Final answer:
The coterminal angle of 5π /6 radians that is between −π and π is −7π /6 radians. We find this result by subtracting 2π from 5π /6, simplifying to get the coterminal angle in the desired range. Option D is the correct answer.
Step-by-step explanation:
We are asked to find an angle coterminal to 5π /6 radians that is between −π and π (inclusive). An angle is coterminal with another angle if the two angles differ by an integer multiple of 2π radians. Coterminal angles have the same initial and terminal sides when drawn in standard position on a coordinate plane.
Since 5π /6 is an angle greater than π/2 and less than π, its coterminal angle that is between −π and π will be 5π /6 minus 2π radians. Performing this subtraction we get:
5π /6 − 2π = 5π /6 − 12π /6.
The result is −7π /6 radians, which falls within the range between −π and π (inclusive).
The correct answer is D) −7π /6.