SOLUTION: find the exact value of cos165
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Question 80909: find the exact value of cos165
Answer by kev82(151) (Show Source): You can put this solution on YOUR website!
Hi,
The trick is to take the angle 165, and write it in terms of some nice angles you can deal with. There may be other choices, but I am going to choose 135 and 30. Using the identity:
 = \cos(A)\cos(B)-\sin(A)\sin(B))
we have
=\cos(135)\cos(30)-\sin(135)\sin(30))
135 is basicaly a 45 degree angle in the second quadrant, so =-1/\sqrt{2})
and =1/\sqrt{2})
. You should already know the sine and cosine of 30(this is important to remember!)
Substituting in to the formula gives:
=-\frac{1+\sqrt{3}}{2\sqrt{2}})
Hope that helps,
Kev
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