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arccot(z)

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3-d plot

Inverse trigonometric functions:

The inverse cotangent function w = arccot(z) gives the solutions of the equation z = cot(w). This function is multi-valued and the image above shows the principal part which is obtained by restricting the argument of z to the interval [-Pi,Pi]. There is a branch line between -i and +i. As z approaches these singularities, the absolute value of arccot(z) approaches infinity.