Chapter C, Problem 9E

(a)

To determine

To graph:

The given angle in the standard position:

  $315°$

Explanation of Solution

Given information:

  $315°$

Graph:

  

Interpretation:

The given value of radian is $315°$ . 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 $360°$ .

Now,

  $315°=360-45$

Thus, the given angle $315°$ measures rotation of full revolution less than $45°$ from the positive $x-$ axis.

(b)

To determine

To graph:

The given angle in the standard position:

  $-\frac{3\pi }{4}rad$

Explanation of Solution

Given information:

  $-\frac{3\pi }{4}rad$

Graph:

  

Interpretation:

The given value of radian is $-\frac{3\pi }{4}rad$ . 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:

  $\begin{array}{l}-\frac{3\pi }{4}rad=-\frac{3\pi }{4}\times \frac{180°}{\pi }\\ -\frac{3\pi }{4}rad=-3\times 45°\\ -\frac{3\pi }{4}rad=-135°\end{array}$

Thus, the given angle $-\frac{3\pi }{4}rad$ measures angle $-135°$ or it is $\frac{3}{4}$ of the half revolution $\left(180°\right)$ from the positive $x-$ axis.