How do you evaluate -sin((13pi)/12)?

1 Answer
Nghi N.
Apr 7, 2016

sqrt(2 - sqrt3)/2

Explanation:

Trig unit circle and property of supplementary arc-->
- sin ((13pi)/12) = - sin (pi/12 + pi) = sin (pi/12)
Evaluate sin (pi/12) by applying the trig identity:
cos 2a = 1 - 2sin^2 a
cos (pi/6) = sqrt3/2 = 1 - 2sin^2 (pi/12)
2sin^2 (pi/12) = 1 - sqrt3/2 = (2 - sqrt3)/2
sin^2 (pi/12) = (2 - sqrt3)/4
sin (pi/12) = +- sqrt(2 - sqrt3)/2 -->
Since sin (pi/12) is positive, therefor:
- sin ((13pi)/12) = sin (pi/12) = sqrt(2 - sqrt3)/2

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