TRIGONOMENTRY FUNCTIONS OF REALOR COMPLEX VARIABLES

Trigonometric functions of real or complex variables

Main article: Trigonometric function

Using the unit circle, one can extend the definitions of trigonometric ratios to all positive and negative arguments^[36] (see trigonometric function).

Graphs of trigonometric functions

The following table summarizes the properties of the graphs of the six main trigonometric functions:^[37][38]

Function	Period	Domain	Range	Graph
sine	${\displaystyle 2\pi }$	${\displaystyle (-\infty ,\infty )}$	${\displaystyle [-1,1]}$
cosine	${\displaystyle 2\pi }$	${\displaystyle (-\infty ,\infty )}$	${\displaystyle [-1,1]}$
tangent	${\displaystyle \pi }$	${\displaystyle x\neq \pi /2+n\pi }$	${\displaystyle (-\infty ,\infty )}$
secant	${\displaystyle 2\pi }$	${\displaystyle x\neq \pi /2+n\pi }$	${\displaystyle (-\infty ,-1]\cup [1,\infty )}$
cosecant	${\displaystyle 2\pi }$	${\displaystyle x\neq n\pi }$	${\displaystyle (-\infty ,-1]\cup [1,\infty )}$
cotangent	${\displaystyle \pi }$	${\displaystyle x\neq n\pi }$	${\displaystyle (-\infty ,\infty )}$