Final answer:
The closest positive coterminal angle to 11π / 12 radians is 35π / 12, and the closest negative coterminal angle is -13π / 12.
Step-by-step explanation:
The question is asking to find the closest positive and negative angles coterminal to 11π / 12 radians. A coterminal angle is one that shares the same initial side and their terminal sides are a full rotation apart (2π radians or 360 degrees). To find the closest positive coterminal angle to 11π/12 radians, we add 2π to it: (11π/12) + 2π = (11π/12) + (24π/12) = 35π/12, which is the positive coterminal angle. To find the closest negative coterminal angle, we subtract 2π from 11π/12: (11π/12) - 2π = (11π/12) - (24π/12) = -13π/12, giving us the negative coterminal angle.
The closest positive angle that is coterminal to 11π / 12 radians can be found by adding 2π radians (or 360°) to the given angle. So, the closest positive angle is:
11π / 12 + 2π = 23π / 12 radians
To find the closest negative angle that is coterminal, subtract 2π radians (or 360°) from the given angle:
11π / 12 - 2π = -13π / 12 radians