Math Question Help!!!?

Question

If sin x= (-4/5) and cos x <0. Then what is tan x equal to?

a. 4/3
b.3/4
c.-4/3
d.-3/4

please show working.

Answer 1

Given that sinx = -4/5 = opposite side / hypotenuse and cosx < 0 

If hypotenuse = -5 then only we will get cosx <0

opposite side = 4

adjacent side = √((-5)^2 - 4^2)    [Since adjacent side = √((hypotenuse)^2 - (opposite side)^2)]

                      = √(25 - 16)

                      = √9

                      = 3

 

Therefore tanx = opposide side / adjacent side

                        = 4 / 3

Therefore the answer is (a).