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NDA 2014
Exam
NDA
Year
2014
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2014 · Mathematics · Inverse Trigonometric Functions

What is ^ -1 (3 π)/(5) equal to?

What is sin⁡−1sin⁡3π5\sin ^{-1} \sin \frac{3 \pi}{5} equal to?

Options

  1. A3π5\frac{3 \pi}{5}
  2. B2π5\frac{2 \pi}{5}
  3. Cπ5\frac{\pi}{5}
  4. DNone of the above

Correct answer

B. 2π5\frac{2 \pi}{5}

Step-by-step solution

sin⁡−1×sin⁡3π5=sin⁡−1[sin⁡(π−2π5)]=sin⁡−1⋅sin⁡2π5=2π5.\begin{aligned} \sin ^{-1} \times \sin \frac{3 \pi}{5} & =\sin ^{-1}\left[\sin \left(\pi-\frac{2 \pi}{5}\right)\right] \\ & =\sin ^{-1} \cdot \sin \frac{2 \pi}{5}=\frac{2 \pi}{5}.\end{aligned}
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