Chapter 14.8, Problem 2ST

To determine

To find:the value of the given trigonometric function.

Answer to Problem 2ST

  $y=\frac{7\pi }{6}$

Explanation of Solution

Given:

The given trigonometric function is ${\sin }^{-1}\left(\sin \frac{7\pi }{6}\right)$ .

Calculation:

As thegiven trigonometric function is ${\sin }^{-1}\left(\sin \frac{7\pi }{6}\right)$ .

Now, to find the value of the given trigonometric function. Therefore,

  $\begin{array}{l}\text{let}y={\sin }^{-1}\left(\sin \frac{7\pi }{6}\right)\{\text{given equation}}\\ \therefore y=\frac{7\pi }{6}\left\{{\sin }^{-1}\sin x=x\right\}\end{array}$

Hence, the value of the given trigonometric function is $y=\frac{7\pi }{6}$ .