In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. -760°

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Understand that coterminal angles differ by full rotations of 360°. To find a positive angle coterminal with -760°, we add or subtract multiples of 360° until the angle lies between 0° and 360°.

Start by adding 360° to -760°: calculate \(-760° + 360° = -400°\). Since -400° is still negative, continue adding 360°.

Add 360° again: \(-400° + 360° = -40°\). This is still negative, so add 360° once more.

Add 360° again: \(-40° + 360° = 320°\). Now, 320° is positive and less than 360°, so this is the positive coterminal angle.

Conclude that the positive angle less than 360° coterminal with -760° is 320°.

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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 until the result lies within the desired range.

Angle Measurement and Positive Angles

Angles can be measured in degrees and can be positive or negative. A positive angle is measured counterclockwise from the initial side, and when asked for a positive angle less than or equal to 360°, you adjust the given angle accordingly to fit this range.

Modulo Operation with Angles

The modulo operation helps find the remainder when dividing by 360°, effectively reducing any angle to its equivalent between 0° and 360°. This is useful for normalizing angles and finding coterminal angles within a standard interval.