sinpi

Compute sin(X*pi) accurately

Syntax

Y = sinpi(X)

Description

Y = sinpi(X)computessin(X*pi)without explicitly computingX*pi. This calculation is more accurate thansin(X*pi)because the floating-point value ofpiis an approximation of π. In particular:

For integers,sinpi(n)is exactly zero.
For odd integers,sinpi(n/2)is +1 or -1.

Examples

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Calculate Sine of Multiples of π

Open Live Script

Compare the accuracy ofsinpi(X)vs.sin(X*pi).

Create a vector of values.

X = [0 1/2 1 3/2 2];

Calculate the sine ofX*piusing the normalsinfunction.

Y = sin(X*pi)

Y =1×50 1.0000 0.0000 -1.0000 -0.0000

The results contain small numerical errors due to the fact thatpiis a floating-point approximation of the true value of $π$ . For instance,Y(3)is notexactlyzero even though $\sin (π) = 0$ .

Y(3)

ans = 1.2246e-16

Usesinpito calculate the same values. In this case, the results are exact.

Z = sinpi(X)

Z =1×50 1 0 -1 0

Z(3)

ans = 0

Input Arguments

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`X`—Input array
scalar|vector|matrix|multidimensional array

Input array, specified as a scalar, vector, matrix, or multidimensional array.

Data Types:single|double
Complex Number Support:Yes

Extended Capabilities

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, seeTall Arrays.

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

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, seeRun MATLAB Functions on a GPU(Parallel Computing Toolbox).

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, seeRun MATLAB Functions with Distributed Arrays(Parallel Computing Toolbox).

MATLAB Documentation

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