# cos

Symbolic cosine function

## Description

example

cos(X) returns the cosine function of X.

## Examples

### Cosine Function for Numeric and Symbolic Arguments

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

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

A = cos([-2, -pi, pi/6, 5*pi/7, 11])
A =
-0.4161   -1.0000    0.8660   -0.6235    0.0044

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

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

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

vpa(symA)
ans =
[ -0.41614683654714238699756822950076,...
-1.0,...
0.86602540378443864676372317075294,...
-0.62348980185873353052500488400424,...
0.0044256979880507857483550247239416]

### Plot Cosine Function

Plot the cosine function on the interval from $-4\pi$ to $4\pi$.

syms x
fplot(cos(x),[-4*pi 4*pi])
grid on

### Handle Expressions Containing Cosine Function

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

Find the first and second derivatives of the cosine function:

syms x
diff(cos(x), x)
diff(cos(x), x, x)
ans =
-sin(x)

ans =
-cos(x)

Find the indefinite integral of the cosine function:

int(cos(x), x)
ans =
sin(x)

Find the Taylor series expansion of cos(x):

taylor(cos(x), x)
ans =
x^4/24 - x^2/2 + 1

Rewrite the cosine function in terms of the exponential function:

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

### Evaluate Units with cos Function

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

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

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

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

## Input Arguments

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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.

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### Cosine Function

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

The cosine of a complex argument, α, is

$\text{cos}\left(\alpha \right)=\frac{{e}^{i\alpha }+{e}^{-i\alpha }}{2}\text{\hspace{0.17em}}.$

## Version History

Introduced before R2006a

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