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

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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.

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°.

Write the expression for the coterminal angle: \(395^\circ - 360^\circ\).

Calculate the result of the subtraction to find the coterminal angle between 0° and 360°.

Verify that the resulting angle is positive and less than or equal to 360°, confirming it is the correct coterminal angle.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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