Question

Find the measure of a negative angle coterminal with (4\pi )/(3) radians. Give the answer in simplest form.

Answer 1

To find the negative angle coterminal with (4\pi) / 3 radians, subtract 2\pi radians to get -2\pi / 3 radians as the result.

Step-by-step explanation:

To find the measure of a negative angle coterminal with (4\pi) / 3 radians, we need to subtract 2\pi radians from it, as angles differ by integral multiples of 2\pi radians to be coterminal. The given angle (4\pi) / 3 is more than \pi, but less than 2\pi, so subtracting 2\pi will give us the negative coterminal angle.

Here's the calculation for the negative coterminal angle:

• Create an angle that's one full rotation (2\pi radians) less than the given angle: (4\pi) / 3 - 2\pi = -2\pi / 3.

The negative coterminal angle of (4\pi) / 3 radians is -2\pi / 3 radians.