Chapter 4, Problem 1CT

(a)

To determine

Sketch the angle in standard position.

Answer to Problem 1CT

Graph is shown below.

Explanation of Solution

Given:

Consider an angle that measures $\frac{5\pi }{4}radians$ .

  

(b)

To determine

Determine two coterminal angles (one positive and one negative).

Answer to Problem 1CT

Two coterminal angles are $\frac{13\pi }{4},-\frac{3\pi }{4}$

Explanation of Solution

Given:

Consider an angle that measures $\frac{5\pi }{4}radians$ .

Coterminal angles for the given angles are,

  $\begin{array}{l}2\pi +\frac{5\pi }{4}=\frac{13\pi }{4}\hfill \\ \text{And}-\frac{3\pi }{4}\hfill \end{array}$

(c)

To determine

Convert the radian measure to degree measure.

Answer to Problem 1CT

The radian measure to degree measure $225$

Explanation of Solution

Given:

Consider an angle that measures $\frac{5\pi }{4}radians$ .

As $lrad=1\left(\frac{180}{\pi }\right)$ degrees. Therefore

  $\begin{array}{cc}\frac{5\pi }{4}& =\frac{5\pi }{4}\left(\frac{180}{\pi }\right)\\ & =5(45)\\ & =225\end{array}$