If ^ -1 x=y, then - Vidyadip

MCQ

If $\sin ^{-1} x=y,$ then

A
$-\frac{\pi}{2} < y < \frac{\pi}{2}$
B
$0 \leq \mathrm{y} \leq \pi$
✓
$-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$
D
$0 < y < \pi$

✓

Answer

Correct option: C.

$-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$

c
It is given that $\sin ^{-1} x=y$

We know that the range of the principal value branch of $\sin ^{-1}$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$

Therefore, $-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$

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