How do you find the exact value of cos 11π/12?

1 Answer
Nghi N.
Oct 24, 2015

Find exact value of cos ((11pi)/12)

Ans: sqrt(2 + sqrt3)/2

Explanation:

On the trig unit circle,
cos ((11pi)/12) = cos (-pi/12 + 2pi) = cos (-pi/12) = cos (pi/12).
First, find cos (pi/12). Call cos (pi/12) = cos x
Apply the trig identity: cos 2x = 2cos^2 x - 1
cos 2x = cos (2pi)/12 = cos (pi/6) = sqrt3/2.
sqrt3/2 = 2cos^2 x - 1.
cos^2 x = (2 + sqrt3)/4
cos x = cos (pi/12) = sqrt(2 + sqrt3)/2.
The negative answer is rejected because the arc (pi/12) is in Quadrant I.
Check by calculator.
cos pi/12 = cos 15^@ = 0.97
sqrt(2 + sqrt3)/2 = 1.93/2 = 0.97 .OK

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