Find the principal value of sin^-1(-√2/2) in radians.

Find the principal value of $sin^{- 1} (- \frac{2}{2})$ in radians.

medium 2 marks Class 12 · Mathematics · Inverse Trigonometric Functions

Answer

\frac{π}{4}

The correct answer is - $\frac{π}{4}$ — Therefore the principal value is $- \frac{π}{4}$ .

The principal range of $sin^{- 1}$ is $[- \frac{π}{2}, \frac{π}{2}]$ .
We need an angle $θ$ in this interval such that $sin θ = - \frac{2}{2}$ .
The reference angle for $\frac{2}{2}$ is $\frac{π}{4}$ .
Since the sine value is negative, $θ = - \frac{π}{4}$ lies in the principal interval.
Therefore the principal value is $- \frac{π}{4}$ .

Common mistake: Choosing

\frac{5 π}{4}

which lies outside the principal range.

Concept tested: Principal value of inverse sine

Published 13 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked