Final answer:
To find the least positive coterminal angle, add or subtract 360° from the given angle until the result is a positive angle less than 360°. The result will either be the original angle if it's already within the range, or it will be 0° if the original angle is a multiple of 360°.
Step-by-step explanation:
Finding the Least Positive Coterminal Angle
To find the measure of the least positive angle that is coterminal with a given angle 'a', you add or subtract multiples of 360° (or 2π radians) from 'a' until you find an angle that lies between 0° and 360°. Coterminal angles have the same initial and terminal sides but may be in different rotations.
Step-by-Step Explanation
- Determine the given angle 'a'.
- If 'a' is negative, add 360° to 'a' until the result is positive and less than 360°.
- If 'a' is positive and greater than 360°, subtract 360° from 'a' until the result is less than 360°.
- If 'a' is positive and less than 360°, the angle itself is the least positive coterminal angle.
However, if 'a' is positive and exactly 360° multiples, the least positive coterminal angle would be 0°, since 360°, 720°, etc., are all coterminal with 0°.