Question

Question #28924

Answer 1

`sin(2x)=-24/25`
`cos(2x)=7/25`
`tan(2x)=-24/7`

Explanation:

Since `90^circ < x < 180^circ` and `cosx=-4/5` we know that `sinx = 3/5`. (I drew a triangle to find that.)

`sin(2x)=2sin(x)cos(x) = 2(3/5)(-4/5)=-24/25`.
`cos(2x)=2cos^2(x)-1=2(-4/5)^2-1=2(16/25)-1`
`cos(2x)=7/25`

Since `tan(2x)=sin(2x)/cos(2x)` we know:

`tan(2x)= (-(24/25))/(7/25)=-24/25 * 25/7 = -24/7`.