Given tan x=3/4, find the value of cos x, if x is an acute angle?

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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.

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