# cot

Symbolic cotangent function

## Description

example

cot(X) returns the cotangent function of X.

## Examples

### Cotangent Function for Numeric and Symbolic Arguments

Depending on its arguments, cot returns floating-point or exact symbolic results.

Compute the cotangent function for these numbers. Because these numbers are not symbolic objects, cot returns floating-point results.

A = cot([-2, -pi/2, pi/6, 5*pi/7, 11])
A =
0.4577   -0.0000    1.7321   -0.7975   -0.0044

Compute the cotangent function for the numbers converted to symbolic objects. For many symbolic (exact) numbers, cot returns unresolved symbolic calls.

symA = cot(sym([-2, -pi/2, pi/6, 5*pi/7, 11]))
symA =
[ -cot(2), 0, 3^(1/2), -cot((2*pi)/7), cot(11)]

Use vpa to approximate symbolic results with floating-point numbers:

vpa(symA)
ans =
[ 0.45765755436028576375027741043205,...
0,...
1.7320508075688772935274463415059,...
-0.79747338888240396141568825421443,...
-0.0044257413313241136855482762848043]

### Plot Cotangent Function

Plot the cotangent function on the interval from $-\pi$ to $\pi$.

syms x
fplot(cot(x),[-pi pi])
grid on

### Handle Expressions Containing Cotangent Function

Many functions, such as diff, int, taylor, and rewrite, can handle expressions containing cot.

Find the first and second derivatives of the cotangent function:

syms x
diff(cot(x), x)
diff(cot(x), x, x)
ans =
- cot(x)^2 - 1

ans =
2*cot(x)*(cot(x)^2 + 1)

Find the indefinite integral of the cotangent function:

int(cot(x), x)
ans =
log(sin(x))

Find the Taylor series expansion of cot(x) around x = pi/2:

taylor(cot(x), x, pi/2)
ans =
pi/2 - x - (x - pi/2)^3/3 - (2*(x - pi/2)^5)/15

Rewrite the cotangent function in terms of the sine and cosine functions:

rewrite(cot(x), 'sincos')
ans =
cos(x)/sin(x)

Rewrite the cotangent function in terms of the exponential function:

rewrite(cot(x), 'exp')
ans =
(exp(x*2i)*1i + 1i)/(exp(x*2i) - 1)

### Evaluate Units with cot Function

cot numerically evaluates these units automatically: radian, degree, arcmin, arcsec, and revolution.

Show this behavior by finding the cotangent of x degrees and 2 radians.

u = symunit;
syms x
cotf = cot(f)
cotf =
[ cot((pi*x)/180), cot(2)]

You can calculate cotf by substituting for x using subs and then using double or vpa.

## Input Arguments

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Input, specified as a symbolic number, variable, expression, or function, or as a vector or matrix of symbolic numbers, variables, expressions, or functions.

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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

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

.