Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. 541°

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Understand that coterminal angles differ by full rotations of 360°. To find an angle coterminal with 541°, you add or subtract multiples of 360°.

Since 541° is greater than 360°, subtract 360° from 541° to find a positive coterminal angle less than 360°: calculate \(541° - 360°\).

Perform the subtraction to get the new angle, which will be coterminal with 541° and between 0° and 360°.

Verify that the resulting angle is positive and less than 360°, ensuring it is the least positive coterminal angle different from the original 541°.

If needed, check by adding or subtracting another 360° to confirm no smaller positive coterminal angle exists.

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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 coterminal angles, you add or subtract multiples of 360° from the given angle. This concept helps identify angles that have the same trigonometric values.

Angle Measurement and Positive Angles

Angles can be measured in degrees and can be positive or negative. The least positive coterminal angle is the smallest positive angle greater than 0° that is coterminal with the given angle. Understanding how to adjust angles to fall within a specific range is essential.

Modulo Operation with Angles

Finding coterminal angles often involves using the modulo operation with 360°, which effectively 'wraps' angles into the standard 0° to 360° range. This operation simplifies the process of finding equivalent angles by reducing large or negative angles to their principal values.