If tanx= -1/3, cos>0, then how do you find cos2x?

2 Answers
Jun 26, 2018

cos 2x = 4/5cos2x=45

Explanation:

tan x = -1/3tanx=13, and cos x > 0. First, find cos x
Use trig identity:
cos ^2 x = 1/(1 + tan^2 x) = 1/(1 + 1/9) = 9/10cos2x=11+tan2x=11+19=910
cos x = 3/sqrt10 = (3sqrt10)/10cosx=310=31010 (cos x > 0)
Next, use trig identity:
cos 2x = 2cos^2 x - 1cos2x=2cos2x1
In this case:
cos 2x = 2(9/10) - 1 = 9/5 - 5/5 = 4/5cos2x=2(910)1=9555=45

Jun 26, 2018

cos 2x = 4/5 = 0.8cos2x=45=0.8

Explanation:

Identity : cos 2x = (1 - tan^2 x) / (1 + tan^2 x)cos2x=1tan2x1+tan2x

Given : tan x = -1/3tanx=13

:. cos 2x = (1 - (-1/3)^2) / (1 + (-1/3)^2)

cos 2x = (1 - 1/9) / (1 + 1/9)

cos 2x = (8/9) / (10/9) = 8/10 = 4/5 = 0.8