**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 |

\[\sin x\] | \[R\] | \[-1\le \sin x\le 1\] |

\[\cos x\] | \[R\] | \[-1\le \cos x\le 1\] |

\[\tan x\] | \[R-\left\{ (2n+1)\frac{\pi }{2},\,n\in I \right\}\] | \[R\] |

\[\text{cosec}\,x\] | \[R-\{n\,\pi ,\,n\in I\}\] | \[R-\{x:-1<x<1\}\] |

\[\sec x\] | \[R-\left\{ (2n+1)\,\frac{\pi }{2},\,n\in I \right\}\] | \[R-\{x\,:\,-1<x<1\}\] |

\[\cot x\] | \[R-\{n\,\pi ,\,n\in I\}\] | \[R\] |

*play_arrow*Introduction*play_arrow*System of Measurement of Angles*play_arrow*Relation Between Three Systems of Measurement of an Angle*play_arrow*Relation Between an arc and an Angle*play_arrow*Domain and Range of a Trigonometrical Function*play_arrow*Trigonometrical Ratios or Functions*play_arrow*Trigonometrical Ratios of Allied Angles*play_arrow*Trigonometrical Ratios for Various Angles*play_arrow*Trigonometrical Ratios for Some Special Angles*play_arrow*Trigonometrical Ratios In Terms of Each Other*play_arrow*Formulae to Rransform The Product Into Sum or Difference*play_arrow*Trigonometric Ratio of Multiple of an Angle*play_arrow*Trigonometric Ratio of Sub-multiple of an Angle*play_arrow*Maximum and Minimum Value of a \[\mathbf{cos}\,\,\mathbf{\theta }\,\,\mathbf{+}\,\mathbf{b}\,\,\mathbf{sin}\,\,\mathbf{\theta }\]*play_arrow*Conditional Trigonometrical Identities

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