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csc

Cosecant of input angle in radians

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Syntax

Y = csc(X)

Description

Y = csc(X) returns the cosecant of the elements of X. The csc function operates element-wise on arrays. The function accepts both real and complex inputs.

  • For real values of X, csc(X) returns real values in the interval [-∞, -1] and [1, ∞].

  • For complex values of X, csc(X) returns complex values.

example

Examples

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Open Live Script

Plot the cosecant function over the domain -π<x<0 and 0<x<π as shown.

x1 = -pi+0.01:0.01:-0.01; 
x2 = 0.01:0.01:pi-0.01;
plot(x1,csc(x1),x2,csc(x2)), grid on

Figure contains an axes object. The axes object contains 2 objects of type line.

Open Live Script

Calculate the cosecant of the complex angles in vector x.

x = [-i pi+i*pi/2 -1+i*4];
y = csc(x)
y = 1×3 complex

   0.0000 + 0.8509i   0.0000 + 0.4345i  -0.0308 - 0.0198i

Input Arguments

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Input angle in radians, specified as a scalar, vector, matrix, multidimensional array, table, or timetable.

Data Types: single | double | table | timetable
Complex Number Support: Yes

Output Arguments

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Cosecant of input angle, returned as a real-valued or complex-valued scalar, vector, matrix, multidimensional array, table, or timetable.

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

csc(α)=2ieiα−e−iα .

Tips

  • In floating-point arithmetic, csc is a bounded function. That is, csc does not return values of Inf or -Inf at points of divergence that are multiples of pi, but a large magnitude number instead. This stems from the inaccuracy of the floating-point representation of π.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Version History

Introduced before R2006a

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See Also

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