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. Understand that two angles are coterminal if they differ by a full rotation of 360°. This means you can add or subtract multiples of 360° to find coterminal angles.
2. Since the given angle is 395°, which is greater than 360°, subtract 360° from 395° to find a positive coterminal angle less than or equal to 360°.
3. Write the expression for the coterminal angle: \(395^\circ - 360^\circ\).
4. Calculate the result of the subtraction to find the coterminal angle between 0° and 360°.
5. Verify that the resulting angle is positive and less than or equal to 360°, confirming it is the correct coterminal angle.

Key Concepts

Coterminal Angles

Coterminal angles are angles that share the same initial and terminal sides but differ by full rotations of 360°. To find a coterminal angle, you add or subtract multiples of 360° from the given angle. This concept helps in simplifying angles to a standard range.

Angle Measurement in Degrees

Angles can be measured in degrees, where one full rotation equals 360°. Understanding how to work within this system is essential for identifying angles within a specific range, such as between 0° and 360°, which is often required in trigonometry problems.

Positive Angle Restriction

When asked to find a positive angle less than or equal to a certain value, it means the solution must be within the first full rotation (0° to 360°). This restriction ensures the angle is expressed in a standard, simplified form suitable for further trigonometric analysis.