Question

How do you find the value of `sin2theta` given `costheta=4/5` and `270<theta<360`?

Answer 1

`-24/25`

Explanation:

Use the trig identity:
sin 2t = 2sin t.cos t
First, find sin t by the identity: `sin^2 t - 1 - cos ^2 t`
`sin^2 t = 1 - cos^2 t = 1 - 16/25 = 9/25`
`sin t = +- 3/5`.
Since t is in Quadrant VI, sin t is negative, then
`sin t = -3/5`
`sin 2t = 2sin t.cos t = 2(-3/5)(4/5) = - 24/25`