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Arcus Tangent

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 non-negative 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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