posted by Beth .
What is the reference angle for (27 pi)/5?
There are 2 pi radians in the units circle, so you want to take (27/5)pi % 2pi. '%' means modulus, or to take the remainder after dividing.
See "Maths" by "Annalee" a few topics down for more details.
Forgot the second step.
Once you find (27/5)pi % 2pi = 1.4pi, to find the reference angle look on the units circle to the closest horizontal axis.
1.4pi is closer to 1*pi than 0 rad or 2pi rad. Because 1.4pi is greater than pi, your reference angle is 1.4pi - pi = 0.4pi.
If your angle was less than 1*pi, but greater than pi/2 (so it is still closer to pi then 0), you would need to subtract that angle from pi.
For example, if your reference angle is 0.8pi, 0.8pi is still closer to pi then 0. So your reference angle is pi - 0.8pi = 0.2pi