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

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

easy MCQ 1 mark Class 12 · Mathematics · Inverse Trigonometric Functions

Answer

- \frac{π}{6}

The correct answer is $- \frac{π}{6}$ — Hence the principal value is $- \frac{π}{6}$ .

Recall that the principal value of $sin^{- 1} y$ lies in $[- \frac{π}{2}, \frac{π}{2}]$ .
Since $sin (- \frac{π}{6}) = - \frac{1}{2}$ , the angle $- \frac{π}{6}$ satisfies the equation.
No other angle in the principal range gives $- \frac{1}{2}$ .
Hence the principal value is $- \frac{π}{6}$ .

Common mistake: Taking

\frac{5 π}{6}

instead of

- \frac{π}{6}

because

sin \frac{5 π}{6} = \frac{1}{2}

Concept tested: Principal value of inverse sine