Chapter 1.3, Problem 1E

a.

To determine

To find the exact radian measure of the angle.

  ${150}^{\circ }$

Answer to Problem 1E

  $\frac{5\pi }{6}$

Explanation of Solution

Given:

  ${150}^{\circ }$

Concept Used:

1. To change radian measure to degrees, multiply by $\frac{180}{\pi }$

2. To change degree measure to radians, multiply by $\frac{\pi }{180}$

Calculation:

In order to find the exact radian measure of ${150}^{\circ }$ , multiply it by $\frac{\pi }{180}$

Thus,

  $\begin{array}{c}{150}^{\circ }={150}^{\circ }\times \frac{\pi }{180}\\ =\frac{15}{18}\pi \\ =\frac{5}{6}\pi \end{array}$

Hence,

  ${150}^{\circ }=\frac{5\pi }{6}$

b.

To determine

To find the exact radian measure of the angle.

  ${120}^{\circ }$

Answer to Problem 1E

  $\frac{2\pi }{3}$

Explanation of Solution

Given:

  ${120}^{\circ }$

Concept Used:

1. To change radian measure to degrees, multiply by $\frac{180}{\pi }$

2. To change degree measure to radians, multiply by $\frac{\pi }{180}$

Calculation:

In order to find the exact radian measure of ${120}^{\circ }$ , multiply it by $\frac{\pi }{180}$

Thus,

  $\begin{array}{c}{120}^{\circ }={120}^{\circ }\times \frac{\pi }{180}\\ =\frac{120\pi }{180}\\ =\frac{2\pi }{3}\end{array}$

Hence,

  ${120}^{\circ }=\frac{2\pi }{3}$

c.

To determine

To find the exact radian measure of the angle.

  ${450}^{\circ }$

Answer to Problem 1E

  $\frac{9\pi }{2}$

Explanation of Solution

Given:

  ${450}^{\circ }$

Concept Used:

1. To change radian measure to degrees, multiply by $\frac{180}{\pi }$

2. To change degree measure to radians, multiply by $\frac{\pi }{180}$

Calculation:

In order to find the exact radian measure of ${450}^{\circ }$ , multiply it by $\frac{\pi }{180}$

Thus,

  $\begin{array}{c}{450}^{\circ }=450\times \frac{\pi }{180}\\ =\frac{450\pi }{180}\\ =\frac{9\pi }{2}\end{array}$

Hence,

  ${450}^{\circ }=\frac{9\pi }{2}$

d.

To determine

To find the exact radian measure of the angle.

  $-{60}^{\circ }$

Answer to Problem 1E

  $\frac{-\pi }{3}$

Explanation of Solution

Given:

  $-{60}^{\circ }$

Concept Used:

1. To change radian measure to degrees, multiply by $\frac{180}{\pi }$

2. To change degree measure to radians, multiply by $\frac{\pi }{180}$

Calculation:

In order to find the exact radian measure of $-{60}^{\circ }$ , multiply it by $\frac{\pi }{180}$

Thus,

  $\begin{array}{c}-{60}^{\circ }=-60\times \frac{\pi }{180}\\ =-\frac{6}{18}\pi \\ =-\frac{1}{3}\pi \\ =\frac{-\pi }{3}\end{array}$

Hence,

  $-{60}^{\circ }=\frac{-\pi }{3}$