What is cos(Θ)?

Question

If tan(Θ)= -1/2 and π/2 < Θ < π, what is cos(Θ)?

Answer 1

I can draw this triangle in the second quadrant. The adjacent leg is -2 and the opposite leg is 1. To find cos I will need the hypotenuse.

a²+b²=c² can be used

1²+2²=c²

1+4 = c²

5 = c²

c=√5

cos = adjacent/hypotenuse = -2/√5

Rationalized: -2√5/5