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. C. 82°8. D. 30°9. E. 38°10. 480° 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 angles greater than 360°, subtract 360° until the angle is between 0° and 360°.

Step 3: Determine the quadrant in which the angle lies. This will help in finding the reference angle.

Step 4: Use the quadrant information to find the reference angle: - Quadrant I: Reference angle = angle - Quadrant II: Reference angle = 180° - angle - Quadrant III: Reference angle = angle - 180° - Quadrant IV: Reference angle = 360° - angle

Step 5: Match the calculated reference angles with the options provided 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 90° or less than 0°. For example, the reference angle for 480° is found by subtracting 360°, resulting in 120°, and then finding the acute angle, which is 60°.

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 crucial for solving problems involving angles. In this context, recognizing that angles can exceed 360° and how to reduce them to their equivalent angles within the first full rotation is essential for identifying reference angles.

Quadrants and Angle Position

The coordinate plane is divided into four quadrants, each affecting the sign of the trigonometric functions based on the angle's position. Knowing which quadrant an angle lies in helps determine its reference angle and the corresponding trigonometric values. For instance, an angle of 480° is in the second quadrant, which influences how we find its reference angle and its sine and cosine values.

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