Chapter 4.1, Problem 25E

(a)

To determine

Find one positive and one negative coterminal angle of the angle $\frac{\text{π}}{\text{6}}$

Answer to Problem 25E

  $\frac{\text{13π}}{\text{6}}$; $-\frac{\text{11π}}{\text{6}}$

Explanation of Solution

Given:

The angle $\frac{\text{π}}{\text{6}}$

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 $\frac{\text{π}}{\text{6}}$ angle, just add $\text{2π}$

First positive coterminal angle = $\frac{\text{π}}{\text{6}}+2\text{π}\text{=}\frac{\text{π}}{\text{6}}+\frac{12\text{π}}{6}=\frac{\text{13π}}{\text{6}}$

To find the negative coterminal angle to $\frac{\text{π}}{\text{6}}$ angle, just Subtract $\text{2π}$

First Negative Coterminal Angle = $\frac{\text{π}}{\text{6}}-2\text{π}\text{=}\frac{\text{π}}{\text{6}}-\frac{12\text{π}}{6}=-\frac{\text{11π}}{\text{6}}$

Thus, two coterminal angle of $\frac{\text{π}}{\text{6}}$ are $\frac{\text{13π}}{\text{6}}$ & $-\frac{\text{11π}}{\text{6}}$

(b)

To determine

Find one positive and one negative coterminal angle of the angle $\frac{\text{2π}}{\text{3}}$

Answer to Problem 25E

  $\frac{\text{8π}}{\text{3}}$; $-\frac{\text{4π}}{\text{3}}$

Explanation of Solution

Given: The angle $\frac{\text{2π}}{\text{3}}$

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 $\frac{\text{2π}}{\text{3}}$ angle, just add $\text{2π}$

First positive coterminal angle = $\frac{\text{2π}}{\text{3}}+2\text{π}\text{=}\frac{\text{2π}}{\text{3}}+\frac{6\text{π}}{3}=\frac{\text{8π}}{\text{3}}$

To find the negative coterminal angle to $\frac{\text{2π}}{\text{3}}$ angle, just Subtract $\text{2π}$

First Negative Coterminal Angle = $\frac{\text{2π}}{\text{3}}-2\text{π}\text{=}\frac{\text{2π}}{\text{3}}-\frac{6\text{π}}{3}=-\frac{\text{4π}}{\text{3}}$

Thus, two coterminal angle of $\frac{\text{2π}}{\text{3}}$ are $\frac{\text{8π}}{\text{3}}$ & $-\frac{\text{4π}}{\text{3}}$