Chapter 4.1, Problem 46E

(a)

To determine

Find one positive and one negative coterminal angle of the angle ${445}^0$

Answer to Problem 46E

  ${805}^0$; $-{275}^0$

Explanation of Solution

Given:

The angle ${445}^0$

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 ${445}^0$ angle, just add ${360}^0$

First positive coterminal angle $={445}^0+{360}^0={805}^0$

To find the negative coterminal angle to ${445}^0$ angle, just Subtract ${360}^0$ or ${720}^0$

First Negative Coterminal Angle $={445}^0-{720}^0=-{275}^0$

Thus, two coterminal angle of ${445}^0$ are ${805}^0$ & $-{275}^0$

(b)

To determine

Find one positive and one negative coterminal angle of the angle $-{740}^0$

Answer to Problem 46E

  ${340}^0$; $-{1100}^0$

Explanation of Solution

Given: The angle $-{740}^0$

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 $-{740}^0$ angle, just add ${360}^0$ or ${720}^0$ or ${1080}^0$

First positive coterminal angle $=-{740}^0+{1080}^0={340}^0$

To find the negative coterminal angle to $-{740}^0$ angle, just Subtract ${360}^0$

First Negative Coterminal Angle $=-{740}^0-{360}^0=-{1100}^0$

Thus, two coterminal angle of $-{740}^0$ are ${340}^0$ & $-{1100}^0$