Chapter 14.8, Problem 7ST

To determine

To find:the value of the given trigonometric function.

Answer to Problem 7ST

  $y=\frac{\pi }{3}$ .

Explanation of Solution

Given:

The given trigonometric function is ${\csc }^{-1}\frac{2\sqrt{3}}{3}$ .

Calculation:

As thegiven trigonometric function is ${\csc }^{-1}\frac{2\sqrt{3}}{3}$ .

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

  $\begin{array}{l}\text{let}y={\csc }^{-1}\frac{2\sqrt{3}}{3}\{\text{given equation}}\\ \therefore \csc y=\frac{2\sqrt{3}}{3}\\ \Rightarrow \csc y=\csc \frac{\pi }{3}\left\{\because \csc \frac{\pi }{3}=\frac{2\sqrt{3}}{3}\right\}\\ y=\frac{\pi }{3}\end{array}$

Hence, the value of the given trigonometric function is $y=\frac{\pi }{3}$ .