Question #d4766

1 Answer
Nghi N
Apr 1, 2017

sin (x/2) = - sqrt(9 + sqrt17)/(3sqrt2)

Explanation:

sin x = - 8/9
cos^2 x = 1 - sin^2 x = 1 - 64/81 = 17/81
cos x = - sqrt17/9 (because x is in Quadrant 3)
Use trig identity:
2sin^2 (x/2) = 1 - cos x = 1 + sqrt17/9 = (9 + sqrt17)/9
sin^2 (x/2) = (9 + sqrt17)/18
sin (x /2) = +- sqrt(9 + sqrt17)/(3sqrt2)
Because x is in Quadrant 3, take the negative value.

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