Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. ―5280°

Key Concepts

Coterminal Angles

Coterminal angles are angles that share the same terminal side when drawn in standard position. To find a coterminal angle, you can add or subtract multiples of 360° (for degrees) or 2π (for radians) from the given angle. For example, if you have an angle of 30°, both 30° and 390° are coterminal because they end at the same position on the unit circle.

Finding Positive Angles

When tasked with finding the least positive coterminal angle, the goal is to ensure the angle is greater than 0° but less than 360°. This often involves adding or subtracting 360° until the resulting angle falls within this range. For instance, if you start with -5280°, you would add 360° repeatedly until you find a positive angle.

Modulo Operation

The modulo operation is a mathematical tool used to find the remainder of a division. In the context of angles, it helps determine the equivalent angle within a standard range. For example, to find a coterminal angle, you can use the formula angle mod 360°, which gives the angle's position within a full rotation, simplifying the process of finding angles that are coterminal.