Find the angle of least positive measure that is coterminal with each angle. 792°

Verified step by step guidance

1. Understand that coterminal angles are angles that share the same initial and terminal sides. To find a coterminal angle, you can add or subtract multiples of 360°.
2. Given the angle 792°, we need to find the least positive coterminal angle. Start by subtracting 360° from 792°.
3. Subtract 360° from 792°: 792° - 360° = 432°.
4. Since 432° is still greater than 360°, subtract 360° again: 432° - 360° = 72°.
5. The least positive angle that is coterminal with 792° is 72° because it is the smallest positive angle obtained after subtracting multiples of 360°.

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, 792° can be reduced by subtracting 360° until the angle falls within the range of 0° to 360°.

Angle Reduction

Angle reduction involves simplifying an angle to find its equivalent within a standard range, typically between 0° and 360° for degrees. This is done by repeatedly subtracting 360° from the angle until it falls within the desired range. This process is essential for identifying the least positive coterminal angle.

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, moving counterclockwise for positive angles and clockwise for negative angles. Understanding this concept is crucial for visualizing and calculating coterminal angles.