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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.

  • 35 Questions around this concept.

Solve by difficulty

QuestionEASY

The largest interval lying in \left ( \frac{-\pi }{2} ,\frac{\pi }{2}\right ) for which the function,

f\left ( x \right )= 4^{-x^{2}}+\cos ^{-1}\left ( \frac{x}{2} -1\right )+\log \left ( \cos x \right ), is defined, is

View Solution

Let f:\left ( -1,1 \right )\rightarrow B, be a function defined by f\left ( x \right )= \tan ^{-1}\left ( \frac{2x}{1-x^{2}} \right )

then f is both one­-one and onto when B is the interval

View Solution

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 y = sin(x) 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 = 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)

Study other Related Concepts

Domain and Range of Trigonometric Functions Current Topic

Measuring Angles
Trigonometric Ratios
Trigonometric Identities
Sign of Trigonometric Functions
Graphs of General Trigonometric Functions
Trigonometric Ratios of Allied Angles
Trigonometric Ratios of Compound Angles
Sum-to-Product and Product-to-Sum Formulas
Product To Sum Formulas
Double Angle Formulas

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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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