Question

If sinx=4/5 and x is in quadrant 2, what is tan2x?

Answer 1

Using the Pythagorean Theorem allows us to solve for the missing side.

Since we're in the second quadrant, our length along the x-axis is negative.

Answer 2

Recall your Tangent Double Angle Identity:\[\Large\rm \tan2x=\frac{2\tan x}{1-\tan^2x}\]

Answer 3

So just use the triangle to simplify this expression: \(\Large\rm \dfrac{2\tan x}{1-\tan^2x}\)

Oh also, in the picture I should called the angle x, not theta. My bad.