Inverse Trigonometric Functions
Principal Values
Premium Question
Grade 12

Question:

The value of $\sin^{-1}(\sin 10)$ (angle in radians) is:
(1) $10$
(2) $10 - 3\pi$
(3) $3\pi - 10$
(4) $3\pi$

Step-by-Step Solution

Key Concept: Range of $\sin^{-1}$ is $[-\pi/2, \pi/2]$. Write $10 = 3\pi + (10 - 3\pi)$, use $\sin(3\pi + \theta) = -\sin \theta$, then apply $\sin^{-1}$ to a negative value.
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Correct Answer: (3)

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