Question

The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is 

 

Options

• `(3pi)/5`

• `-pi/10`

• `pi/10`

• `(7pi)/5`

Answer 1

(b) `-pi/10`

\[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right) = \sin^{- 1} \left\{ \cos\left( 6\pi + \frac{3\pi}{5} \right) \right\}\]
\[ = \sin^{- 1} \left\{ \cos\left( \frac{3\pi}{5} \right) \right\}\]
\[ = \sin^{- 1} \left\{ \sin\left( \frac{\pi}{2} - \frac{3\pi}{5} \right) \right\}\]
\[ = \frac{\pi}{2} - \frac{3\pi}{5}\]
\[ = - \frac{\pi}{10}\]
\[\]