SOLUTION: Find the exact value by using a half-angle identity. (4 points) cos(5pi/12) Here is my work, can someone please check to see if I did it right? cos ((5 pi/6)/2) = +/- sqrt(

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value by using a half-angle identity. (4 points) cos(5pi/12) Here is my work, can someone please check to see if I did it right? cos ((5 pi/6)/2) = +/- sqrt(      Log On


   

Question 979506: Find the exact value by using a half-angle identity. (4 points)
cos(5pi/12)
Here is my work, can someone please check to see if I did it right?
cos ((5 pi/6)/2) = +/- sqrt( (1+cos (5 pi/6))/2 )
cos(5 pi/6) = -sqrt(3)/2
cos (5 pi/12) = +/- sqrt( (2/2-sqrt(3)/2)/2 )
cos (5 pi/12) = +/- sqrt( ((2-sqrt(3))/2)/2 )
cos (5 pi/12) = sqrt( ( (2-sqrt(3))/4 ) )
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!

Find the exact value by using a half-angle identity. (4 points)
cos%285pi%2F12%29.

Here is my work, can someone please check to see if I did it right?

cos+%28%285pi%2F6%29%2F2%29 = +/- sqrt%28+%281%2Bcos+%285pi%2F6%29%29%2F2+%29     correct

cos%285pi%2F6%29 = -sqrt%283%29%2F2                                      correct

cos+%285pi%2F12%29 = +/- sqrt%28+%282%2F2-sqrt%283%29%2F2%29%2F2+%29                       correct

cos+%285+pi%2F12%29 = +/- sqrt%28+%28%282-sqrt%283%29%29%2F2%29%2F2+%29                   correct

cos+%285pi%2F12%29 = sqrt%28+%282-sqrt%283%29%29%2F4+%29                               correct


EVERYTHING IS CORRECT.
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You can write the last expression as

cos+%285pi%2F12%29 = sqrt%282-sqrt%283%29%29%2F2.