cot

Symbolic cotangent function

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Syntax

cot(X)

Description

cot(X) returns the cotangent function of X.

example

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 $- π$ to $π$ .

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

Figure contains an axes object. The axes object contains an object of type functionline.

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
f = [x*u.degree 2*u.radian];
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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`X` — Input
symbolic number | symbolic scalar variable | symbolic matrix variable | symbolic expression | symbolic function | symbolic matrix function | symbolic vector | symbolic matrix

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

More About

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Cotangent Function

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

$cot (α) = \frac{1}{\tan (α)} = \frac{adjacent side}{opposite side} = \frac{b}{a} .$

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

$cot (α) = \frac{i (e^{i α} + e^{- i α})}{(e^{i α} - e^{- i α})} .$

Version History

Introduced before R2006a

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R2022a: Compute cotangent of symbolic matrix functions

The cot function accepts an input argument of type symfunmatrix.

R2021b: Compute cotangent of symbolic matrix variables

The cot function accepts an input argument of type symmatrix.

cot