Question

If tan(x) =4/3 and x is in quadrant III, find cos(x

Answer 1

in third quadrent cos will be negative

Answer 2

cosx= -3/5

Answer 3

Part 1. Quadrant 3 - Cosine is negative. This is because Cosine = Base/Hypotenuse. In Quadrant 3, Base is Negative (measured along negative direction of X Axis).
We'll come back to Part 1.

Part 2. We know that Tan(x) = Sin(x)/Cos(x). Let A=Sin(x) and B=Cos(x). Thus, A/B = 4/3. Also, A^2 + B^2 = 1. Solve these two equations, tie it up with Part 1 and, voila!