Documentation

# cot

## Description

example

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.

## Examples

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Plot the cotangent function over the domain $-\pi and $0 .

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, or multidimensional array.

Data Types: single | double
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 or multidimensional array.

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### Cotangent Function

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

.

The cotangent of a complex argument α is

$\text{cot}\left(\alpha \right)=\frac{i\left({e}^{i\alpha }+{e}^{-i\alpha }\right)}{\left({e}^{i\alpha }-{e}^{-i\alpha }\right)}\text{\hspace{0.17em}}.$

.

## Tips

• 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.