Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. 26° 30'

Key Concepts

Coterminal Angles

Coterminal angles are angles that share the same terminal side when drawn in standard position. To find a coterminal angle, you can add or subtract multiples of 360° (or 2π radians) from the given angle. For example, if you have an angle of 30°, adding 360° gives you 390°, which is coterminal with 30°.

Degrees and Minutes

Angles can be expressed in degrees and minutes, where 1 degree equals 60 minutes. In the given angle of 26° 30', the '26' represents the degrees and '30' represents the minutes. To convert this to a decimal format, you can use the formula: degrees + (minutes/60), resulting in 26.5°.

Finding the Least Positive Angle

To find the least positive angle that is coterminal with a given angle, you typically subtract 360° until the angle is within the range of 0° to 360°. In this case, since the angle is already positive and less than 360°, you would look for the next coterminal angle by adding or subtracting 360° as needed.