Question

Find the value of $cos⁡(sin^{-1}⁡\frac{\sqrt{3}}{2})$ is _____

(a) $\frac{\sqrt{3}}{2}$

(b) $\frac{1}{4}$

(c) $\frac{1}{2}$

(d) 0

The question was posed to me during an interview.

This intriguing question comes from Inverse Trigonometric Functions Basics in chapter Inverse Trigonometric Functions of Mathematics – Class 12

Answer 1

Right answer is (c) $\frac{1}{2}$

For explanation I would say: $sin⁡\frac{π}{3}=\frac{\sqrt{3}}{2}$

∴$sin^{-1}⁡\frac{\sqrt{3}}{2}=\frac{π}{3}$

⇒$cos⁡(sin^{-1}⁡\frac{\sqrt{3}}{2})=cos⁡(\frac{π}{3})=\frac{1}{2}$.