Find the angle between 0 and 2π radians that is coterminal with the given angle

Question

Find the angle between 0 and 2π radians that is coterminal with the given angle

-π/4

Answer 1

First we should define coterminal:

angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side

With this definition in mind we can begin finding a coterminal angle to -π/4

1. Where is the terminal side of this angle on the unit circle?
2. There are 2 ways to get to any spot on the unit circle: clockwise or counterclockwise. Negative angles are used to represent going clockwise and positive angles represent traversing the circle counterclockwise. Any terminal side in the unit circle can be represented either as a positive angle or as the aforementioned positive angle minus a full rotation around the circle, 2π. In other words we have: -π/4 = θ - 2π
3. solving for θ we find one angle that is coterminal with -π/4, which is 7π/4

Answer 2

-pi/4 = - 45 degrees

coterminal with 7pi/4 radians

2pi = 8pi/4

subtract

8pi/4 - pi/4 = 7pi/4 = 360-45 = 315 degrees