How to Find Coterminal Angle Between 0 and 360 Degrees

TLDR; Determining a coterminal angle between 0 and 360 degrees involves adding or subtracting multiples of 360 degrees to obtain the desired angle.

💡 Determining a Coterminal Angle

The task is to determine an angle between 0 and 360 degrees that is coterminal to 1,524 degrees.

Coterminal angles have the same terminal side when sketched in standard position, and in this case, the angle is positive and will be rotated counterclockwise from the positive x-axis.

To find the coterminal angle, we can subtract multiples of 360 degrees from 1,524 degrees until we obtain an angle between 0 and 360 degrees.

The key to answering the question is to determine the additional rotation needed from the positive x-axis to reach 1,524 degrees, which is 84 degrees.

This is the measured angle we are looking for that's coterminal to the given angle between 0 and 360 degrees.

🔄 Using Multiples of 360 Degrees

In the most general case, any angle coterminal to a given angle can be expressed as the given angle plus 360 degrees multiplied by an integer (θ + 360° x k, where k is some integer).

By adding or subtracting multiples of 360 degrees (360° x k, where k is an integer) to the given angle at 1,524 degrees, we can obtain an angle between 0 and 360 degrees.

For this specific example, by letting k = -4, we can add -1,440 degrees to 1,524 degrees, resulting in a sum of 84 degrees, which is the coterminal angle between 0 and 360 degrees.

For any value of k, as long as k is an integer, we can obtain an angle that's coterminal to the given angle between 0 and 360 degrees.