The principal value of sin − 1 x lies in the interval

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The principal value of $\sin ^{-1}$ x lies in the interval

MathematicsInverse Trigonometric FunctionsNDANDA 2017 (Phase 2)

Options:

A $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$
B $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$
C $\left[0, \frac{\pi}{2}\right]$
D $[0, \pi]$

Solution:

1971 Upvotes Verified Answer

The correct answer is: $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$

The principal value of $\sin ^{-1} x$ lies in it's range. The range of $\sin ^{-1} x$ is $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$.

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