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cos

Symbolic cosine function

Syntax

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 -4π to 4π.

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
f = [x*u.degree 2*u.radian];
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, variable, expression, or function, or as a vector or matrix of symbolic numbers, variables, expressions, or functions.

More About

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Cosine Function

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

cos(α)=adjacent sidehypotenuse=bh.

The cosine of a complex argument, α, is

cos(α)=eiα+eiα2.

See Also

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Introduced before R2006a