COMEDK · Maths · 23. Inverse Trigonometric Functions
\(\text { The value of } \sin ^{-1}\left[\cos \left(39 \dfrac{\pi}{5}\right)\right] \text { is }\)
- A \(\dfrac{\pi}{2}\)
- B \(\dfrac{3 \pi}{5}\)
- C \(\dfrac{-3 \pi}{10}\)
- D \(\dfrac{3 \pi}{10}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{3 \pi}{10}\)
Step-by-step Solution
Detailed explanation
The given expression is \(\sin^{-1}\left[\cos\left(39 \dfrac{\pi}{5}\right)\right]\). First, simplify the angle \(39 \dfrac{\pi}{5}\) by dividing by \(2\pi\): \(39 \dfrac{\pi}{5} = 7\pi + 4 \dfrac{\pi}{5} = 8\pi - \dfrac{\pi}{5}\). Using the periodicity of the cosine function,…
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