Question

If sinx = -3/5, x is in quadrant III, then how do you find tan2x?

Answer 1

`24/7`

Explanation:

`sin x = - 3/5` . Find cos x by identity: `cos^2 x = 1 - sin^2 x`
`cos^2 x = 1 - 9/25 = 16/25`
`cos x = +- 4/5.`
Since x is in Quadrant III, then cos x is negative.
`tan x = sin/(cos) = (-3/5)(-5/4) = 3/4`
Use trig identity:
`tan 2x = (2tan x)/(1 - tan^2 x)`
`tan 2x = (6/4)/(1 - 9/16) = (6/4)(16/7) = 24/7`