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    Domain and Range of Trigonometric Functions - Practice Questions & MCQ

    Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

    Quick Facts

    • Domain and range of Inverse Trigonometric Function (Part 1) is considered one the most difficult concept.

    • 56 Questions around this concept.

    Solve by difficulty

    Let $f:(-1,1) \rightarrow B$, be a function defined by $f(x)=\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)$ then $f$ is both one-one and onto when $B$ is the interval

    What is the solution for $\tan ^{-1}x>\pi / 4$ ?

    Number of solutions of x where its satisfy $\left(\sin ^{-1} x\right)^2-2 \sin ^{-1} x+1 \leq 0$

    $-\tan ^{-1}\left(\frac{\pi}{3}\right)=$

    $\tan ^{-1}(-1)=$

    Which of the following functions as the below graph?

    The range of $\cos ^{-1}([x])$ is $\left(\left[\left.x\right|_{\text {represents Greatest Integer Function })}\right.\right.$

     

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    $Domain\, \, of \, \, \csc ^{-1}x\, \, is:$

    $Range \, of\, \sec^{-1}x\,\, is:$

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    Concepts Covered - 2

    Domain and range of Inverse Trigonometric Function (Part 1)

    Domain and range of Inverse Trigonometric Function (Part 1)

    $y=\sin ^{-1}(x)$

    The function is many one so it is not invertible. Now consider the small portion of the function

     $\mathrm{y=\sin x,\;x\in\left [ -\frac{\pi}{2},\frac{\pi}{2}\right ]\;\;and\;\;y\in[-1,1]}$

                 

    Which is strictly increasing, Hence, one-one and inverse is $y=\sin ^{-1}(x)$

    $\mathrm{Domain\;is\;[-1,1]\;\;and\;\;Range\;\;is\;\;\left [ \frac{-\pi}{2},\frac{\pi}{2} \right ]}$

    $y=\cos ^{-1}(x)$

    $\mathrm{Domain\;is\;[-1,1]\;\;and\;\;Range\;\;is\;\;\left [ 0,\pi\right ]}$

    $y=\tan ^{-1}(x)$

     

    $\mathrm{Domain\;is\;\mathbb{R}\;\;and\;\;Range\;\;is\;\;\left ( \frac{-\pi}{2},\frac{\pi}{2} \right )}$

    Domain and range of Inverse Trigonometric Function (Part 2)

    Domain and range of Inverse Trigonometric Function (Part 2)

    $y=\cot ^{-1}(x)$


     

    $\mathrm{Domain\;is\;\mathbb{R}\;\;and\;\;Range\;\;is\;\; ( 0,\pi)}$

    $y=\sec ^{-1}(x)$

    $\mathrm{Domain\;is\;\mathbb{R}-(-1,1)\;\;and\;\;Range\;\;is\;\;[0,\pi]-\left \{ \frac{\pi}{2} \right \}}$

    $y=\operatorname{cosec}^{-1}(x)$


     

    $\mathrm{Domain\;is\;\mathbb{R}-(-1,1)\;\;and\;\;Range\;\;is\;\;\left [- \frac{\pi}{2},\frac{\pi}{2} \right ]-\left \{ 0 \right \}}$

    Study it with Videos

    Domain and range of Inverse Trigonometric Function (Part 1)
    Domain and range of Inverse Trigonometric Function (Part 2)

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    Books

    Reference Books

    Domain and range of Inverse Trigonometric Function (Part 1)

    Mathematics for Joint Entrance Examination JEE (Advanced) : Trigonometry

    Page No. : 7.2

    Line : 10

    Domain and range of Inverse Trigonometric Function (Part 2)

    Mathematics for Joint Entrance Examination JEE (Advanced) : Trigonometry

    Page No. : 7.2

    Line : 11

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