Chapter 4.1, Problem 43E

(a)

To determine

Find one positive and one negative coterminal angle of the angle ${52}^0$

Answer to Problem 43E

  ${412}^0$; $-{308}^0$

Explanation of Solution

Given:

The angle ${52}^0$

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 ${360}^0$ or 2p to each angle, depending on whether the given angle is in degrees or radians.

To find the positive coterminal angle to ${52}^0$ angle, just add ${360}^0$

First positive coterminal angle = ${52}^0+{360}^0={412}^0$

To find the negative coterminal angle to ${52}^0$ angle, just Subtract ${360}^0$

First Negative Coterminal Angle = ${52}^0-{360}^0=-{308}^0$

Thus, two coterminal angle of ${52}^0$ are ${412}^0$ & $-{308}^0$

(b)

To determine

Find one positive and one negative coterminal angle of the angle $-{36}^0$

Answer to Problem 43E

  ${324}^0$; $-{396}^0$

Explanation of Solution

Given: The angle $-{36}^0$

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 ${360}^0$ or 2p to each angle, depending on whether the given angle is in degrees or radians.

To find the positive coterminal angle to $-{36}^0$ angle, just add ${360}^0$

First positive coterminal angle $=-{36}^0+{360}^0={324}^0$

To find the negative coterminal angle to $-{36}^0$ angle, just Subtract ${360}^0$

First Negative Coterminal Angle $=-{36}^0-{360}^0=-{396}^0$

Thus, two coterminal angle of $-{36}^0$ are ${324}^0$ & $-{396}^0$