Question

cos(285[degrees])
Exact value?

Answer 1

what is the reference angle. Do you know how to compute it?

Answer 2

I have to evaluate a few problems without a calculator and I'm not sure how. I don't think a reference angle is relevant?

Answer 3

Hopefully, you realize that 285 is in the 4th quadrant. Thus, the reference angle is 75 degrees. To calculate what the cos of this is, one needs the following identity. cos(a+b)=cos(a)cos(b)-sin(a)sin(b). You know that in your case a+b have to add to 75. So pick a and b so you know their values. In this case, pick a=30 and b=45. Thus you obtain, cos(75)=cos(30)cos(45)-sin(30)sin(45). That you should be able to simplify :)