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Symbolic cosecant function




csc(X) returns the cosecant function of X.


Cosecant Function for Numeric and Symbolic Arguments

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

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

A = csc([-2, -pi/2, pi/6, 5*pi/7, 11])
A =
   -1.0998   -1.0000    2.0000    1.2790   -1.0000

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

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

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

ans =
[ -1.0997501702946164667566973970263,...

Plot Cosecant Function

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

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

Handle Expressions Containing Cosecant Function

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

Find the first and second derivatives of the cosecant function:

syms x
diff(csc(x), x)
diff(csc(x), x, x)
ans =
ans =
1/sin(x) + (2*cos(x)^2)/sin(x)^3

Find the indefinite integral of the cosecant function:

int(csc(x), x)
ans =

Find the Taylor series expansion of csc(x) around x = pi/2:

taylor(csc(x), x, pi/2)
ans =
(x - pi/2)^2/2 + (5*(x - pi/2)^4)/24 + 1

Rewrite the cosecant function in terms of the exponential function:

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

Evaluate Units with csc Function

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

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

u = symunit;
syms x
f = [x* 2*u.radian];
cosecf = csc(f)
cosecf =
[ 1/sin((pi*x)/180), 1/sin(2)]

You can calculate cosecf 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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Cosecant Function

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

csc(α)=1sin(α)=hypotenuseopposite side=ha.

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

The cosecant of a complex argument, α, is


Version History

Introduced before R2006a

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See Also

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