Final answer:
Coterminal angles have the same initial and terminal sides but differ in their measures, while reference angles are positive acute angles formed between the terminal side of an angle and the x-axis in standard position.
Step-by-step explanation:
In mathematics, coterminal angles and reference angles are two concepts related to angles.
Coterminal angles:
Coterminal angles are angles that have the same initial and terminal sides but differ in their measures. To find coterminal angles, you can add or subtract a multiple of 360 degrees (or 2π radians) to the given angle.
This means that if an angle is measured as 60 degrees, an angle coterminal to it could be 420 degrees or -300 degrees (60 + 360 = 420 and 60 - 360 = -300). So, coterminal angles go around the unit circle multiple times.
Reference angles:
A reference angle is the positive acute angle formed between the terminal side of an angle and the x-axis in standard position (having the initial side on the positive x-axis).
The reference angle is always between 0 degrees and 90 degrees (or 0 radians and π/2 radians) regardless of the quadrant the terminal side of the angle lies in. To find the reference angle, you can subtract multiples of 90 degrees (or π/2 radians) from the given angle until you get an angle between 0 and 90 degrees (or 0 and π/2 radians).