Question 1204852
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Grab a calculator to find that
{{{(23pi)/6 = 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.
{{{(23pi)/6-2pi}}}


{{{(23pi)/6-2pi*(6/6)}}}


{{{(23pi)/6-(12pi)/6}}}


{{{(23pi-12pi)/6}}}


{{{(11pi)/6}}}


As a check, this result should be between 0 and 6.28 radians.
{{{(11pi)/6 = 5.759587}}} approximately


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Another approach


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


Multiply by {{{180/pi}}} to convert from radians to degrees.


{{{((23pi)/6)*(180/pi) = 690}}}


This means {{{matrix(1,5,(23pi)/6,"radians","=",690,"degrees")}}}
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/180}}} which is the reciprocal of the previous conversion factor used.


{{{330*(pi/180) = (11pi)/6}}}


{{{matrix(1,5,330,"degrees","=",(11pi)/6,"radians")}}}
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