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


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