Name an angle between 0° and 360° that is coterminal with the following angle. -135°
Name an angle between 0° and 360° that is coterminal with the following angle. -135°
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
![### Educational Resource on Coterminal Angles
#### Understanding Coterminal Angles
**Task:** Name an angle between 0° and 360° that is coterminal with the following angle: -135°.
To find an angle coterminal with -135°, we need to add or subtract 360° (a full rotation) until we obtain an angle between 0° and 360°.
\[ \text{Coterminal Angle} = -135° + 360° = 225° \]
Thus, the angle 225° is coterminal with -135°.
#### Diagram Explanation
Below is a unit circle diagram used to visualize angles:
- The diagram is a circle centered at the origin (0,0) with a radius of 1.
- The positive x-axis represents 0°.
- Angles increase in a counterclockwise direction.
- The positive y-axis represents 90°.
- The negative x-axis represents 180°.
- The negative y-axis represents 270°.
- Each quarter of the circle is divided into 30° increments.
- Points are marked at 30°, 45°, 60°, 90°, 120°, 135°, 150°, and 180°, continuing around the circle up to 360°.
### Summary
- An angle coterminal with -135° that lies within 0° to 360° is 225°.
- The unit circle helps visualize angles and their coterminal equivalents.
This information is useful in trigonometry and other mathematical applications involving periodic phenomena.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3e9f930-7347-4a0a-9949-50203265dda3%2F2faa2119-74a8-430e-807a-c2ce67681c76%2F64krwrn.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Resource on Coterminal Angles
#### Understanding Coterminal Angles
**Task:** Name an angle between 0° and 360° that is coterminal with the following angle: -135°.
To find an angle coterminal with -135°, we need to add or subtract 360° (a full rotation) until we obtain an angle between 0° and 360°.
\[ \text{Coterminal Angle} = -135° + 360° = 225° \]
Thus, the angle 225° is coterminal with -135°.
#### Diagram Explanation
Below is a unit circle diagram used to visualize angles:
- The diagram is a circle centered at the origin (0,0) with a radius of 1.
- The positive x-axis represents 0°.
- Angles increase in a counterclockwise direction.
- The positive y-axis represents 90°.
- The negative x-axis represents 180°.
- The negative y-axis represents 270°.
- Each quarter of the circle is divided into 30° increments.
- Points are marked at 30°, 45°, 60°, 90°, 120°, 135°, 150°, and 180°, continuing around the circle up to 360°.
### Summary
- An angle coterminal with -135° that lies within 0° to 360° is 225°.
- The unit circle helps visualize angles and their coterminal equivalents.
This information is useful in trigonometry and other mathematical applications involving periodic phenomena.
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