id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6146	Khan, Sameen Ahmed; Kankarej, Manisha; Khan, Mohammad Nazrul Islam	Deducing Trigonometric Functions from Differential Equations: An Educational Perspective	2025	14	.pdf	application/pdf	5962	453	71	In this Section, we deduced the basic properties of the trigonometric functions, sinx and cosx starting with the second-order linear differential equation y′′ + y = 0, using the qualitative properties of differential equations (essentially the uniqueness of the solutions). If y = s(x), then y′ = c(x) and c2(x) + s2(x) = C. Using the initial conditions, s(0) = 0 and c(0) = 1, we have C = 1.	cache/ejpam-6146.pdf	txt/ejpam-6146.txt