how do i find cosX if i am given sin x= -4/5 and tan <o???

Answer 1

Isn't the sine negative in the III and IV quadrants, and isn't the tangent negative in the II and IV quadrant.
So clearly our angle x must be in IV

Make a triangle using sinx = 4/5
The third side (the adjacent) would be 3 and cosx = 3/5, but we are in quadrant IV, and in IV the cosine is positive, so ..
cosx = 3/5

Answer 2

cos^2x+ sin^2 x=1

the tangent being negative tells you which of the two answers is correct.