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

3. Unit Circle

Reference Angles

Trigonometry

3. Unit Circle

Reference Angles

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2:26 minutes

Problem 39

Textbook Question

In Exercises 35–60, find the reference angle for each angle.355°

Verified step by step guidance

Identify the given angle: 355°.

Determine if the angle is greater than 360° or less than 0°. Since 355° is between 0° and 360°, it is already in standard position.

Find the reference angle by subtracting the given angle from 360°: Reference angle = 360° - 355°.

The reference angle is the acute angle formed with the x-axis, which is always positive and less than 90°.

Conclude that the reference angle for 355° is the result from the subtraction in step 3.

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Key Concepts

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

Reference Angle

The reference angle is the acute angle formed by the terminal side of a given angle and the x-axis. It is always measured as a positive angle and is typically between 0° and 90°. For angles greater than 360° or negative angles, the reference angle can be found by first reducing the angle to its equivalent within the standard range of 0° to 360°.

Angle Reduction

Angle reduction involves converting an angle that exceeds 360° or is negative into an equivalent angle within the standard range of 0° to 360°. This is done by subtracting or adding 360° as necessary. For example, to find the equivalent angle of 355°, you can simply use it as is since it is already within the desired range.

Quadrants of the Unit Circle

The unit circle is divided into four quadrants, each representing a range of angles. The first quadrant contains angles from 0° to 90°, the second from 90° to 180°, the third from 180° to 270°, and the fourth from 270° to 360°. Understanding which quadrant an angle lies in helps determine the reference angle, as it influences the calculation of the acute angle with respect to the x-axis.