How do you evaluate cos((11pi) / 12)?

1 Answer
Nghi N.
Mar 20, 2016

sqrt(2 + sqrt3)/2

Explanation:

On the trig unit circle,
cos((11pi)/12) = cos (pi/12).
Evaluate cos (pi/12) bu applying the identity:
cos 2a = 2cos^2 a - 1
cos (pi/6) = sqrt3/2 = 2cos^2 (pi/12) - 1
2cos^2 (pi/12) = 1 + sqrt3/2 = (2 + sqrt3)/2
cos^2 (pi/12) = (2 + sqrt3)/4
cos (pi/12) = sqrt(2 + sqrt3)/2 (cos (pi/12) is positive)

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