Chapter 4.1, Problem 44E

(a)

To determine

Find one positive and one negative coterminal angle of the angle ${114}^0$

Answer to Problem 44E

  ${474}^0$; $-{246}^0$

Explanation of Solution

Given:

The angle ${114}^0$

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 ${114}^0$ angle, just add ${360}^0$

First positive coterminal angle = ${114}^0+{360}^0={474}^0$

To find the negative coterminal angle to ${114}^0$ angle, just Subtract ${360}^0$

First Negative Coterminal Angle = ${114}^0-{360}^0=-{246}^0$

Thus, two coterminal angle of ${114}^0$ are ${474}^0$ & $-{246}^0$

(b)

To determine

Find one positive and one negative coterminal angle of the angle $-{390}^0$

Answer to Problem 44E

  ${330}^0$; $-{750}^0$

Explanation of Solution

Given: The angle $-{390}^0$

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 $-{390}^0$ angle, just add ${360}^0$ or ${720}^0$

First positive coterminal angle = $-{390}^0+{720}^0={330}^0$

To find the negative coterminal angle to $-{390}^0$ angle, just Subtract ${360}^0$

First Negative Coterminal Angle $=-{390}^0-{360}^0=-{750}^0$

Thus, two coterminal angle of $-{390}^0$ are ${330}^0$ & $-{750}^0$