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Question: The value of \(\sin ^ { - 1 } ( \sin 10 )\)is....

The value of sin⁡−1(sin⁡10)\sin ^ { - 1 } ( \sin 10 )is.

A

10

B

10−3π10 - 3 \pi

C

3π−103 \pi - 10

D

None of these

Answer

3π−103 \pi - 10

Explanation

Solution

Since 3π<10<3π+π2⇒0<10−3π<π23 \pi < 10 < 3 \pi + \frac { \pi } { 2 } \Rightarrow 0 < 10 - 3 \pi < \frac { \pi } { 2 }

⇒−π2<3π−10<0\Rightarrow \frac { - \pi } { 2 } < 3 \pi - 10 < 0 ⇒sin⁡−1{sin⁡(3π−10)}=3π−10\Rightarrow \sin ^ { - 1 } \{ \sin ( 3 \pi - 10 ) \} = 3 \pi - 10.