Q190 / 270 · NDA 2018 (Phase 1) · Mathematics

What is the principal value of $\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)$ ?

  • A
    $\frac{\pi}{4}$
  • B
    $\frac{\pi}{2}$
  • Correct answer
    C
    $\frac{\pi}{3}$
  • D
    $\frac{2 \pi}{3}$

Solution

$\begin{aligned} & \sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)=\sin ^{-1}\left(\sin \left(\pi-\frac{\pi}{3}\right)\right) \\ & =\sin ^{-1}\left(\sin \frac{\pi}{3}\right)=\frac{\pi}{3}\end{aligned}$

Hence, the correct answer is option: 'C'.

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