The value of ^ -1 ( 33 5 ) is: - Vidyadip

MCQ

The value of $\sin^{-1}\Big(\cos\frac{33\pi}{5}\Big)$ is:

A
$\frac{33}{5}$
✓
$-\frac{\pi}{10}$
C
$\frac{\pi}{10}$
D
$\frac{7\pi}{5}$

✓

Answer

Correct option: B.

$-\frac{\pi}{10}$

$\sin^{-1}\Big(\cos\frac{33\pi}{5}\Big)$
$=\sin^{-1}\Big(\cos\Big(6\pi+\frac{3\pi}{5}\Big)\Big)$
$=\sin^{-1}\Big(\cos\Big(\frac{3\pi}{5}\Big)\Big)$
$=\sin^{-1}\Big(\sin\Big(\frac{\pi}{2}-\frac{3\pi}{5}\Big)\Big)$
$=\frac{\pi}{2}-\frac{3\pi}{5}$
$=\frac{-\pi}{10}$

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