Question

Find the closest positive angle and the closest negative angle that is coterminal to

2π / 3 radians.

Answer 1

The closest positive coterminal angle to 2π / 3 is the angle itself, which is 2π / 3 radians. The closest negative coterminal angle is -4π / 3 radians, found by subtracting 2π from 2π / 3.

Step-by-step explanation:

To find the closest positive angle and the closest negative angle coterminal to 2π / 3 radians, one must add and subtract multiples of 2π radians (360°), the full angle of a circle, to the given angle.

For the closest positive coterminal angle to 2π / 3, since 2π / 3 is already positive and less than 2π, it is itself the closest positive coterminal angle. Hence, the closest positive coterminal angle is 2π / 3 radians.

To find the closest negative coterminal angle, subtract 2π radians from 2π / 3 radians:
(2π / 3) - 2π = -4π / 3
This gives us the closest negative coterminal angle which is -4π / 3 radians.