In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle.-150°

Verified step by step guidance

1. Identify the given angle: -150°.
2. Recall that coterminal angles differ by full rotations of 360°. Therefore, add 360° to the given angle to find a positive coterminal angle.
3. Calculate: -150° + 360°.
4. Verify that the resulting angle is positive and less than 360°.
5. Conclude that the resulting angle is the positive coterminal angle you are looking for.

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) to the given angle. For example, -150° can be made positive by adding 360°, resulting in a coterminal angle of 210°.

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 helps visualize how angles relate to one another in the coordinate plane.

Angle Measurement

Angles can be measured in degrees or radians, with 360° equivalent to 2π radians. In trigonometry, degrees are often used for practical applications, while radians are preferred in calculus and higher mathematics. Knowing how to convert between these two systems is essential for solving problems involving angles, especially when determining coterminal angles.