How do you evaluate cos ((7pi)/12)?

1 Answer
Nghi N.
May 10, 2016

- sqrt(2 - sqrt3)/2

Explanation:

Use the trig identity: cos 2a = 2cos^2 a - 1
cos 2a = cos ((14pi)/12) = cos ((7pi)/6) = cos (pi/6 + pi) =
-cos (pi/6) = - sqrt3/2
cos ((7pi)/6) = -sqrt3/2 = 2cos^2 ((7pi)/12) - 1
2cos^2 ((7pi)/12) = 1 - sqrt3/2 = (2 - sqrt3)/2
cos^2 ((7pi)/12) = (2 - sqrt3)/4
cos ((7pi)/12) = +- sqrt(2 - sqrt3)/2
Since (7pi)/12 is in Quadrant II, its cos is negative -->
cos ((7pi)/12) = - sqrt(2 - sqrt3)/2

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