Question
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Answer
\( \sin^{-1}(-1) \) is approximately -1.570796 or \(-\frac{\pi}{2}\).
Solution
Calculate or simplify the expression \( \arcsin(-1) \).
Calculate the value by following steps:
- step0: Calculate:
\(\arcsin\left(-1\right)\)
- step1: Rewrite the expression:
\(-\arcsin\left(1\right)\)
- step2: Calculate:
\(-\frac{\pi }{2}\)
The value of \( \sin^{-1}(-1) \) is approximately -1.570796 or \(-\frac{\pi}{2}\).
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Simplify this solution Mind Expander
The function \( \sin^{-1}(x) \), also known as arcsine, returns the angle whose sine is \( x \). For \( \sin^{-1}(-1) \), we are looking for an angle whose sine is \( -1 \). This occurs at \( \theta = -\frac{\pi}{2} \) or \( \theta = \frac{3\pi}{2} \). However, since the range of \( \sin^{-1}(x) \) is restricted to \( [-\frac{\pi}{2}, \frac{\pi}{2}] \), the valid answer is \( \sin^{-1}(-1) = -\frac{\pi}{2} \).
