Question

range of an inverse trignometric function does not contain -pi/ 4. which function is that?


a) cos -1 x
b) sin -1 x
c) cosec -1 x
d) tan -1 x
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Answer 1

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Answer 2

Given : Inverse trigonometric functions

To Find :  range of which inverse trigonometric function does not contain -π/ 4

a) cos⁻¹x

b) sin⁻¹x

c) cosec⁻¹ x

d) tan⁻¹ x

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Solution:

a) cos⁻¹x

Domain is [- 1 , 1]

Principal Range is [0 , π]

This does not contain s -π/4

b) sin⁻¹x

Domain is [- 1 , 1]

Principal Range is [-π/2 , π/2]

This contains -π/4

c) cosec⁻¹x

Domain is   R  -  (- 1 , 1)

Principal Range is  [-π/2 , π/2] - { 0 }

This contains -π/4

b) tan ⁻¹x

Domain is [- ∞ , ∞]   or R

Principal Range is (-π/2 , π/2)

This contains -π/4

Hence range  cos⁻¹x  does not contain    -π/ 4

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