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 |
| \[\sin x\] | \[R\] | \[-1\le \sin x\le 1\] |
| \[\cos x\] | \[R\] | \[-1\le \cos x\le 1\] |
| \[\tan x\] | \[R-\left\{ (2n+1)\frac{\pi }{2},\,n\in I \right\}\] | \[R\] |
| \[\text{cosec}\,x\] | \[R-\{n\,\pi ,\,n\in I\}\] | \[R-\{x:-1<x<1\}\] |
| \[\sec x\] | \[R-\left\{ (2n+1)\,\frac{\pi }{2},\,n\in I \right\}\] | \[R-\{x\,:\,-1<x<1\}\] |
| \[\cot x\] | \[R-\{n\,\pi ,\,n\in I\}\] | \[R\] |
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