Question

if y= sin-1x then x belongs to the interval​

Answer 1

Given :   y  = Sin⁻¹x

To Find : the interval​ x belongs to

Solution:

y  = Sin⁻¹x

Taking sin both sides

=> sin y = Sin (Sin⁻¹x )

=> Sin y  =  x

=> x = Sin y

-1 ≤  Sin y ≤ 1

=>  -1 ≤  x ≤ 1

Hence x ∈ [-1 , 1]

x ∈ [-1 , 1]

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Answer 2

SOLUTION

COMPLETE QUESTION

TO CHOOSE THE CORRECT OPTION

$\sf{If \: \: y = { \sin}^{ - 1}x }$

then x belongs to the interval

(a)(0,π)

(b) (-1,1)

(c) [-1,1]

(d) [0,π]

EVALUATION

Here it is given that

$\sf{y = { \sin}^{ - 1}x }$

$\sf{ \implies x = \sin y}$

$\sf{Now \: \: - 1 \leqslant \sin y \leqslant 1}$

$\sf{ \implies \: - 1 \leqslant x \leqslant 1}$

$\sf{ \implies x \in [ \: - 1 \: , \: 1 \: ] }$

FINAL ANSWER

The correct option is (c) [ -1 , 1 ]

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