Determining Reference Angles in Radians and Degrees (Given Large Angles)

The reference angle for any nonacute angle θ is the positive acute angle θ′ formed by the terminal side of θ and the x-axis.

Q. Find the reference angle for each of the following angles:
a) θ=665°
The trick is to find a coterminal angle between 0 and 360° by adding or subtracting 360°.
b) θ=15π/4

c) θ=−11π/3