How to Rename Coterminal Angles

Any angle can have many, many descriptions in terms of angle measures, because an angle is equivalent to its coterminal angles. The most frequently used positive angle measures are those that measure between 0 and 360 degrees. Rules for coterminal angles involve adding or subtracting rotations (or multiples of 360 degrees).

The first equation that follows shows what happens when you add a full rotation over and over. The second shows what happens when you subtract a full rotation many times. The results are all coterminal angles.

image0.png

So an angle measuring 100 degrees is coterminal with the following:

image1.png

Here's an example: Suppose you want to give new measures for angles of 800 degrees and –1,040 degrees by finding an equivalent angle measure between 0 and 360 degrees.

  1. Subtract 360 degrees from 800 until the result is less than 360.

    image2.png

    An angle measuring 800 degrees is coterminal with an angle of 80 degrees.

  2. Add 360 degrees to –1,040 until the result is positive.

    image3.png

    An angle measuring –1,040 degrees is coterminal with an angle of 40 degrees.

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