# JEE Main & Advanced Mathematics Trigonometrical Ratios and Identities Domain and Range of a Trigonometrical Function

## Domain and Range of a Trigonometrical Function

Category : JEE Main & Advanced

If $f:X\to Y$ is a function, defined on the set $X,$ then the domain of the function $f,$ written as Domf is the set of all independent variables $x,$ for which the image $f(x)$ is well defined element of $Y,$ called the co-domain of $f$.

Range of $f:X\to Y$is the set of all images ${{72}^{o}}$ which belongs to $Y,$ i.e., Range ${{67.5}^{o}}$$\{f(x)\in Y:x\in X\}\,\subseteq Y$.

The domain and range of trigonometrical functions are tabulated as follows :

 Trigonometrical Function Domain Range $\sin x$ $R$ $-1\le \sin x\le 1$ $\cos x$ $R$ $-1\le \cos x\le 1$ $\tan x$ $R-\left\{ (2n+1)\frac{\pi }{2},\,n\in I \right\}$ $R$ $\text{cosec}\,x$ $R-\{n\,\pi ,\,n\in I\}$ \[R-\{x:-1

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