find the exact value of the following expression, if possible.\n sin^{-1}left(sin\frac{pi}{5}\right)…

find the exact value of the following expression, if possible.\n sin^{-1}left(sin\frac{pi}{5}\right) \nselect the correct choice below and fill in any answer boxes in your choice.\na. sin^{-1}left(sin\frac{pi}{5}\right)= \n(simplify your answer. type an exact answer, using ( pi ) as needed. use integers or fractions for any numbers in the expression.)\nb. the answer is undefined.

find the exact value of the following expression, if possible.\n sin^{-1}left(sin\frac{pi}{5}\right) \nselect the correct choice below and fill in any answer boxes in your choice.\na. sin^{-1}left(sin\frac{pi}{5}\right)= \n(simplify your answer. type an exact answer, using ( pi ) as needed. use integers or fractions for any numbers in the expression.)\nb. the answer is undefined.

Answer

Explanation:

Step1: Recall the property of inverse - sine function

The property of the inverse - sine function (y = \sin^{-1}(x)) is that (\sin^{-1}(\sin\theta)=\theta) when (\theta\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]).

Step2: Check the range of (\frac{\pi}{5})

We know that (-\frac{\pi}{2}\approx - 1.57) and (\frac{\pi}{2}\approx1.57), and (\frac{\pi}{5}=0.2\pi\approx0.63). Since (-\frac{\pi}{2}<\frac{\pi}{5}<\frac{\pi}{2}).

Answer:

A. (\sin^{-1}\left(\sin\frac{\pi}{5}\right)=\frac{\pi}{5})