tan

Symbolic tangent function

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Syntax

tan(X)

Description

tan(X) returns the tangent function of X.

example

Examples

Tangent Function for Numeric and Symbolic Arguments

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

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

A = tan([-2, -pi, pi/6, 5*pi/7, 11])

A =
    2.1850    0.0000    0.5774   -1.2540 -225.9508

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

symA = tan(sym([-2, -pi, pi/6, 5*pi/7, 11]))

symA =
[ -tan(2), 0, 3^(1/2)/3, -tan((2*pi)/7), tan(11)]

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

vpa(symA)

ans =
[ 2.1850398632615189916433061023137,...
0,...
0.57735026918962576450914878050196,...
-1.2539603376627038375709109783365,...
-225.95084645419514202579548320345]

Plot Tangent Function

Plot the tangent function on the interval from $- π$ to $π$ .

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

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

Handle Expressions Containing Tangent Function

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

Find the first and second derivatives of the tangent function:

syms x
diff(tan(x), x)
diff(tan(x), x, x)

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

Find the indefinite integral of the tangent function:

int(tan(x), x)

ans =
-log(cos(x))

Find the Taylor series expansion of tan(x):

taylor(tan(x), x)

ans =
(2*x^5)/15 + x^3/3 + x

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

rewrite(tan(x), 'sincos')

ans =
sin(x)/cos(x)

Rewrite the tangent function in terms of the exponential function:

rewrite(tan(x), 'exp')

ans =
-(exp(x*2i)*1i - 1i)/(exp(x*2i) + 1)

Evaluate Units with `tan` Function

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

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

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

tanf =
[ tan((pi*x)/180), tan(2)]

You can calculate tanf 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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Tangent Function

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

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

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 tangent of α is defined as the opposite side a divided by the adjacent side b.

The tangent of a complex argument, α, is

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

Version History

Introduced before R2006a

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R2022a: Compute tangent of symbolic matrix functions

The tan function accepts an input argument of type symfunmatrix.

R2021a: Compute tangent of symbolic matrix variables

The tan function accepts an input argument of type symmatrix.

tan