Question

If `costheta=-4/5` and `pi/2<theta<pi`, how do you find `sin2theta`?

Answer 1

`- 24/25`

Explanation:

`cos t = -4/5`. Find sin t
`sin^2 t = (1 - cos^2 t) = 1 - 16/25 = 9/25`
`sin t = +- 3/5`
Since t is in Quadrant 2, then sin t is positive.
To find sin 2t, use trig identity
sin 2t = 2sin t.cos t
`sin 2t = 2(3/5)(-4/5) = - 24/25`