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.

u = symunit;
syms x
f = [x*u.degree 2*u.radian];
cotf = cot(f)

cotf =
[ cot((pi*x)/180), cot(2)]