Coterminal Angles Formula

The formula to find the coterminal angles of an angle θ depending upon whether it is in terms of degrees or radians is:

• Degrees: θ ± 360 n
• Radians: θ ± 2πn

In the above formula, θ ± 360n, 360n means a multiple of 360, where n is an integer and it denotes the number of rotations around the coordinate plane.

Thus we can conclude that 45°, -315°, 405°, – 675°, 765° ….. are all coterminal angles. They differ only by a number of complete circles. We can conclude that “two angles are said to be coterminal if the difference between the angles is a multiple of 360° (or 2π, if the angle is in terms of radians)”