SOLUTION: What is the measure of the principal angle that is coterminal with the given angle? 23π/6 11π/6 is in the answer key, but I can’t solve it.

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Question 1204852: What is the measure of the principal angle that is coterminal with the given angle?
23π/6
11π/6 is in the answer key, but I can’t solve it.
Found 3 solutions by MathLover1, math_tutor2020, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
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if given coterminal angle, then subtract 2pi ( full circle) to find principal angle:
23pi%2F6-2pi=23pi%2F6-12pi%2F6=11pi%2F6

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Grab a calculator to find that
%2823pi%29%2F6+=+12.042772 approximately
Recall that 2pi+=+6.28 approximately, so we need to find a coterminal angle between 0 and 6.28 roughly.
Unfortunately 12.042772 is not between 0 and 6.28

Subtract off 2pi to rotate the angle 360 degrees, and land on a coterminal angle.
%2823pi%29%2F6-2pi

%2823pi%29%2F6-2pi%2A%286%2F6%29

%2823pi%29%2F6-%2812pi%29%2F6

%2823pi-12pi%29%2F6

%2811pi%29%2F6

As a check, this result should be between 0 and 6.28 radians.
%2811pi%29%2F6+=+5.759587 approximately

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Another approach

This method is a bit longer, but it's something to consider.

Multiply by 180%2Fpi to convert from radians to degrees.

%28%2823pi%29%2F6%29%2A%28180%2Fpi%29+=+690

This means matrix%281%2C5%2C%2823pi%29%2F6%2C%22radians%22%2C%22=%22%2C690%2C%22degrees%22%29
The angle 690 degrees is not between 0 and 360.
Subtract off 360 (repeatedly) until landing somewhere in this interval.

690-360 = 330
We're now between 0 and 360.

Angles 690 degrees and 330 degrees are coterminal.
They point in the same direction (somewhere in the southeast quadrant).

Lastly, we convert from degrees to radians.
Use the conversion factor pi%2F180 which is the reciprocal of the previous conversion factor used.

330%2A%28pi%2F180%29+=+%2811pi%29%2F6

matrix%281%2C5%2C330%2C%22degrees%22%2C%22=%22%2C%2811pi%29%2F6%2C%22radians%22%29

Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


Add or subtract multiples of 2pi (a full circle) until you get a measure between 0 and 2pi.

23pi/6 - 2pi = 23pi/6 - 12pi/6 = 11pi/6, which is less than 2pi.

ANSWER: 11pi/6