Question

How do you find the value of the sin of θ/2 given that cos a = 5/13 and a is in Quadrant IV?

Answer 1

`sin (a/2) = - (2sqrt13)/13`

Explanation:

Use the trig identity:
`2sin^2 a = 1 - cos 2a.`
`2sin^2 a/2 = 1 - cos a = 1 - 5/13 = 8/13`
`sin^2 a/2 = 8/26`
`sin (a/2) = +- 2sqrt2/sqrt26 = +- 2/sqrt13 = +- 2sqrt13/13`
Since a is in Quadrant IV, `sin (a/2)` is negative, then
`sin (a/2) = - (2sqrt13)/13`