Question

Evaluate sin^-1 (sin 9) 
1. 9
2. π - 9
3. 2π - 9
4. 3π - 9

Answer 1

Correct Answer - Option 4 : 3π - 9

Concept: 

sin^-1 (sin θ ) = θ , if \(\rm -\frac{π}{2}\leq θ\leq \frac{π}{2}\) 

Calculation: 

We have , θ = 9 radian , which is not lie between \(\rm -\frac{π}{2}\) and \(\rm \frac{π}{2}\) . But, 3π - θ  i.e,  3π - 9 lies between \(\rm -\frac{π}{2}\) and \(\rm \frac{π}{2}\) . 

Also , sin (3π - 9) = sin 9.

∴  sin^-1 (sin 9) = sin^-1 ( sin (3π - 9) ) = 3π - 9 .

The correct option is 4.