applications	application	NOUN
ajtas-1767	27	21	.	.	PUNCT
ajtas-1767	28	1	trigonometric	trigonometric	ADJ
ajtas-1767	28	2	identities	identity	NOUN
ajtas-1767	28	3	,	,	PUNCT
ajtas-1767	28	4	equations	equation	NOUN
ajtas-1767	28	5	,	,	PUNCT
ajtas-1767	28	6	and	and	CCONJ
ajtas-1767	28	7	formulas	formula	NOUN
ajtas-1767	28	8	are	be	AUX
ajtas-1767	28	9	used	use	VERB
ajtas-1767	28	10	to	to	PART
ajtas-1767	28	11	solve	solve	VERB
ajtas-1767	28	12	problems	problem	NOUN
ajtas-1767	28	13	with	with	ADP
ajtas-1767	28	14	triangles	triangle	NOUN
ajtas-1767	28	15	,	,	PUNCT
ajtas-1767	28	16	circles	circle	NOUN
ajtas-1767	28	17	,	,	PUNCT
ajtas-1767	28	18	and	and	CCONJ
ajtas-1767	28	19	periodic	periodic	ADJ
ajtas-1767	28	20	phenomena	phenomenon	NOUN
ajtas-1767	28	21	.	.	PUNCT
ajtas-1767	29	1	some	some	DET
ajtas-1767	29	2	key	key	ADJ
ajtas-1767	29	3	concepts	concept	NOUN
ajtas-1767	29	4	and	and	CCONJ
ajtas-1767	29	5	topics	topic	NOUN
ajtas-1767	29	6	in	in	ADP
ajtas-1767	29	7	trigonometry	trigonometry	NOUN
ajtas-1767	29	8	include	include	VERB
ajtas-1767	29	9	unit	unit	NOUN
ajtas-1767	29	10	circle	circle	NOUN
ajtas-1767	29	11	,	,	PUNCT
ajtas-1767	29	12	radian	radian	ADJ
ajtas-1767	29	13	measure	measure	NOUN
ajtas-1767	29	14	,	,	PUNCT
ajtas-1767	29	15	trigonometric	trigonometric	ADJ
ajtas-1767	29	16	identities	identity	NOUN
ajtas-1767	29	17	(	(	PUNCT
ajtas-1767	29	18	e.g.	e.g.	ADV
ajtas-1767	29	19	pythagorean	pythagorean	VERB
ajtas-1767	29	20	identity	identity	NOUN
ajtas-1767	29	21	and	and	CCONJ
ajtas-1767	29	22	dual	dual	ADJ
ajtas-1767	29	23	-	-	PUNCT
ajtas-1767	29	24	angle	angle	NOUN
ajtas-1767	29	25	identity	identity	NOUN
ajtas-1767	29	26	)	)	PUNCT
ajtas-1767	29	27	,	,	PUNCT
ajtas-1767	29	28	inverse	inverse	NOUN
ajtas-1767	29	29	trigonometric	trigonometric	NOUN
ajtas-1767	29	30	functions	function	NOUN
ajtas-1767	29	31	,	,	PUNCT
ajtas-1767	29	32	sine	sine	NOUN
ajtas-1767	29	33	and	and	CCONJ
ajtas-1767	29	34	cosine	cosine	NOUN
ajtas-1767	29	35	laws	law	NOUN
ajtas-1767	29	36	.	.	PUNCT
ajtas-1767	30	1	a	a	DET
ajtas-1767	30	2	fixed	fix	VERB
ajtas-1767	30	3	notion	notion	NOUN
ajtas-1767	30	4	of	of	ADP
ajtas-1767	30	5	trigonometry	trigonometry	NOUN
ajtas-1767	30	6	is	be	AUX
ajtas-1767	30	7	necessary	necessary	ADJ
ajtas-1767	30	8	for	for	ADP
ajtas-1767	30	9	more	more	ADJ
ajtas-1767	30	10	modern	modern	ADJ
ajtas-1767	30	11	mathematical	mathematical	ADJ
ajtas-1767	30	12	concepts	concept	NOUN
ajtas-1767	30	13	such	such	ADJ
ajtas-1767	30	14	as	as	ADP
ajtas-1767	30	15	calculus	calculus	NOUN
ajtas-1767	30	16	and	and	CCONJ
ajtas-1767	30	17	complex	complex	ADJ
ajtas-1767	30	18	numbers	number	NOUN
ajtas-1767	30	19	.	.	PUNCT
ajtas-1767	31	1	trigonometric	trigonometric	ADJ
ajtas-1767	31	2	functions	function	NOUN
ajtas-1767	31	3	are	be	AUX
ajtas-1767	31	4	one	one	NUM
ajtas-1767	31	5	of	of	ADP
ajtas-1767	31	6	the	the	DET
ajtas-1767	31	7	important	important	ADJ
ajtas-1767	31	8	classes	class	NOUN
ajtas-1767	31	9	of	of	ADP
ajtas-1767	31	10	functions	function	NOUN
ajtas-1767	31	11	.	.	PUNCT
ajtas-1767	32	1	it	it	PRON
ajtas-1767	32	2	is	be	AUX
ajtas-1767	32	3	distinguished	distinguish	VERB
ajtas-1767	32	4	from	from	ADP
ajtas-1767	32	5	the	the	DET
ajtas-1767	32	6	main	main	ADJ
ajtas-1767	32	7	problems	problem	NOUN
ajtas-1767	32	8	of	of	ADP
ajtas-1767	32	9	the	the	DET
ajtas-1767	32	10	theory	theory	NOUN
ajtas-1767	32	11	of	of	ADP
ajtas-1767	32	12	trigonometric	trigonometric	ADJ
ajtas-1767	32	13	functions	function	NOUN
ajtas-1767	32	14	.	.	PUNCT
ajtas-1767	33	1	some	some	DET
ajtas-1767	33	2	important	important	ADJ
ajtas-1767	33	3	results	result	NOUN
ajtas-1767	33	4	of	of	ADP
ajtas-1767	33	5	the	the	DET
ajtas-1767	33	6	theory	theory	NOUN
ajtas-1767	33	7	of	of	ADP
ajtas-1767	33	8	trigonometric	trigonometric	ADJ
ajtas-1767	33	9	functions	function	NOUN
ajtas-1767	33	10	:	:	PUNCT
ajtas-1767	33	11	1	1	X
ajtas-1767	33	12	.	.	X
ajtas-1767	33	13	for	for	ADP
ajtas-1767	33	14	a	a	DET
ajtas-1767	33	15	finite	finite	ADJ
ajtas-1767	33	16	function	function	NOUN
ajtas-1767	33	17	f	f	PROPN
ajtas-1767	33	18	(	(	PUNCT
ajtas-1767	33	19	x	x	X
ajtas-1767	33	20	)	)	PUNCT
ajtas-1767	33	21	on	on	ADP
ajtas-1767	33	22	a	a	DET
ajtas-1767	33	23	dimensional	dimensional	ADJ
ajtas-1767	33	24	and	and	CCONJ
ajtas-1767	33	25	almost	almost	ADV
ajtas-1767	33	26	prime	prime	ADJ
ajtas-1767	33	27	earth	earth	NOUN
ajtas-1767	33	28	,	,	PUNCT
ajtas-1767	33	29	there	there	PRON
ajtas-1767	33	30	are	be	VERB
ajtas-1767	33	31	trigonometric	trigonometric	ADJ
ajtas-1767	33	32	functions	function	NOUN
ajtas-1767	34	1	[	[	X
ajtas-1767	34	2	[	[	X
ajtas-1767	34	3	that	that	DET
ajtas-1767	34	4	converge	converge	NOUN
ajtas-1767	34	5	to	to	ADP
ajtas-1767	34	6	f	f	PROPN
ajtas-1767	34	7	(	(	PUNCT
ajtas-1767	34	8	x	x	NOUN
ajtas-1767	34	9	)	)	PUNCT
ajtas-1767	34	10	almost	almost	ADV
ajtas-1767	34	11	everywhere	everywhere	ADV
ajtas-1767	34	12	.	.	PUNCT
ajtas-1767	35	1	2	2	X
ajtas-1767	35	2	.	.	X
ajtas-1767	35	3	the	the	DET
ajtas-1767	35	4	fourier	fourier	PROPN
ajtas-1767	35	5	series	series	NOUN
ajtas-1767	35	6	of	of	ADP
ajtas-1767	35	7	integrable	integrable	ADJ
ajtas-1767	35	8	functions	function	NOUN
ajtas-1767	35	9	that	that	PRON
ajtas-1767	35	10	move	move	VERB
ajtas-1767	35	11	away	away	ADV
ajtas-1767	35	12	from	from	ADP
ajtas-1767	35	13	the	the	DET
ajtas-1767	35	14	hamma	hamma	NOUN
ajtas-1767	35	15	earth	earth	NOUN
ajtas-1767	36	1	[	[	X
ajtas-1767	36	2	[	[	X
ajtas-1767	36	3	exist	exist	VERB
ajtas-1767	36	4	.	.	PUNCT
ajtas-1767	37	1	3	3	X
ajtas-1767	37	2	.	.	X
ajtas-1767	37	3	for	for	ADP
ajtas-1767	37	4	each	each	DET
ajtas-1767	37	5	dimensional	dimensional	ADJ
ajtas-1767	37	6	function	function	NOUN
ajtas-1767	37	7	f	f	NOUN
ajtas-1767	37	8	(	(	PUNCT
ajtas-1767	37	9	x	x	NOUN
ajtas-1767	37	10	)	)	PUNCT
ajtas-1767	37	11	,	,	PUNCT
ajtas-1767	37	12	the	the	DET
ajtas-1767	37	13	trigonometric	trigonometric	ADJ
ajtas-1767	37	14	functions	function	NOUN
ajtas-1767	37	15	approximating	approximate	VERB
ajtas-1767	37	16	f	f	X
ajtas-1767	37	17	(	(	PUNCT
ajtas-1767	37	18	x	x	X
ajtas-1767	37	19	)	)	PUNCT
ajtas-1767	37	20	by	by	ADP
ajtas-1767	37	21	measure	measure	NOUN
ajtas-1767	37	22	[	[	X
ajtas-1767	37	23	[	[	X
ajtas-1767	37	24	exist	exist	VERB
ajtas-1767	37	25	.	.	PUNCT
ajtas-1767	38	1	trigonometric	trigonometric	ADJ
ajtas-1767	38	2	functions	function	NOUN
ajtas-1767	38	3	have	have	VERB
ajtas-1767	38	4	wide	wide	ADJ
ajtas-1767	38	5	applications	application	NOUN
ajtas-1767	38	6	in	in	ADP
ajtas-1767	38	7	number	number	NOUN
ajtas-1767	38	8	theory	theory	NOUN
ajtas-1767	38	9	(	(	PUNCT
ajtas-1767	38	10	"	"	PUNCT
ajtas-1767	38	11	method	method	NOUN
ajtas-1767	38	12	of	of	ADP
ajtas-1767	38	13	trigonometric	trigonometric	ADJ
ajtas-1767	38	14	sums")and	sums")and	NOUN
ajtas-1767	38	15	in	in	ADP
ajtas-1767	38	16	mathematical	mathematical	ADJ
ajtas-1767	38	17	physics	physics	NOUN
ajtas-1767	38	18	equations	equation	NOUN
ajtas-1767	38	19	(	(	PUNCT
ajtas-1767	38	20	"	"	PUNCT
ajtas-1767	38	21	fourier	fouri	ADJ
ajtas-1767	38	22	method	method	NOUN
ajtas-1767	38	23	"	"	PUNCT
ajtas-1767	38	24	)	)	PUNCT
ajtas-1767	38	25	.	.	PUNCT
ajtas-1767	39	1	trigonometric	trigonometric	ADJ
ajtas-1767	39	2	functions	function	NOUN
ajtas-1767	39	3	were	be	AUX
ajtas-1767	39	4	first	first	ADV
ajtas-1767	39	5	defined	define	VERB
ajtas-1767	39	6	by	by	ADP
ajtas-1767	39	7	l.	l.	PROPN
ajtas-1767	39	8	found	find	VERB
ajtas-1767	39	9	in	in	ADP
ajtas-1767	39	10	5mler	5mler	NUM
ajtas-1767	39	11	cases	case	NOUN
ajtas-1767	39	12	.	.	PUNCT
ajtas-1767	40	1	after	after	ADP
ajtas-1767	40	2	the	the	DET
ajtas-1767	40	3	introduction	introduction	NOUN
ajtas-1767	40	4	of	of	ADP
ajtas-1767	40	5	lebeg	lebeg	ADJ
ajtas-1767	40	6	intephaly	intephaly	NOUN
ajtas-1767	40	7	,	,	PUNCT
ajtas-1767	40	8	the	the	DET
ajtas-1767	40	9	current	current	ADJ
ajtas-1767	40	10	rigorous	rigorous	ADJ
ajtas-1767	40	11	theory	theory	NOUN
ajtas-1767	40	12	of	of	ADP
ajtas-1767	40	13	trigonometric	trigonometric	ADJ
ajtas-1767	40	14	functions	function	NOUN
ajtas-1767	40	15	was	be	AUX
ajtas-1767	40	16	created	create	VERB
ajtas-1767	40	17	.	.	PUNCT
ajtas-1767	41	1	trigonometric	trigonometric	ADJ
ajtas-1767	41	2	identities	identity	NOUN
ajtas-1767	41	3	are	be	AUX
ajtas-1767	41	4	relevant	relevant	ADJ
ajtas-1767	41	5	for	for	ADP
ajtas-1767	41	6	all	all	DET
ajtas-1767	41	7	values	value	NOUN
ajtas-1767	41	8	corresponding	correspond	VERB
ajtas-1767	41	9	to	to	ADP
ajtas-1767	41	10	the	the	DET
ajtas-1767	41	11	angle	angle	NOUN
ajtas-1767	41	12	α	α	NOUN
ajtas-1767	41	13	of	of	ADP
ajtas-1767	41	14	trigonometric	trigonometric	ADJ
ajtas-1767	41	15	equality	equality	NOUN
ajtas-1767	41	16	,	,	PUNCT
ajtas-1767	41	17	that	that	ADV
ajtas-1767	41	18	is	is	ADV
ajtas-1767	41	19	,	,	PUNCT
ajtas-1767	41	20	the	the	DET
ajtas-1767	41	21	basic	basic	ADJ
ajtas-1767	41	22	branch	branch	NOUN
ajtas-1767	41	23	of	of	ADP
ajtas-1767	41	24	trigonometry	trigonometry	NOUN
ajtas-1767	41	25	,	,	PUNCT
ajtas-1767	41	26	where	where	SCONJ
ajtas-1767	41	27	the	the	DET
ajtas-1767	41	28	left	left	NOUN
ajtas-1767	41	29	and	and	CCONJ
ajtas-1767	41	30	right	right	ADJ
ajtas-1767	41	31	part	part	NOUN
ajtas-1767	41	32	have	have	VERB
ajtas-1767	41	33	equal	equal	ADJ
ajtas-1767	41	34	meanings	meaning	NOUN
ajtas-1767	41	35	.	.	PUNCT
ajtas-1767	42	1	equalities	equality	NOUN
ajtas-1767	42	2	that	that	PRON
ajtas-1767	42	3	are	be	AUX
ajtas-1767	42	4	appropriate	appropriate	ADJ
ajtas-1767	42	5	for	for	ADP
ajtas-1767	42	6	all	all	DET
ajtas-1767	42	7	possible	possible	ADJ
ajtas-1767	42	8	values	value	NOUN
ajtas-1767	42	9	of	of	ADP
ajtas-1767	42	10	the	the	DET
ajtas-1767	42	11	letters	letter	NOUN
ajtas-1767	42	12	included	include	VERB
ajtas-1767	42	13	in	in	ADP
ajtas-1767	42	14	it	it	PRON
ajtas-1767	42	15	,	,	PUNCT
ajtas-1767	42	16	that	that	ADV
ajtas-1767	42	17	is	is	ADV
ajtas-1767	42	18	,	,	PUNCT
ajtas-1767	42	19	those	those	PRON
ajtas-1767	42	20	that	that	PRON
ajtas-1767	42	21	are	be	AUX
ajtas-1767	42	22	correct	correct	ADJ
ajtas-1767	42	23	for	for	ADP
ajtas-1767	42	24	all	all	DET
ajtas-1767	42	25	values	value	NOUN
ajtas-1767	42	26	of	of	ADP
ajtas-1767	42	27	its	its	PRON
ajtas-1767	42	28	left	left	ADJ
ajtas-1767	42	29	and	and	CCONJ
ajtas-1767	42	30	right	right	ADJ
ajtas-1767	42	31	parts	part	NOUN
ajtas-1767	42	32	that	that	PRON
ajtas-1767	42	33	make	make	VERB
ajtas-1767	42	34	sense	sense	NOUN
ajtas-1767	42	35	,	,	PUNCT
ajtas-1767	42	36	are	be	AUX
ajtas-1767	42	37	called	call	VERB
ajtas-1767	42	38	equalities	equality	NOUN
ajtas-1767	42	39	,	,	PUNCT
ajtas-1767	42	40	issues	issue	NOUN
ajtas-1767	42	41	related	relate	VERB
ajtas-1767	42	42	to	to	ADP
ajtas-1767	42	43	the	the	DET
ajtas-1767	42	44	proof	proof	NOUN
ajtas-1767	42	45	of	of	ADP
ajtas-1767	42	46	such	such	ADJ
ajtas-1767	42	47	equalities	equality	NOUN
ajtas-1767	42	48	are	be	AUX
ajtas-1767	42	49	called	call	VERB
ajtas-1767	42	50	questions	question	NOUN
ajtas-1767	42	51	related	relate	VERB
ajtas-1767	42	52	to	to	ADP
ajtas-1767	42	53	the	the	DET
ajtas-1767	42	54	proof	proof	NOUN
ajtas-1767	42	55	of	of	ADP
ajtas-1767	42	56	identities	identity	NOUN
ajtas-1767	42	57	.	.	PUNCT
ajtas-1767	43	1	in	in	ADP
ajtas-1767	43	2	today	today	NOUN
ajtas-1767	43	3	's	's	PART
ajtas-1767	43	4	lesson	lesson	NOUN
ajtas-1767	43	5	,	,	PUNCT
ajtas-1767	43	6	we	we	PRON
ajtas-1767	43	7	will	will	AUX
ajtas-1767	43	8	learn	learn	VERB
ajtas-1767	43	9	to	to	PART
ajtas-1767	43	10	prove	prove	VERB
ajtas-1767	43	11	trigonometric	trigonometric	ADJ
ajtas-1767	43	12	identities	identity	NOUN
ajtas-1767	43	13	.	.	PUNCT
ajtas-1767	44	1	there	there	PRON
ajtas-1767	44	2	are	be	VERB
ajtas-1767	44	3	4	4	NUM
ajtas-1767	44	4	main	main	ADJ
ajtas-1767	44	5	ways	way	NOUN
ajtas-1767	44	6	to	to	PART
ajtas-1767	44	7	prove	prove	VERB
ajtas-1767	44	8	trigonometric	trigonometric	ADJ
ajtas-1767	44	9	identities	identity	NOUN
ajtas-1767	44	10	:	:	PUNCT
ajtas-1767	44	11	method	method	NOUN
ajtas-1767	44	12	1	1	NUM
ajtas-1767	44	13	.	.	PUNCT
ajtas-1767	44	14	to	to	PART
ajtas-1767	44	15	show	show	VERB
ajtas-1767	44	16	that	that	SCONJ
ajtas-1767	44	17	in	in	ADP
ajtas-1767	44	18	the	the	DET
ajtas-1767	44	19	left	left	ADJ
ajtas-1767	44	20	part	part	NOUN
ajtas-1767	44	21	of	of	ADP
ajtas-1767	44	22	the	the	DET
ajtas-1767	44	23	mirror	mirror	NOUN
ajtas-1767	44	24	the	the	DET
ajtas-1767	44	25	mirror	mirror	NOUN
ajtas-1767	44	26	form	form	NOUN
ajtas-1767	44	27	is	be	AUX
ajtas-1767	44	28	equal	equal	ADJ
ajtas-1767	44	29	to	to	ADP
ajtas-1767	44	30	the	the	DET
ajtas-1767	44	31	right	right	ADJ
ajtas-1767	44	32	part	part	NOUN
ajtas-1767	44	33	of	of	ADP
ajtas-1767	44	34	it	it	PRON
ajtas-1767	44	35	,	,	PUNCT
ajtas-1767	44	36	performing	perform	VERB
ajtas-1767	44	37	substitutions	substitution	NOUN
ajtas-1767	44	38	.	.	PUNCT
ajtas-1767	45	1	method	method	NOUN
ajtas-1767	45	2	2	2	NUM
ajtas-1767	45	3	.	.	PUNCT
ajtas-1767	46	1	in	in	ADP
ajtas-1767	46	2	the	the	DET
ajtas-1767	46	3	right	right	ADJ
ajtas-1767	46	4	part	part	NOUN
ajtas-1767	46	5	of	of	ADP
ajtas-1767	46	6	the	the	DET
ajtas-1767	46	7	mirror	mirror	NOUN
ajtas-1767	46	8	,	,	PUNCT
ajtas-1767	46	9	the	the	DET
ajtas-1767	46	10	mirror	mirror	NOUN
ajtas-1767	46	11	figure	figure	NOUN
ajtas-1767	46	12	performs	perform	VERB
ajtas-1767	46	13	substitutions	substitution	NOUN
ajtas-1767	46	14	to	to	PART
ajtas-1767	46	15	show	show	VERB
ajtas-1767	46	16	that	that	SCONJ
ajtas-1767	46	17	it	it	PRON
ajtas-1767	46	18	is	be	AUX
ajtas-1767	46	19	equal	equal	ADJ
ajtas-1767	46	20	to	to	ADP
ajtas-1767	46	21	the	the	DET
ajtas-1767	46	22	left	left	ADJ
ajtas-1767	46	23	part	part	NOUN
ajtas-1767	46	24	.	.	PUNCT
ajtas-1767	47	1	method	method	PROPN
ajtas-1767	47	2	3	3	NUM
ajtas-1767	47	3	.	.	PUNCT
ajtas-1767	47	4	to	to	PART
ajtas-1767	47	5	show	show	VERB
ajtas-1767	47	6	that	that	SCONJ
ajtas-1767	47	7	the	the	DET
ajtas-1767	47	8	subtraction	subtraction	NOUN
ajtas-1767	47	9	of	of	ADP
ajtas-1767	47	10	the	the	DET
ajtas-1767	47	11	left	left	ADJ
ajtas-1767	47	12	and	and	CCONJ
ajtas-1767	47	13	right	right	ADJ
ajtas-1767	47	14	parts	part	NOUN
ajtas-1767	47	15	of	of	ADP
ajtas-1767	47	16	the	the	DET
ajtas-1767	47	17	mirror	mirror	NOUN
ajtas-1767	47	18	is	be	AUX
ajtas-1767	47	19	zero	zero	NUM
ajtas-1767	47	20	.	.	PUNCT
ajtas-1767	48	1	american	american	ADJ
ajtas-1767	48	2	journal	journal	PROPN
ajtas-1767	48	3	of	of	ADP
ajtas-1767	48	4	technology	technology	NOUN
ajtas-1767	48	5	and	and	CCONJ
ajtas-1767	48	6	applied	apply	VERB
ajtas-1767	48	7	sciences	science	NOUN
ajtas-1767	48	8	volume	volume	NOUN
ajtas-1767	48	9	20	20	NUM
ajtas-1767	48	10	,	,	PUNCT
ajtas-1767	48	11	january	january	PROPN
ajtas-1767	48	12	2024	2024	NUM
ajtas-1767	48	13	p	p	NOUN
ajtas-1767	48	14	a	a	PRON
ajtas-1767	48	15	g	g	NOUN
ajtas-1767	48	16	e	e	NOUN
ajtas-1767	48	17	|	|	ADV
ajtas-1767	48	18	54	54	NUM
ajtas-1767	48	19	www.americanjournal.org	www.americanjournal.org	NOUN
ajtas-1767	48	20	method	method	NOUN
ajtas-1767	48	21	4	4	NUM
ajtas-1767	48	22	.	.	PUNCT
ajtas-1767	48	23	to	to	PART
ajtas-1767	48	24	make	make	VERB
ajtas-1767	48	25	changes	change	NOUN
ajtas-1767	48	26	of	of	ADP
ajtas-1767	48	27	the	the	DET
ajtas-1767	48	28	same	same	ADJ
ajtas-1767	48	29	shape	shape	NOUN
ajtas-1767	48	30	in	in	ADP
ajtas-1767	48	31	the	the	DET
ajtas-1767	48	32	left	left	ADJ
ajtas-1767	48	33	and	and	CCONJ
ajtas-1767	48	34	right	right	ADJ
ajtas-1767	48	35	parts	part	NOUN
ajtas-1767	48	36	of	of	ADP
ajtas-1767	48	37	the	the	DET
ajtas-1767	48	38	mirror	mirror	NOUN
ajtas-1767	48	39	and	and	CCONJ
ajtas-1767	48	40	to	to	PART
ajtas-1767	48	41	express	express	VERB
ajtas-1767	48	42	them	they	PRON
ajtas-1767	48	43	the	the	DET
ajtas-1767	48	44	same	same	ADJ
ajtas-1767	48	45	.	.	PUNCT
ajtas-1767	49	1	the	the	DET
ajtas-1767	49	2	law	law	NOUN
ajtas-1767	49	3	of	of	ADP
ajtas-1767	49	4	berunius	berunius	PROPN
ajtas-1767	49	5	is	be	AUX
ajtas-1767	49	6	given	give	VERB
ajtas-1767	49	7	in	in	ADP
ajtas-1767	49	8	the	the	DET
ajtas-1767	49	9	work	work	NOUN
ajtas-1767	49	10	"	"	PUNCT
ajtas-1767	49	11	the	the	DET
ajtas-1767	49	12	table	table	NOUN
ajtas-1767	49	13	of	of	ADP
ajtas-1767	49	14	sines	sine	NOUN
ajtas-1767	49	15	with	with	ADP
ajtas-1767	49	16	an	an	DET
ajtas-1767	49	17	interval	interval	NOUN
ajtas-1767	49	18	of	of	ADP
ajtas-1767	49	19	15	15	NUM
ajtas-1767	49	20	minutes	minute	NOUN
ajtas-1767	49	21	,	,	PUNCT
ajtas-1767	49	22	the	the	DET
ajtas-1767	49	23	table	table	NOUN
ajtas-1767	49	24	of	of	ADP
ajtas-1767	49	25	tangents	tangent	NOUN
ajtas-1767	49	26	with	with	ADP
ajtas-1767	49	27	an	an	DET
ajtas-1767	49	28	interval	interval	NOUN
ajtas-1767	49	29	of	of	ADP
ajtas-1767	49	30	1	1	NUM
ajtas-1767	49	31	°	°	NOUN
ajtas-1767	49	32	with	with	ADP
ajtas-1767	49	33	an	an	DET
ajtas-1767	49	34	accuracy	accuracy	NOUN
ajtas-1767	49	35	of	of	ADP
ajtas-1767	49	36	up	up	ADP
ajtas-1767	49	37	to	to	PART
ajtas-1767	49	38	10	10	NUM
ajtas-1767	49	39	-8	-8	NOUN
ajtas-1767	49	40	.	.	PUNCT
ajtas-1767	50	1	in	in	ADP
ajtas-1767	50	2	this	this	DET
ajtas-1767	50	3	case	case	NOUN
ajtas-1767	50	4	,	,	PUNCT
ajtas-1767	50	5	the	the	DET
ajtas-1767	50	6	table	table	NOUN
ajtas-1767	50	7	of	of	ADP
ajtas-1767	50	8	sines	sine	NOUN
ajtas-1767	50	9	is	be	AUX
ajtas-1767	50	10	given	give	VERB
ajtas-1767	50	11	with	with	ADP
ajtas-1767	50	12	an	an	DET
ajtas-1767	50	13	interval	interval	NOUN
ajtas-1767	50	14	of	of	ADP
ajtas-1767	50	15	1	1	NUM
ajtas-1767	50	16	minute	minute	NOUN
ajtas-1767	50	17	,	,	PUNCT
ajtas-1767	50	18	the	the	DET
ajtas-1767	50	19	table	table	NOUN
ajtas-1767	50	20	of	of	ADP
ajtas-1767	50	21	tangents	tangent	NOUN
ajtas-1767	50	22	is	be	AUX
ajtas-1767	50	23	given	give	VERB
ajtas-1767	50	24	with	with	ADP
ajtas-1767	50	25	an	an	DET
ajtas-1767	50	26	interval	interval	NOUN
ajtas-1767	50	27	of	of	ADP
ajtas-1767	50	28	1	1	NUM
ajtas-1767	50	29	minute	minute	NOUN
ajtas-1767	50	30	from	from	ADP
ajtas-1767	50	31	0	0	NUM
ajtas-1767	50	32	°	°	NOUN
ajtas-1767	50	33	to	to	ADP
ajtas-1767	50	34	45	45	NUM
ajtas-1767	50	35	°	°	NOUN
ajtas-1767	50	36	,	,	PUNCT
ajtas-1767	50	37	and	and	CCONJ
ajtas-1767	50	38	the	the	DET
ajtas-1767	50	39	interval	interval	NOUN
ajtas-1767	50	40	from	from	ADP
ajtas-1767	50	41	46	46	NUM
ajtas-1767	50	42	°	°	NOUN
ajtas-1767	50	43	to	to	ADP
ajtas-1767	50	44	90	90	NUM
ajtas-1767	50	45	°	°	NOUN
ajtas-1767	50	46	is	be	AUX
ajtas-1767	50	47	given	give	VERB
ajtas-1767	50	48	with	with	ADP
ajtas-1767	50	49	an	an	DET
ajtas-1767	50	50	accuracy	accuracy	NOUN
ajtas-1767	50	51	of	of	ADP
ajtas-1767	50	52	up	up	ADP
ajtas-1767	50	53	to	to	PART
ajtas-1767	50	54	5	5	NUM
ajtas-1767	50	55	minutes	minute	NOUN
ajtas-1767	50	56	bi	bi	PROPN
ajtas-1767	50	57	lan	lan	PROPN
ajtas-1767	50	58	10	10	NUM
ajtas-1767	50	59	-10	-10	X
ajtas-1767	50	60	.	.	PUNCT
ajtas-1767	51	1	ghiyosiddin	ghiyosiddin	VERB
ajtas-1767	51	2	jamshid	jamshid	PROPN
ajtas-1767	51	3	al	al	PROPN
ajtas-1767	51	4	-	-	PUNCT
ajtas-1767	51	5	koshiy	koshiy	PROPN
ajtas-1767	51	6	,	,	PUNCT
ajtas-1767	51	7	,	,	PUNCT
ajtas-1767	51	8	in	in	ADP
ajtas-1767	51	9	his	his	PRON
ajtas-1767	51	10	ri	ri	PROPN
ajtas-1767	51	11	sola	sola	NOUN
ajtas-1767	51	12	on	on	ADP
ajtas-1767	51	13	watar	watar	NOUN
ajtas-1767	51	14	and	and	CCONJ
ajtas-1767	51	15	sinus	sinu	NOUN
ajtas-1767	51	16	,	,	PUNCT
ajtas-1767	51	17	calculates	calculate	VERB
ajtas-1767	51	18	sin1	sin1	PROPN
ajtas-1767	51	19	°	°	PROPN
ajtas-1767	51	20	after	after	ADP
ajtas-1767	51	21	commas	comma	NOUN
ajtas-1767	51	22	at	at	ADP
ajtas-1767	51	23	17	17	NUM
ajtas-1767	51	24	room	room	NOUN
ajtas-1767	51	25	resolution	resolution	NOUN
ajtas-1767	51	26	:	:	PUNCT
ajtas-1767	51	27	sin1	sin1	PROPN
ajtas-1767	51	28	°	°	PROPN
ajtas-1767	52	1	=	=	PUNCT
ajtas-1767	52	2	0,017452406437283512	0,017452406437283512	PROPN
ajtas-1767	52	3	...	...	PUNCT
ajtas-1767	52	4	in	in	ADP
ajtas-1767	52	5	the	the	DET
ajtas-1767	52	6	course	course	NOUN
ajtas-1767	52	7	of	of	ADP
ajtas-1767	52	8	geometry	geometry	NOUN
ajtas-1767	52	9	,	,	PUNCT
ajtas-1767	52	10	the	the	DET
ajtas-1767	52	11	sine	sine	NOUN
ajtas-1767	52	12	,	,	PUNCT
ajtas-1767	52	13	cosine	cosine	NOUN
ajtas-1767	52	14	,	,	PUNCT
ajtas-1767	52	15	and	and	CCONJ
ajtas-1767	52	16	of	of	ADP
ajtas-1767	52	17	the	the	DET
ajtas-1767	52	18	angle	angle	NOUN
ajtas-1767	52	19	represented	represent	VERB
ajtas-1767	52	20	by	by	ADP
ajtas-1767	52	21	the	the	DET
ajtas-1767	52	22	degree	degree	NOUN
ajtas-1767	52	23	tangency	tangency	NOUN
ajtas-1767	52	24	is	be	AUX
ajtas-1767	52	25	included.the	included.the	DET
ajtas-1767	52	26	sine	sine	NOUN
ajtas-1767	52	27	and	and	CCONJ
ajtas-1767	52	28	cosine	cosine	NOUN
ajtas-1767	52	29	of	of	ADP
ajtas-1767	52	30	an	an	DET
ajtas-1767	52	31	arbitrary	arbitrary	ADJ
ajtas-1767	52	32	angle	angle	NOUN
ajtas-1767	52	33	are	be	AUX
ajtas-1767	52	34	defined	define	VERB
ajtas-1767	52	35	as	as	ADP
ajtas-1767	52	36	:	:	PUNCT
ajtas-1767	52	37	α	α	PROPN
ajtas-1767	52	38	is	be	AUX
ajtas-1767	52	39	said	say	VERB
ajtas-1767	52	40	to	to	PART
ajtas-1767	52	41	be	be	AUX
ajtas-1767	52	42	the	the	DET
ajtas-1767	52	43	sine	sine	NOUN
ajtas-1767	52	44	of	of	ADP
ajtas-1767	52	45	an	an	DET
ajtas-1767	52	46	angle	angle	NOUN
ajtas-1767	52	47	(	(	PUNCT
ajtas-1767	52	48	1;0	1;0	NUM
ajtas-1767	52	49	)	)	PUNCT
ajtas-1767	52	50	to	to	ADP
ajtas-1767	52	51	the	the	DET
ajtas-1767	52	52	ordinate	ordinate	NOUN
ajtas-1767	52	53	of	of	ADP
ajtas-1767	52	54	the	the	DET
ajtas-1767	52	55	point	point	NOUN
ajtas-1767	52	56	formed	form	VERB
ajtas-1767	52	57	by	by	ADP
ajtas-1767	52	58	tilting	tilt	VERB
ajtas-1767	52	59	the	the	DET
ajtas-1767	52	60	point	point	NOUN
ajtas-1767	52	61	to	to	ADP
ajtas-1767	52	62	an	an	DET
ajtas-1767	52	63	α	α	NOUN
ajtas-1767	52	64	angle	angle	NOUN
ajtas-1767	52	65	around	around	ADP
ajtas-1767	52	66	the	the	DET
ajtas-1767	52	67	head	head	NOUN
ajtas-1767	52	68	of	of	ADP
ajtas-1767	52	69	coordinates	coordinate	NOUN
ajtas-1767	52	70	,	,	PUNCT
ajtas-1767	52	71	and	and	CCONJ
ajtas-1767	52	72	is	be	AUX
ajtas-1767	52	73	defined	define	VERB
ajtas-1767	52	74	in	in	ADP
ajtas-1767	52	75	sina	sina	PROPN
ajtas-1767	52	76	style	style	PROPN
ajtas-1767	52	77	.	.	PUNCT
ajtas-1767	53	1	the	the	DET
ajtas-1767	53	2	cosine	cosine	NOUN
ajtas-1767	53	3	of	of	ADP
ajtas-1767	53	4	angle	angle	NOUN
ajtas-1767	53	5	α	α	PROPN
ajtas-1767	53	6	is	be	AUX
ajtas-1767	53	7	said	say	VERB
ajtas-1767	53	8	to	to	PART
ajtas-1767	53	9	be	be	AUX
ajtas-1767	53	10	the	the	DET
ajtas-1767	53	11	abscissa	abscissa	NOUN
ajtas-1767	53	12	of	of	ADP
ajtas-1767	53	13	the	the	DET
ajtas-1767	53	14	point	point	NOUN
ajtas-1767	53	15	formed	form	VERB
ajtas-1767	53	16	by	by	ADP
ajtas-1767	53	17	tilting	tilt	VERB
ajtas-1767	53	18	the	the	DET
ajtas-1767	53	19	point	point	NOUN
ajtas-1767	53	20	(	(	PUNCT
ajtas-1767	53	21	0;1	0;1	NOUN
ajtas-1767	53	22	)	)	PUNCT
ajtas-1767	53	23	to	to	PART
ajtas-1767	53	24	angle	angle	VERB
ajtas-1767	53	25	α	α	NOUN
ajtas-1767	53	26	around	around	ADP
ajtas-1767	53	27	the	the	DET
ajtas-1767	53	28	head	head	NOUN
ajtas-1767	53	29	of	of	ADP
ajtas-1767	53	30	coordinates	coordinate	NOUN
ajtas-1767	53	31	is	be	AUX
ajtas-1767	53	32	cosa	cosa	NOUN
ajtas-1767	53	33	-	-	PUNCT
ajtas-1767	53	34	style	style	NOUN
ajtas-1767	53	35	defined	define	VERB
ajtas-1767	53	36	.	.	PUNCT
ajtas-1767	54	1	α	α	PROPN
ajtas-1767	54	2	is	be	AUX
ajtas-1767	54	3	said	say	VERB
ajtas-1767	54	4	to	to	PART
ajtas-1767	54	5	be	be	AUX
ajtas-1767	54	6	the	the	DET
ajtas-1767	54	7	tangent	tangent	NOUN
ajtas-1767	54	8	of	of	ADP
ajtas-1767	54	9	the	the	DET
ajtas-1767	54	10	angle	angle	NOUN
ajtas-1767	54	11	α	α	X
ajtas-1767	54	12	to	to	ADP
ajtas-1767	54	13	the	the	DET
ajtas-1767	54	14	ratio	ratio	NOUN
ajtas-1767	54	15	of	of	ADP
ajtas-1767	54	16	the	the	DET
ajtas-1767	54	17	sine	sine	NOUN
ajtas-1767	54	18	of	of	ADP
ajtas-1767	54	19	the	the	DET
ajtas-1767	54	20	angle	angle	NOUN
ajtas-1767	54	21	to	to	ADP
ajtas-1767	54	22	its	its	PRON
ajtas-1767	54	23	cosine	cosine	NOUN
ajtas-1767	54	24	,	,	PUNCT
ajtas-1767	54	25	and	and	CCONJ
ajtas-1767	54	26	is	be	AUX
ajtas-1767	54	27	defined	define	VERB
ajtas-1767	54	28	as	as	ADP
ajtas-1767	54	29	tga	tga	PROPN
ajtas-1767	54	30	.	.	PUNCT
ajtas-1767	55	1	literature	literature	PROPN
ajtas-1767	55	2	used	use	VERB
ajtas-1767	55	3	1	1	NUM
ajtas-1767	55	4	.	.	PUNCT
ajtas-1767	56	1	sh.a.alimov	sh.a.alimov	PROPN
ajtas-1767	56	2	,	,	PUNCT
ajtas-1767	56	3	a.r.halmukhamedov	a.r.halmukhamedov	NOUN
ajtas-1767	56	4	,	,	PUNCT
ajtas-1767	56	5	m.a.mirzakhmedov.algebra.4th	m.a.mirzakhmedov.algebra.4th	NOUN
ajtas-1767	56	6	edition.tashkent	edition.tashkent	ADJ
ajtas-1767	56	7	:	:	PUNCT
ajtas-1767	56	8	"	"	PUNCT
ajtas-1767	56	9	teacher	teacher	NOUN
ajtas-1767	56	10	"	"	PUNCT
ajtas-1767	56	11	nmiu	nmiu	NOUN
ajtas-1767	56	12	,	,	PUNCT
ajtas-1767	56	13	20	20	NUM
ajtas-1767	56	14	fundamentals	fundamental	NOUN
ajtas-1767	56	15	of	of	ADP
ajtas-1767	56	16	algebra	algebra	NOUN
ajtas-1767	56	17	and	and	CCONJ
ajtas-1767	56	18	mathematics	mathematic	NOUN
ajtas-1767	56	19	analysis	analysis	NOUN
ajtas-1767	56	20	"	"	PUNCT
ajtas-1767	56	21	200619	200619	NUM
ajtas-1767	56	22	.	.	PUNCT
ajtas-1767	57	1	2	2	X
ajtas-1767	57	2	.	.	X
ajtas-1767	57	3	nasritdinov	nasritdinov	PROPN
ajtas-1767	57	4	g'.n	g'.n	PROPN
ajtas-1767	57	5	.	.	PUNCT
ajtas-1767	57	6	,	,	PUNCT
ajtas-1767	57	7	mirzaahmedov	mirzaahmedov	PROPN
ajtas-1767	58	1	m.a	m.a	PROPN
ajtas-1767	58	2	.	.	PROPN
ajtas-1767	58	3	,	,	PUNCT
ajtas-1767	58	4	usmanov	usmanov	PROPN
ajtas-1767	58	5	f.r	f.r	PROPN
ajtas-1767	58	6	.	.	PROPN
ajtas-1767	58	7	,	,	PUNCT
ajtas-1767	58	8	aripova	aripova	PROPN
ajtas-1767	58	9	sh.r	sh.r	PROPN
ajtas-1767	58	10	.	.	PUNCT
ajtas-1767	59	1	algebra	algebra	NOUN
ajtas-1767	59	2	.	.	PUNCT
ajtas-1767	60	1	t.	t.	NOUN
ajtas-1767	60	2	:	:	PUNCT
ajtas-1767	61	1	"	"	PUNCT
ajtas-1767	61	2	publishing	publish	VERB
ajtas-1767	61	3	house	house	NOUN
ajtas-1767	61	4	named	name	VERB
ajtas-1767	61	5	after	after	ADP
ajtas-1767	61	6	ghafurgulam	ghafurgulam	NOUN
ajtas-1767	61	7	-	-	PUNCT
ajtas-1767	61	8	creative	creative	ADJ
ajtas-1767	61	9	house	house	NOUN
ajtas-1767	61	10	of	of	ADP
ajtas-1767	61	11	printing	printing	NOUN
ajtas-1767	61	12	"	"	PUNCT
ajtas-1767	61	13	,	,	PUNCT
ajtas-1767	61	14	2012	2012	NUM
ajtas-1767	61	15	.	.	PUNCT
ajtas-1767	62	1	3	3	X
ajtas-1767	62	2	.	.	X
ajtas-1767	62	3	alikhanov	alikhanov	PROPN
ajtas-1767	62	4	s.	s.	PROPN
ajtas-1767	62	5	methodology	methodology	PROPN
ajtas-1767	62	6	of	of	ADP
ajtas-1767	62	7	teaching	teach	VERB
ajtas-1767	62	8	mathematics	mathematic	NOUN
ajtas-1767	62	9	.	.	PUNCT
ajtas-1767	63	1	t.	t.	NOUN
ajtas-1767	63	2	:	:	PUNCT
ajtas-1767	63	3	"	"	PUNCT
ajtas-1767	63	4	teacher	teacher	NOUN
ajtas-1767	63	5	"	"	PUNCT
ajtas-1767	63	6	,	,	PUNCT
ajtas-1767	63	7	2008	2008	NUM
ajtas-1767	63	8	.	.	PUNCT