Given tan x=3/4, find the value of cos x, if x is an acute angle?
We know that the tangent function is the ratio of the opposite cathetus and adjacent cathetus or the ratio of sine and cosine functions.
tan x = sin x/cos x
We know, from enunciation, that tan x = 3/4
3/4 = sin x/cos x
We'll apply the fundamental formula of trigonometry:
(tan x)^2 + 1 = 1/(cos x)^2
cos x = 1/sqrt((tan x)^2 + 1)
cos x = 1/sqrt[(3/4)^2 + 1]
cos x = 1/sqrt [(9+16)/4] => cos x = 1/sqrt (25/4) => cos x = 2/5 or cos x = -2/5
Since x angle is an acute angle, then it is located in the 1st quadrant.
In the 1st quadrant, the value of the cosine angle is positive, therefore we'll keep only the positive value for cos x = 2/5.
I think that the answer of giorgiana1976 is technically right but she made a very small mistake: (3/4)^2 + 1 = 9/16 + 16/16 = 25/16 and the sqrt of 25/16 is 5/4, so the answer I think is 4/5.