SOLUTION: usa a sum or difference identity to find the exact value of the expression cos(5pi/12)

Algebra ->  College  -> Linear Algebra -> SOLUTION: usa a sum or difference identity to find the exact value of the expression cos(5pi/12)      Log On


   



Question 1051954: usa a sum or difference identity to find the exact value of the expression cos(5pi/12)
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
   

5pi%2F12 is not a special angle.  We see if we 
can break 5pi%2F12 into a sum or difference of 
the three special angles pi%2F4, pi%2F6, 
and pi%2F3.

We change the special angles so as to have denominator 12:

pi%2F4%22%22=%22%223pi%2F12, pi%2F6%22%22=%22%222pi%2F12, pi%2F3%22%22=%22%224pi%2F12

So we see that pi%2F4%2Bpi%2F6%22%22=%22%223pi%2F12%2B2pi%2F12%22%22=%22%225pi%2F12

We use the identity: cos%28alpha%2Bbeta%29%22%22=%22%22cos%28alpha%29cos%28beta%29-sin%28alpha%29sin%28beta%29

cos%285pi%2F12%29%22%22=%22%22cos%28pi%2F4%2Bpi%2F6%29%22%22=%22%22cos%28pi%2F4%29cos%28pi%2F6%29-sin%28pi%2F4%29sin%28pi%2F6%29%22%22=%22%22

%28sqrt%282%29%2F2%29%28sqrt%283%29%2F2%29-%28sqrt%282%29%2F2%29%281%2F2%29%22%22=%22%22sqrt%286%29%2F4-sqrt%282%29%2F4%22%22=%22%22%28sqrt%286%29-sqrt%282%29%29%2F4

Edwin