Question

Given `sintheta=-7/25` and `((3pi)/2<theta<2pi`, how do you find `sin2theta`?

Answer 1

`sin 2t = - 336/625`

Explanation:

`sin t = - 7/25`
`cos^2 t = 1 - sin^2 t = 1 - 49/625 = 576/625`
`cos t = +- 24/25`
Since t is in Quadrant 4, cos t is positive.
`sin 2t = 2sin t.cos t = (2)(-7/25)(24/25) = - 336/625`