Chapter 4.1, Problem 17E

a.

To determine

Find the complement and supplement for the given angle.

Answer to Problem 17E

The complement of the angle is $\frac{\pi }{3}$ and the supplementis $\frac{2\pi }{3}$ .

Explanation of Solution

Given:

The given angle is $\frac{\pi }{3}$ .

Calculation:

Two positive angles $\alpha$ and $\beta$ are complementary (complements of each other) when their sum is $\frac{\pi }{2}$ . Two positive angles $\alpha$ and $\beta$ are supplementary (supplement of each other) when their sum is $\pi$ .

The complement of $\frac{\pi }{3}$ is

  $\frac{\pi }{2}-\frac{\pi }{3}=\frac{\pi }{6}$

The supplement of $\frac{\pi }{3}$ is

  $\pi -\frac{\pi }{3}=\frac{2\pi }{3}$

Hence the complement of the angle is $\frac{\pi }{3}$ and the supplementis $\frac{2\pi }{3}$ .

b.

To determine

Find the complement and supplement for the given angle.

Answer to Problem 17E

The complement of the angle is $\frac{\pi }{4}$ and the supplementis $\frac{3\pi }{4}$ .

Explanation of Solution

Given:

The given angle is $\frac{\pi }{4}$ .

Calculation:

Two positive angles $\alpha$ and $\beta$ are complementary (complements of each other) when their sum is $\frac{\pi }{2}$ . Two positive angles $\alpha$ and $\beta$ are supplementary (supplement of each other) when their sum is $\pi$ .

The complement of $\frac{\pi }{4}$ is

  $\frac{\pi }{2}-\frac{\pi }{4}=\frac{\pi }{4}$

The supplement of $\frac{\pi }{4}$ is

  $\pi -\frac{\pi }{4}=\frac{3\pi }{4}$

Hence the complement of the angle is $\frac{\pi }{4}$ and the supplementis $\frac{3\pi }{4}$ .