How to find tan(2x)

Question

If cos= -4/5, and 180° < x < 270°, what is tan(2x)?

Answer 1

cos143.13=-.8

cos36.87=.8

cos216.87=-.8

If x=216.87; tan433.74=3.428617....

Answer 2

Here's the double-angle formula for tangent:

We are given the cos as -4/5. This tells us that we have a 3-4-5 right triangle. cos is adjacent/hypotenuese, so we know that the opposite is -3 (O and A both - )

Thus the tangent is -3/-4 = 3/4

Plug into the above formula:

tan2α = 2* 3/4 ) / 1- (3/4)²

3/2 / (1 - 9/16) = ( 3/2 ) / (7/16) = 24/7 = 3.4286

With a calculator, the easy out is tan (2*arccos(-4/5)) = tan(2 * 216.87) = 3.4286