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

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Understand that two angles are coterminal if they differ by a full rotation, which is 360°. To find a positive angle coterminal with -150°, we add or subtract multiples of 360° until the result is positive and less than or equal to 360°.

Start by adding 360° to -150°: calculate \(-150° + 360°\).

Evaluate the sum to find the positive coterminal angle.

Verify that the resulting angle is between 0° and 360°, inclusive.

Conclude that this angle is the positive coterminal angle less than or equal to 360° corresponding to -150°.

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주요 개념

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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 identifying equivalent angles within a specified range.

Positive Angle Measurement

A positive angle is measured counterclockwise from the initial side, typically starting at 0°. When asked to find a positive angle coterminal with a negative angle, you add 360° until the result is positive and within the desired range, ensuring the angle lies between 0° and 360°.

Angle Range Constraints

The problem requires finding an angle less than or equal to 360° and positive. Understanding how to restrict angles within a specific interval, such as 0° to 360°, is essential. This involves adjusting the given angle by adding or subtracting full rotations to fit the required domain.