Question:
The principal value of \( \sin^{-1} \left( \sin \frac{5\pi}{3} \right) \) is:
The principal value of \( \sin^{-1} \left( \sin \frac{5\pi}{3} \right) \) is:
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For inverse trigonometric functions, always find the angle within the specified range for the principal value.
Updated On: Jan 12, 2026
- \( -\frac{5\pi}{3} \)
- \( \frac{5\pi}{3} \)
- \( \frac{\pi}{3} \)
- \( \frac{4\pi}{3} \)
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The Correct Option is C
Solution and Explanation
Step 1: The principal value of the inverse sine function is in the range \( \left[ -\frac{\pi}{2}, \frac{\pi}{2} \right] \).
Step 2: \( \sin \frac{5\pi}{3} \) is equivalent to \( -\frac{\pi}{3} \), so the principal value is \( \frac{\pi}{3} \).
Final Answer: \[ \boxed{\frac{\pi}{3}} \]
Step 2: \( \sin \frac{5\pi}{3} \) is equivalent to \( -\frac{\pi}{3} \), so the principal value is \( \frac{\pi}{3} \).
Final Answer: \[ \boxed{\frac{\pi}{3}} \]
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