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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2018 · Mathematics · Inverse Trigonometric Functions

What is the principal value of ^ -1 ( (2 π)/(3)) ?

What is the principal value of sin⁡−1(sin⁡2π3)\sin ^{-1} \left(\sin \frac{2 \pi}{3}\right)?

Options

  1. Aπ4\frac{\pi}{4}
  2. Bπ2\frac{\pi}{2}
  3. Cπ3\frac{\pi}{3}
  4. D2π3\frac{2 \pi}{3}

Correct answer

C. π3\frac{\pi}{3}

Step-by-step solution

sin⁡−1(sin⁡2π3)=sin⁡−1(sin⁡(π−π3))=sin⁡−1(sin⁡π3)=π3\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}
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