Question

How does one find sin2x, cos2x, and tan2x if x is in quadrant IV and equals -2/`sqrt13`?

Answer 1

`sin 2x = - 12/13`
`cos 2x = 5/13`
`tan 2x = - 12/5`

Explanation:

`sin x = - 2/sqrt13` (x is in Quadrant 4). Find cos x
`cos ^2 x = 1 - sin^2 x = 1 - 4/13 = 9/13`
`cos x = 3/(sqrt13)` (because x is in Q. 4)
`sin 2x = 2sin x.cos x = 2(-2/sqrt13)(3/sqrt13) = -12/13`
`cos^2 2x = 1 - sin^2 2x = 1 - 144/169 = 25/169`
`cos 2x = 5/13`
`tan 2x = (sin 2x)/(cos 2x) = (-12/13)(13/5) = - 12/5`