Question

How do you find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas?

sin u= -4/5, 3`pi`/2 < u < 2`pi`

Answer 1

`sin 2u = - 12/25`
`cos 2u = -9/15`
`tan 2u = 4/5`

Explanation:

`sin u = -4/5`, and u lies in Quadrant 4.
`cos^2 u = 1 - sin^2 u = 1 - 16/25 = 9/25`
`cos u = 3/5` (cos u is positive because u lies in Q.4)
`sin 2u = 2sin u.cos u = (-4/5)(3/5) = - 12/25`
`cos^2 2u = 1 - sin^2 2u = 1 - 144/225 = 81/225`
`cos 2u = - 9/15`
(cos 2u is negative because u = - 53.13, so, 2u lies in Quadrant 3)
`tan 2u = (sin 2u)/(cos 2u) = (-12/25)/(-15/9) = 4/5`