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sin

Symbolic sine function

Syntax

Description

example

sin(X) returns the sine function of X.

Examples

Sine Function for Numeric and Symbolic Arguments

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

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

A = sin([-2, -pi, pi/6, 5*pi/7, 11])
A =
   -0.9093   -0.0000    0.5000    0.7818   -1.0000

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

symA = sin(sym([-2, -pi, pi/6, 5*pi/7, 11]))
symA =
[ -sin(2), 0, 1/2, sin((2*pi)/7), sin(11)]

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

vpa(symA)
ans =
[ -0.90929742682568169539601986591174,...
0,...
0.5,...
0.78183148246802980870844452667406,...
-0.99999020655070345705156489902552]

Plot Sine Function

Plot the sine function on the interval from -4π to 4π.

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

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

Handle Expressions Containing Sine Function

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

Find the first and second derivatives of the sine function:

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

Find the indefinite integral of the sine function:

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

Find the Taylor series expansion of sin(x):

taylor(sin(x), x)
ans =
x^5/120 - x^3/6 + x

Rewrite the sine function in terms of the exponential function:

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

Evaluate Units with sin Function

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

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

u = symunit;
syms x
f = [x*u.degree 2*u.radian];
sinf = sin(f)
sinf =
[ sin((pi*x)/180), sin(2)]

You can calculate sinf 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.

More About

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Sine Function

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

sin(α)=opposite sidehypotenuse=ah.

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 sine of α is defined as the opposite side a divided by the hypotenuse h.

The sine of a complex argument, α, is

sin(α)=eiαeiα2i.

Version History

Introduced before R2006a

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See Also

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