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Cotangent of angle in radians



Y = cot(X) returns the cotangent of elements of X. The cot function operates element-wise on arrays. The function accepts both real and complex inputs.

  • For real values of X, cot(X) returns real values in the interval [-∞, ∞].

  • For complex values of X, cot(X) returns complex values.


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Plot the cotangent function over the domain -π<x<0 and 0<x<π.

x1 = -pi+0.01:0.01:-0.01; 
x2 = 0.01:0.01:pi-0.01;
plot(x1,cot(x1),x2,cot(x2)), grid on

Calculate the cotangent of the complex angles in vector x.

x = [-i pi+i*pi/2 -1+i*4];
y = cot(x)
y = 1×3 complex

   0.0000 + 1.3130i  -0.0000 - 1.0903i  -0.0006 - 0.9997i

Input Arguments

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Input angle in radians, specified as a scalar, vector, matrix, multidimensional array, table, or timetable.

Data Types: single | double | table | timetable
Complex Number Support: Yes

Output Arguments

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Cotangent of input angle, returned as a real-valued or complex-valued scalar, vector, matrix, multidimensional array, table, or timetable.

More About

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Cotangent Function

The cotangent of an angle, α, defined with reference to a right angled triangle is

cot(α)=1tan(α)=adjacent sideopposite side=ba.


Right triangle with vertices A, B, and C. The vertex A has an angle α, and the vertex C has a right angle. The hypotenuse, or side AB, is labeled as h. The opposite side of α, or side BC, is labeled as a. The adjacent side of α, or side AC, is labeled as b. The cotangent of α is defined as the adjacent side b divided by the opposite side a.

The cotangent of a complex argument α is




  • In floating-point arithmetic, cot is a bounded function. That is, cot does not return values of Inf or -Inf at points of divergence that are multiples of pi, but a large magnitude number instead. This stems from the inaccuracy of the floating-point representation of π.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Version History

Introduced before R2006a

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See Also

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