Arcus tangent, written as atan or tan^1, is the inverse function to the tangent function. For given argument x (any real number) it returns a number y (from pi/2 to pi/2) such that tan(y) = x.
Approximation: Near 0 atan(x) can very rougly be approximated simply by x. For a large argument atan(x) can be approximated by pi/2  1/x (as atan's limit is pi/2). The following formula { created by me ~drummyfish } approximates atan with a poylnomial for nonnegative argument with error smaller than 2%:
atan(x) ~= (x * (2.96088 + 4.9348 * x))/(3.2 + 3.88496 * x + pi * x^2)
 y
pi/2 +
 _..''''''
 _.''
 .'
.+'+++++> x
_.' 0 1 2 3 4 5
_' 
.'' 
pi/2 +

plot of atan(x)
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