Chapter 9.3, Problem 7GP

Solution

To sketch: the given angle and to find its reference angle.

  

The reference angle is ${\theta }^{\prime }=\frac{2\pi }{9}$ .

Given:

  $-\frac{7\pi }{9}$ .

Calculation:

Let $\theta =-\frac{7\pi }{9}$ .

The coterminal angle of the given angle is,

  $\begin{array}{c}\theta =-\frac{7\pi }{9}+2\pi \\ =\frac{11\pi }{9}\end{array}$

Now the sketch of the given angle is,

  

Here, the terminal side of $\theta$ lies in Quadrant III.

So, the reference angle is

  $\begin{array}{c}{\theta }^{\prime }=\frac{11\pi }{9}-\pi \\ =\frac{2\pi }{9}\end{array}$