Question

which of the following statements best describes two coterminal angles?
select the correct answer below.
a. two angles in standard position are coterminal if they have the same initial side.
b. two angles in standard position are coterminal if they both have the same amount of rotation.
c. two angles in standard position are coterminal if the terminal sides of both angles lie in the same quadrant.
d. two angles in standard position are coterminal if they have the same terminal side.

Explanation:

To determine the correct description of coterminal angles, we recall the definition: Coterminal angles in standard position have the same terminal side (they differ by a multiple of \(360^\circ\) or \(2\pi\) radians).

• Option A: All angles in standard position have the same initial side (the positive x - axis), so this does not define coterminal angles.
• Option B: Angles with the same amount of rotation are equal angles, not necessarily coterminal (coterminal angles can have different amounts of rotation, differing by multiples of \(360^\circ\)).
• Option C: Angles with terminal sides in the same quadrant are not necessarily coterminal (e.g., \(30^\circ\) and \(120^\circ\) are in the same quadrant but not coterminal).
• Option D: Matches the definition of coterminal angles.

Answer:

D. Two angles in standard position are coterminal if they have the same terminal side.