In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle.395°

Verified step by step guidance

1. Start by understanding that 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 full rotations (360°) from the given angle.
2. Given the angle is 395°, we need to find a positive angle less than 360° that is coterminal with it.
3. Subtract 360° from 395° to find a coterminal angle: 395° - 360°.
4. The result from the subtraction will give you the positive coterminal angle that is less than 360°.
5. Verify that the resulting angle is indeed positive and less than 360°, ensuring it meets the problem's requirements.

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, 395° can be made coterminal by subtracting 360°, resulting in 35°.

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). Understanding this helps visualize how angles relate to one another.

Angle Measurement

Angles can be measured in degrees or radians, with 360° equivalent to 2π radians. This measurement is crucial for determining the position of angles on the unit circle. When working with angles greater than 360°, converting them to a coterminal angle within the 0° to 360° range simplifies calculations and comparisons.