Final answer:
The closest positive and negative angles coterminal with 3π / 4 are 11π / 4 radians and -5π / 4 radians, respectively. To find them, simply add or subtract 2π, a full rotation in radians, from the original angle.
Step-by-step explanation:
The question asks us to find the closest positive and negative angles that are coterminal with 3π / 4 radians. Coterminal angles are angles that share the same initial and terminal sides but may differ by any number of full rotations. A full rotation in radians is 2π. To find the closest positive angle, we add 2π to 3π / 4. To find the closest negative angle, we subtract 2π from 3π / 4.
The closest positive angle that is coterminal to 3π / 4 radians is 7π / 4 radians. To find the positive coterminal angle, we can add a full revolution of 2π radians to the given angle:
3π / 4 + 2π = 7π / 4
The closest negative angle that is coterminal to 3π / 4 radians is -π / 4 radians. To find the negative coterminal angle, we can subtract a full revolution of 2π radians from the given angle:
3π / 4 - 2π = -π / 4