# How do you find #sin^-1(sin ((5pi)/6))#?

Let

Then, from the definition of arcsine,

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**Answer:**

Here,

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To find ( \sin^{-1}(\sin(\frac{5\pi}{6})) ), first, calculate ( \sin(\frac{5\pi}{6}) ), which equals ( \frac{\sqrt{3}}{2} ). Then, since ( \sin^{-1}(\sin(\theta)) = \theta ) only if ( -\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2} ), and ( \frac{5\pi}{6} ) lies in the second quadrant, the answer is ( \frac{\pi}{6} ).

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