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# Find the Exact Value

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Find the exact value.

$$sin^{-1}(sin(\frac{3\pi}{8}))$$

I would know how to do this if $$\frac{3\pi}{8}$$ was on the unit circle.

May 14, 2019

#1
+115
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Well, since this is inverse sine of a sine it cancels out to return to the given angle of $$\frac{3\pi}{8}$$.

But, we should always check where stuff is defined with inverse trig functions and make sure $$\frac{3\pi}{8}$$ is within it. The range of $$sin^{-1}$$ is $$[-\frac{\pi}{2},\frac{\pi}{2}]$$, and $$\frac{3\pi}{8}<\frac{\pi}{2}$$, so the answer is $$\frac{3\pi}{8}$$

May 14, 2019