Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

1. Measuring Angles

Angles in Standard Position

Trigonometry

1. Measuring Angles

Angles in Standard Position

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1:50 minutes

Problem 14

Textbook Question

In Exercises 13–17, find a positive angle less than 360° or 2𝜋 that is coterminal with the given angle.-445°

Verified step by step guidance

Start by understanding that coterminal angles are angles that share the same terminal side. To find a coterminal angle, you can add or subtract full rotations (360° for degrees or 2𝜋 for radians) from the given angle.

Given the angle is -445°, we need to find a positive coterminal angle less than 360°.

Add 360° to -445° to find a coterminal angle: -445° + 360°.

If the result is still negative, add another 360° to the result: (result from previous step) + 360°.

Continue this process until you obtain a positive angle that is less than 360°. This will be your coterminal angle.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Coterminal Angles

Coterminal angles are angles that share the same terminal side when drawn in standard position, differing only by full rotations of 360° (or 2π radians). To find a coterminal angle, you can add or subtract multiples of 360° to the given angle until the result falls within the desired range, typically between 0° and 360°.

Angle Measurement

Angles can be measured in degrees or radians, with 360° equivalent to 2π radians. Understanding how to convert between these two systems is essential for solving problems involving angles, especially when determining coterminal angles. In this case, the angle -445° needs to be adjusted to find a positive equivalent within the standard range.

Standard Position of an Angle

An angle is in standard position when its vertex is at the origin of a coordinate system and its initial side lies along the positive x-axis. The terminal side of the angle is determined by the angle's measure, which can be positive (counterclockwise) or negative (clockwise). This concept is crucial for visualizing and calculating coterminal angles.