Final answer:
The closest positive coterminal angle to 13π / 12 is 37π / 12, and the closest negative coterminal angle is -11π / 12. Integer multiples of 2π radians are added or subtracted to find these angles.
Step-by-step explanation:
To find the closest positive angle and the closest negative angle that is coterminal with 13π / 12 radians, we must add or subtract integer multiples of 2π radians to the given angle until we find the angles that are within one complete rotation, either in the positive or negative direction.
A full rotation in radians is 2π, which is approximately 6.2832. Since 13π / 12 is slightly more than π, subtracting one full rotation (2π) from the angle will give us the closest negative coterminal angle, and adding one full rotation will give us the closest positive coterminal angle.
The closest positive coterminal angle:
- 13π / 12 + 2π = 13π / 12 + 24π / 12 = 37π / 12
The closest negative coterminal angle:
- 13π / 12 - 2π = 13π / 12 - 24π / 12 = -11π / 12