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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
avatar+116 
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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

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