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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2:12 minutes

Problem 7

Textbook Question

Concept Check Match each angle in Column I with its reference angle in Column II. Choices may be used once, more than once, or not at all. See Example 1. I. II.5. A. 45°6. B. 60°7. -135° C. 82°8. D. 30°9. E. 38°10. F. 32°

Verified step by step guidance

Step 1: Understand that a reference angle is the smallest angle that the terminal side of a given angle makes with the x-axis.

Step 2: For an angle in standard position, if the angle is negative, add 360° to find its positive coterminal angle.

Step 3: For -135°, add 360° to get 225°, which is in the third quadrant.

Step 4: In the third quadrant, the reference angle is found by subtracting 180° from the angle, so calculate 225° - 180°.

Step 5: Match the calculated reference angle with the options in Column II.

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Key Concepts

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

Reference Angle

A reference angle is the acute angle formed by the terminal side of an angle in standard position and the x-axis. It is always measured as a positive angle and is used to simplify the calculation of trigonometric functions. For angles greater than 180° or less than 0°, the reference angle is found by subtracting or adding to 180° or 360°, respectively, to find the corresponding acute angle.

Angle Measurement

Angles can be measured in degrees or radians, with degrees being the more common unit in basic trigonometry. A full circle is 360 degrees, and angles can be positive (counterclockwise) or negative (clockwise). Understanding how to convert between these measurements and how to interpret negative angles is essential for finding reference angles.

Quadrants of the Coordinate Plane

The coordinate plane is divided into four quadrants, each defined by the signs of the x and y coordinates. The location of an angle determines its reference angle and the corresponding trigonometric values. Knowing which quadrant an angle lies in helps in determining the correct reference angle and its associated sine, cosine, and tangent values.