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.