Question

Determine whether the angles in each given pair are coterminal 123.4,-236.6

Answer 1

To determine whether two angles are coterminal, we check if they differ by a multiple of 360 degrees.

Let's first find the coterminal angle for 123.4 degrees. We can add or subtract 360 degrees until we find an angle within the range of 0 to 360 degrees.

123.4 degrees + 360 degrees = 483.4 degrees (not within the range)
123.4 degrees - 360 degrees = -236.6 degrees (within the range)

The coterminal angle for 123.4 degrees within the range is -236.6 degrees.

Now, let's check if -236.6 degrees is coterminal with -236.6 degrees. We subtract 360 degrees until we find an angle within the range.

-236.6 degrees - 360 degrees = -596.6 degrees (not within the range)
-236.6 degrees + 360 degrees = 123.4 degrees (within the range)

The coterminal angle for -236.6 degrees within the range is 123.4 degrees.

Therefore, the angles 123.4 degrees and -236.6 degrees are coterminal.