Chapter 4.1, Problem 27E

(a)

To determine

Find one positive and one negative coterminal angle of the angle $\frac{\text{9π}}{\text{4}}$

Answer to Problem 27E

  $\frac{\text{17π}}{4}$; $-\frac{\text{7π}}{4}$

Explanation of Solution

Given:

The angle $\frac{\text{9π}}{\text{4}}$

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 $\frac{\text{9π}}{\text{4}}$ angle, just add $\text{2π}$

First positive coterminal angle = $\frac{\text{9π}}{\text{4}}+2\text{π}\text{=}\frac{\text{9π}}{4}+\frac{\text{8π}}{4}=\frac{\text{17π}}{4}$

To find the negative coterminal angle to $\frac{\text{9π}}{\text{4}}$ angle, just Subtract $\text{2π}$ or $4\text{π}$

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

Thus, two coterminal angle of $\frac{\text{9π}}{\text{4}}$ are $\frac{\text{17π}}{4}$ & $-\frac{\text{7π}}{4}$

(b)

To determine

Find one positive and one negative coterminal angle of the angle $-\frac{\text{2π}}{15}$

Answer to Problem 27E

  $\frac{\text{28π}}{\text{15}}$; $-\frac{\text{32π}}{\text{15}}$

Explanation of Solution

Given: The angle $-\frac{\text{2π}}{15}$

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 $-\frac{\text{2π}}{15}$ angle, just add $\text{2π}$

First positive coterminal angle = $-\frac{\text{2π}}{15}+2\text{π}\text{=}-\frac{\text{2π}}{\text{15}}+\frac{\text{30π}}{15}=\frac{\text{28π}}{\text{15}}$

To find the negative coterminal angle to $-\frac{\text{2π}}{15}$ angle, just Subtract $\text{2π}$

First Negative Coterminal Angle = $-\frac{\text{2π}}{15}-2\text{π}\text{=}-\frac{\text{2π}}{\text{15}}-\frac{\text{30π}}{15}=-\frac{\text{32π}}{\text{15}}$

Thus, two coterminal angle of $-\frac{\text{2π}}{15}$ are $\frac{\text{28π}}{\text{15}}$ & $-\frac{\text{32π}}{\text{15}}$