Chapter 4.1, Problem 36E

a.

To determine

Find the radian measurement for the given angle as a multiple of $\pi$ .

Answer to Problem 36E

The radian form of $-{60}^{°}$ is $-\frac{\pi }{3}$ .

Explanation of Solution

Given:

The given angle is $-{60}^{°}$ .

Calculation:

The conversion rules between degrees and radians.

To convert degrees to radians,

multiply degrees by $\frac{\pi \text{rad}}{{180}^{°}}$ .

To convert radians to degrees,

multiply radians by $\frac{{180}^{°}}{\pi \text{rad}}$ .

Now,

  $-{60}^{°}=-{60}^{°}\times \frac{\pi \text{rad}}{{180}^{°}}=-\frac{\pi }{3}$

Hence the radian form of $-{60}^{°}$ is $-\frac{\pi }{3}$ .

b.

To determine

Find the radian measurement for the given angle as a multiple of $\pi$ .

Answer to Problem 36E

The radian form of ${144}^{°}$ is $\frac{4\pi }{5}$ .

Explanation of Solution

Given:

The given angle is ${144}^{°}$ .

Calculation:

The conversion rules between degrees and radians.

To convert degrees to radians,

multiply degrees by $\frac{\pi \text{rad}}{{180}^{°}}$ .

To convert radians to degrees,

multiply radians by $\frac{{180}^{°}}{\pi \text{rad}}$ .

Now,

  ${144}^{°}={144}^{°}\times \frac{\pi \text{rad}}{{180}^{°}}=\frac{4\pi }{5}$

Hence the radian form of ${144}^{°}$ is $\frac{4\pi }{5}$ .