Limits Of Trigonometric Functions

Sine

${\lim }_{x\to \infty }\sin x=DNE$ ${\lim }_{x\to -\infty }\sin x=DNE$ ${\lim }_{x\to 0}\sin x=0$ ${\lim }_{x\to 0}\frac{\sin x}{x}=1$

Cos

${\lim }_{x\to \infty }\cos x=DNE$ ${\lim }_{x\to -\infty }\cos x=DNE$ ${\lim }_{x\to 0}\frac{1-\cos x}{x}=0$

Tan

${\lim }_{x\to \infty }\tan x=DNE$ ${\lim }_{x\to -\infty }\tan x=DNE$ ${\lim }_{x\to \infty }\arctan x=\frac{\pi }{2}$ ${\lim }_{x\to -\infty }\arctan x=-\frac{\pi }{2}$

Cosecant

${\lim }_{x\to \infty }\csc x=DNE$ ${\lim }_{x\to -\infty }\csc x=DNE$

Secant

${\lim }_{x\to \infty }\sec x=DNE$ ${\lim }_{x\to -\infty }\sec x=DNE$

Cotangent

${\lim }_{x\to \infty }\cot x=DNE$ ${\lim }_{x\to -\infty }\cot x=DNE$