Question

How do you find sin 2x, cos 2x, and tan 2x from the given information: `tan x=-6/5` and x is in the second quadrant?

Answer 1

There is another way. Call tan x = t. Use the trig identity:

`cos 2x = (1 - t^2)/(1 + t^2)`, and `sin 2x = 2t/(1 + t^2)`
`cos 2x = (25 - 36)/(25 + 36) = -11/61`

`sin 2x = 2(-6/5)/(61/25) = -12(5)/61 = -60/61`

`tan 2x = sin (2x)/cos (2x) = 61/11`