Main Content

cot

Symbolic cotangent function

Syntax

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 -π to π.

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
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

collapse all

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

More About

collapse all

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.

.

The cotangent of a complex argument α is

cot(α)=i(eiα+eiα)(eiαeiα).

.

See Also

| | | | | | | | | |

Introduced before R2006a