We start solving the problem by using the Pythagorean identity: sin^2(x) + cos^2(x) = 1. We know the value of cos(x) is 0.595, so to find sin(x), we rearrange the formula to:
sin(x) = sqrt(1 - cos^2(x))
Substituting the given value of cos(x), we have sin(x) = sqrt(1 - (0.595)^2) = 0.8037256994771288.
The value of sin(x) is positive because we know that if the cosine of an angle is positive, then the angle exists either in the first or fourth quadrant, and in our case, let's consider it in the first quadrant where both sine and cosine are positive.
Next, we use the definition of tangent, where tan(x) = sin(x) / cos(x). Substituting the calculated value of sin(x) and the given value of cos(x), we find
tan(x) = 0.8037256994771288 / 0.595 = 1.3507994949195443.
Lastly, we are asked to calculate the value of tan(x/4).
Considering that tangent is a periodic function with a period of pi, we can simplify tan(x/4) to be tan(x) / 4. Substituting our calculated value of tan(x), we get
tan(x/4) = 1.3507994949195443 / 4 = 0.3376998737298861.
So, if cos(x) = 0.595, the value of tan(x/4) will approximately equal to 0.3377.