Unit 4 - Objective 1 - Angles

An angle is formed by two rays that have the same endpoint.  This common endpoint is called the vertex of the the angle and  the two rays are called the sides of the angle.

Angles may be measured using degrees or radians.  If the rotation of the terminal side from the initial side is counterclockwise, the angle is positive.   If the rotation is clockwise, the angle is negative.

Examples:

If there is no degree symbol (°) after the angle measure, then assume that it is a radian measure.  Each degree is divided into 60 minutes and each minute into 60 seconds.  The symbol ' is used for minutes and " for seconds.   So 60' = 1° and 60"=1'.  In decimal degrees:

15' = (15/60)° = 0.25° and 27" = (27/3600)° = 0.0075°

Conversion between Degrees and Radians

• To change from radians to degrees, multiply the number of radians by 180°/p
• To change from degrees to radians, multiply by p/180°

Examples:

 1

 1 radian = 1 (180°/p) 180°/3.1416 57.296° or 57°

 2
 1° = 1° (p/180°) 3.1416/180° 0.01745 radians

 3
 p/4 radians = p/4 (180°/p) = 180°/4 = 45°

 4
 60° = 60° (p/180°) = p/3 radians

Unit 4 Outline // Course Outline // Home Page

Copyright © 1996 by B. Chambers and P. Lowry. All Rights Reserved.
The text passage provides definitions and examples related to angles, including their measurement in degrees and radians, and conversion between the two units. It includes several examples of converting between degrees and radians.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Unit 4 - Objective 1 - Angles

An angle is formed by two rays that have the same endpoint.  This common endpoint is called the vertex of the the angle and  the two rays are called the sides of the angle.

Angles may be measured using degrees or radians.  If the rotation of the terminal side from the initial side is counterclockwise, the angle is positive.   If the rotation is clockwise, the angle is negative.

Examples:

If there is no degree symbol (°) after the angle measure, then assume that it is a radian measure.  Each degree is divided into 60 minutes and each minute into 60 seconds.  The symbol ' is used for minutes and " for seconds.   So 60' = 1° and 60"=1'.  In decimal degrees:

15' = (15/60)° = 0.25° and 27" = (27/3600)° = 0.0075°

Conversion between Degrees and Radians

• To change from radians to degrees, multiply the number of radians by 180°/p
• To change from degrees to radians, multiply by p/180°

Examples:

 1

 1 radian = 1 (180°/p) 180°/3.1416 57.296° or 57°

 2
 1° = 1° (p/180°) 3.1416/180° 0.01745 radians

 3
 p/4 radians = p/4 (180°/p) = 180°/4 = 45°

 4
 60° = 60° (p/180°) = p/3 radians

Unit 4 Outline // Course Outline // Home Page

Copyright © 1996 by B. Chambers and P. Lowry. All Rights Reserved.
user
The text passage provides definitions and examples related to angles, including their measurement in degrees and radians, and conversion between the two units. It includes several examples of converting between degrees and radians.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS