Question

Question #d4766

Answer 1

`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.