Question

Given tan theta = -2 and pi/2 < theta < pi; find cos2theta.

a. - 4/3
b.- 4/5
c. 3/4
d. - 3/5

PLEASE HELP ASAP

Answer 1

Cos 2theta = -3/5

Explanation:

Given that;

tan theta = -2

tan theta = -2/1 = opp/adj

hyp^2 = (-2)^2+1^2

hyp = √4+1

hyp = √5

sin theta = opp/hyp

sin theta = -2/√5

Cos theta = adj/hyp

Cos theta = -2/√5

Cos 2theta = 1-2sin^2 theta

Cos 2theta = 1- 2(-2/√5)^2

Cos 2theta = 1- 2(4/5)

Cos 2theta = 1- 8/5

Cos 2theta = (5-8)/5

Cos 2theta = -3/5