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

2 Answers
Jun 26, 2018

Answer:

#cos 2x = 4/5#

Explanation:

#tan x = -1/3#, and cos x > 0. First, find cos x
Use trig identity:
#cos ^2 x = 1/(1 + tan^2 x) = 1/(1 + 1/9) = 9/10#
#cos x = 3/sqrt10 = (3sqrt10)/10# (cos x > 0)
Next, use trig identity:
#cos 2x = 2cos^2 x - 1#
In this case:
#cos 2x = 2(9/10) - 1 = 9/5 - 5/5 = 4/5#

Jun 26, 2018

Answer:

#cos 2x = 4/5 = 0.8#

Explanation:

Identity : #cos 2x = (1 - tan^2 x) / (1 + tan^2 x)#

Given : #tan x = -1/3#

#:. 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#