Chapter C, Problem 10E

(a)

To determine

To graph:

The given angle in the standard position:

  $\frac{7\pi }{3}rad$

Explanation of Solution

Given information:

  $\frac{7\pi }{3}rad$

Graph:

  

Interpretation:

The given value of radian is $\frac{7\pi }{3}rad$ . It is positive angle value that means the rotation is measured from the $x-$ axis as counter-clockwise direction.

Know that:

In one full rotation the angle is $2\pi$ . And the relation between the degree and radian is shown by below expression:

  $\pi rad=180°$

Now, rewrite the given angle in the standard position:

  $\begin{array}{l}\frac{7\pi }{3}rad=\frac{6\pi }{3}+\frac{\pi }{3}\\ \frac{7\pi }{3}rad=2\pi +\frac{\pi }{3}\\ \frac{7\pi }{3}rad=2\pi +\frac{\pi }{3}\end{array}$

Since, $\pi rad=180°$

  $\frac{\pi }{3}=\frac{180}{3}=60°$

Thus, the given angle $\frac{7\pi }{3}rad$ measures a full revolution plus $60°$ from the positive $x-$ axis.

(b)

To determine

To graph:

The given angle in the standard position:

  $-3rad$

Explanation of Solution

Given information:

  $-3rad$

Graph:

  

Interpretation:

The given value of radian is $-3rad$ . It is negative angle value that means the rotation is measured from the $x-$ axis as clockwise direction.

Know that:

In one full rotation the angle is $2\pi$ . And the relation between the degree and radian is shown by below expression:

  $\begin{array}{l}\pi rad=180°\\ 1rad=\frac{180°}{\pi }\end{array}$

Now, rewrite the given angle in the standard position:

  $\begin{array}{l}-3rad=-3\times \frac{180°}{\pi }\\ -3rad=-172°\end{array}$

Thus, the given angle $-3rad$ measures angle $-172°$ less than half revolution $\left(180°\right)$ from the positive $x-$ axis.