Chapter 4.1, Problem 28E

(a)

To determine

Find one positive and one negative coterminal angle of the angle $-\frac{\text{7π}}{8}$

Answer to Problem 28E

  $\frac{\text{7π}}{4}$; $-\frac{\text{9π}}{4}$

Explanation of Solution

Given:

The angle $-\frac{\text{7π}}{8}$

Concept Used:

Coterminal Angles are angles who share the same initial side and terminal sides. Finding coterminal angles is as simple as adding or subtracting 360° or 2p to each angle, depending on whether the given angle is in degrees or radians. There are an infinite number of coterminal angles that can be found.

Calculation:

Finding coterminal angles is as simple as adding or subtracting 360° or 2p to each angle, depending on whether the given angle is in degrees or radians.

To find the positive coterminal angle to $-\frac{\text{7π}}{8}$ angle, just add $\text{2π}$

First positive coterminal angle = $-\frac{\text{7π}}{8}+2\text{π}\text{=}-\frac{\text{2π}}{8}+\frac{\text{16π}}{8}=\frac{\text{14π}}{8}=\frac{\text{7π}}{4}$

To find the negative coterminal angle to $-\frac{\text{7π}}{8}$ angle, just Subtract $\text{2π}$

First Negative Coterminal Angle = $-\frac{\text{7π}}{8}-2\text{π}\text{=}-\frac{\text{2π}}{8}-\frac{\text{16π}}{8}=-\frac{\text{18π}}{8}=-\frac{\text{9π}}{4}$

Thus, two coterminal angle of $-\frac{\text{7π}}{8}$ are $\frac{\text{7π}}{4}$ & $-\frac{\text{9π}}{4}$

(b)

To determine

Find one positive and one negative coterminal angle of the angle $\frac{\text{π}}{\text{12}}$

Answer to Problem 28E

  $\frac{\text{25π}}{12}$; $-\frac{\text{23π}}{12}$

Explanation of Solution

Given: The angle $\frac{\text{π}}{\text{12}}$

Concept Used:

Coterminal Angles are angles who share the same initial side and terminal sides. Finding coterminal angles is as simple as adding or subtracting 360° or 2p to each angle, depending on whether the given angle is in degrees or radians. There are an infinite number of coterminal angles that can be found.

Calculation:

Finding coterminal angles is as simple as adding or subtracting 360° or 2p to each angle, depending on whether the given angle is in degrees or radians.

To find the positive coterminal angle to $\frac{\text{π}}{\text{12}}$ angle, just add $\text{2π}$

First positive coterminal angle = $\frac{\text{π}}{\text{12}}+2\text{π}\text{=}\frac{\text{π}}{12}+\frac{\text{24π}}{12}=\frac{\text{25π}}{12}$

To find the negative coterminal angle to $\frac{\text{π}}{\text{12}}$ angle, just Subtract $\text{2π}$

First Negative Coterminal Angle = $\frac{\text{π}}{\text{12}}-2\text{π}\text{=}\frac{\text{π}}{12}-\frac{\text{24π}}{12}=-\frac{\text{23π}}{12}$

Thus, two coterminal angle of $\frac{\text{π}}{\text{12}}$ are $\frac{\text{25π}}{12}$ & $-\frac{\text{23π}}{12}$