In Exercises 13–17, find a positive angle less than 360° or 2𝜋 that is coterminal with the given angle. -445°

Key Concepts

Coterminal Angles

Coterminal angles are angles that share the same terminal side when drawn in standard position, differing only by full rotations of 360° (or 2π radians). To find a coterminal angle, you can add or subtract multiples of 360° to the given angle until the result falls within the desired range, typically between 0° and 360°.

Angle Measurement

Angles can be measured in degrees or radians, with 360° equivalent to 2π radians. Understanding how to convert between these two systems is essential for solving problems involving angles, especially when determining coterminal angles. In this case, the angle -445° needs to be adjusted to find a positive equivalent within the standard range.

Standard Position of an Angle

An angle is in standard position when its vertex is at the origin of a coordinate system and its initial side lies along the positive x-axis. The terminal side of the angle is determined by the angle's measure, which can be positive (counterclockwise) or negative (clockwise). This concept is crucial for visualizing and calculating coterminal angles.