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) (Show Source): You can put this solution on YOUR website!
if given coterminal angle, then subtract ( full circle) to find principal angle:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
Grab a calculator to find that
approximately
Recall that 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 to rotate the angle 360 degrees, and land on a coterminal angle.
As a check, this result should be between 0 and 6.28 radians.
approximately
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Another approach
This method is a bit longer, but it's something to consider.
Multiply by to convert from radians to degrees.
This means
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 which is the reciprocal of the previous conversion factor used.
Answer by greenestamps(13215) (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
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