Match each expression in Column I with its equivalent in Column II. See Example 3. I II. a. 6° A. 0 b. -6° B. 1 c. (-6)° C. -1 d. -(-6)° D. 6 E. -6

Verified step by step guidance

1. Step 1: Understand that the degree symbol (°) indicates an angle measurement.
2. Step 2: Recognize that a positive angle, such as 6°, remains positive, so it matches with option D (6).
3. Step 3: Identify that a negative angle, such as -6°, remains negative, so it matches with option E (-6).
4. Step 4: Note that (-6)° is equivalent to -6°, so it also matches with option E (-6).
5. Step 5: Realize that -(-6)° is the negation of -6°, which results in a positive 6°, matching with option D (6).

Key Concepts

Angle Measurement

Angles can be measured in degrees or radians, with 360 degrees equivalent to a full rotation. Understanding how to convert between positive and negative angles is crucial, as negative angles indicate a clockwise rotation from the positive x-axis. This concept is fundamental for interpreting the expressions in the question.

Reference Angles

Reference angles are the acute angles formed by the terminal side of an angle and the x-axis. They help in determining the sine, cosine, and tangent values of angles, especially when dealing with negative angles or angles greater than 360 degrees. This concept is essential for matching the expressions in Column I with their equivalents in Column II.

Trigonometric Values of Standard Angles

Certain angles, such as 0°, 30°, 45°, 60°, and 90°, have known sine, cosine, and tangent values. Recognizing these standard angles and their corresponding trigonometric values is vital for solving problems involving angle equivalences. This knowledge will aid in accurately matching the expressions from the two columns.