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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1:48 minutes

Problem 6

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. 212° B. 60°7. 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 a given angle makes with the x-axis. It is always positive and less than or equal to 90°.

Step 2: For an angle in standard position, determine which quadrant it lies in. For example, 212° is in the third quadrant.

Step 3: Calculate the reference angle for an angle in the third quadrant by subtracting 180° from the given angle. For 212°, compute 212° - 180°.

Step 4: Match the calculated reference angle with the options provided in Column II.

Step 5: Repeat the process for any other angles given in Column I, ensuring to identify the correct quadrant and use the appropriate formula to find the reference angle.

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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 analysis of angles in different quadrants. For example, the reference angle for 212° is found by subtracting it from 360° or determining its equivalent acute angle.

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 in determining its reference angle and associated trigonometric values.

Angle Measurement

Angles can be measured in degrees or radians, with degrees being the more common unit in basic trigonometry. A full rotation is 360°, and angles can be positive (counterclockwise) or negative (clockwise). Recognizing how to convert between degrees and radians is essential for solving problems involving angles and their reference angles.