Question

Given `sin theta =-3/5` and `pi<theta<(3pi)/2`, how do you find `sin 2theta`?

Answer 1

`24/25`

Explanation:

`sin t = -3/5`. Find cos t
Use trig identity: `cos^2 t = 1 - sin^2 t`
`cos^2 t = 1 - 9/25 = 16/25` --> `cos t = +- 4/5`
Since t is in Quadrant III, cos t and sin t are both negative.
To find sin 2t, use the trig identity:
`sin 2t = 2sint.cos t`
`sin 2t = 2(-3/5)(-4/5) = 24/25`