# Determining exact values for non-special angles

• Nov 2nd 2010, 04:58 PM
qswdefrg
Determining exact values for non-special angles
Q: Use an appropriate compound angle formula to determine an exact value for $cos(11pi/12)$

I know that you have to express the angle as a sum/difference of two special angles. In this case, cos(165) = cos(45 + 120). I get stuck here. Does this mean I have to break down 120 into (60 + 60)? :/

any sort of help/hints would be greatly appreciated.
• Nov 2nd 2010, 05:15 PM
Quote:

Originally Posted by qswdefrg
Q: Use an appropriate compound angle formula to determine an exact value for $cos(11pi/12)$

I know that you have to express the angle as a sum/difference of two special angles. In this case, cos(165) = cos(45 + 120). I get stuck here. Does this mean I have to break down 120 into (60 + 60)? :/

any sort of help/hints would be greatly appreciated.

That would be appropriate, after first writing the identity for $Cos\left(45^o+120^o\right)$.

You could also write $Cos120^o=Cos\left(180^o-60^o\right)=-Cos60^o$

and $Sin120^o=Sin60^o$ having written the compound angle identity for $Cos(A+B).$
• Nov 2nd 2010, 08:38 PM
mr fantastic
Quote:

Originally Posted by qswdefrg
Q: Use an appropriate compound angle formula to determine an exact value for $cos(11pi/12)$

I know that you have to express the angle as a sum/difference of two special angles. In this case, cos(165) = cos(45 + 120). I get stuck here. Does this mean I have to break down 120 into (60 + 60)? :/

any sort of help/hints would be greatly appreciated.

You should know from symmetry the exact values of sin(120) and cos(120).