Chapter 4.1, Problem 45E

(a)

To determine

Find one positive and one negative coterminal angle of the angle $-{300}^0$

Answer to Problem 45E

  ${60}^0$; $-{660}^0$

Explanation of Solution

Given:

The angle $-{300}^0$

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 $-{300}^0$ angle, just add ${360}^0$

First positive coterminal angle $=-{300}^0+{360}^0={60}^0$

To find the negative coterminal angle to $-{300}^0$ angle, just Subtract ${360}^0$

First Negative Coterminal Angle = $-{300}^0-{360}^0=-{660}^0$

Thus, two coterminal angle of $-{300}^0$ are ${60}^0$ & $-{660}^0$

(b)

To determine

Find one positive and one negative coterminal angle of the angle ${230}^0$

Answer to Problem 45E

  ${590}^0$; $-{130}^0$

Explanation of Solution

Given: The angle ${230}^0$

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 ${230}^0$ angle, just add ${360}^0$ or ${720}^0$

First positive coterminal angle $={230}^0+{360}^0={590}^0$

To find the negative coterminal angle to ${230}^0$ angle, just Subtract ${360}^0$

First Negative Coterminal Angle = ${230}^0-{360}^0=-{130}^0$

Thus, two coterminal angle of ${230}^0$ are ${590}^0$ & $-{130}^0$