Question

which of the following statements is not true concerning angle measure?

select the correct choice below.

a. the angle in standard position formed by rotating the terminal side of angle one complete counterclockwise rotation has a radian measure of \\(\pi\\) radians.

b. the angle in standard position formed by rotating the terminal side of an angle one complete counterclockwise rotation has a measure of 360 degrees.

c. if an angle has positive measure, then the direction of its rotation is counterclockwise.

d. if an angle has negative measure, then the direction of its rotation is clockwise.

Explanation:

• Recall the concepts of angle measure in radians and degrees, and the sign convention for rotation direction:
• A full counterclockwise rotation (one complete circle) is \( 360^\circ \) or \( 2\pi \) radians.
• Positive angles are associated with counterclockwise rotations, and negative angles with clockwise rotations.
• Analyze each option:
• Option A: A full counterclockwise rotation should be \( 2\pi \) radians, not \( \pi \) radians. So this statement is false.
• Option B: A full counterclockwise rotation is \( 360^\circ \), so this statement is true.
• Option C: By definition, positive - measured angles are formed by counterclockwise rotation, so this statement is true.
• Option D: By definition, negative - measured angles are formed by clockwise rotation, so this statement is true.

Answer:

A. The angle in standard position formed by rotating the terminal side of angle one complete counterclockwise rotation has a radian measure of \( \pi \) radians.