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# acot

computes the element-wise inverse cotangent of the argument.

### Syntax

`y = acot(x)`

### Arguments

x

a real or complex array.

y

a real or complex array.

### Description

Computes the element-wise inverse cotangent of the argument. For real argument the result is real.

The following equalities hold: ```acot(z) = %pi-acot(-z)=%pi/2-atan(z)=%i*acoth(%i*z)+%pi/2*(1-csgn(z+%i))``` .

### Examples

```x=[1 2 -2 sqrt(2) -sqrt(2) 2/sqrt(3) -2/sqrt(3) -1];
acot(x)/%pi```

### See also

• acotd — computes the element-wise inverse cotangent of the argument, result in degree.
• cotg — cotangent
• csgn — returns the sign of a vector of real of complex values
• acoth — element wise hyperbolic cotangent inverse.
• atan — 2-quadrant and 4-quadrant inverse tangent

### References

• Kahan, W., "Branch cuts for complex elementary functions, or, Much ado about nothing's sign bit", Proceedings of the joing IMA/SIAM conference on The State of the Art in Numerical Analysis, University of Birmingham, A. Iserles and M.J.D. Powell, eds, Clarendon Press, Oxford, 1987, 165-210.

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