Question

How do you determine an exact value for cos(2x) when angle x lies in 3rd quadrant and `tanx=7/24`?

Answer 1

Call `tan x = t = 7/24`. Use the trig identity:`cos 2x = (1 - t^2)/(1 + t^2)`

`cos 2x = (1 - 49/576)/(1 + 49/576) = 527/625 = 0.84`

`cos 2x = 0.84 -> 2x = +- 32.50 deg`

Since x lies in Quadrant III, then we choose cos 2x = cos (32.50 + 360) = 0.84.

Note:`x = (360 + 32.50)/2 = 196.25` deg (Q. III)