Y = sinpi(X) computes
sin(X*pi) without explicitly computing X*pi. This
calculation is more accurate than sin(X*pi) because the floating-point
value of pi is an approximation of π. In particular:

Calculate the sine of X*pi using the normal sin function.

Y = sin(X*pi)

Y = 1×5
0 1.0000 0.0000 -1.0000 -0.0000

The results contain small numerical errors due to the fact that pi is a floating-point approximation of the true value of $\pi $. For instance, Y(3) is not exactly zero even though $\mathrm{sin}\left(\pi \right)=0$.

Y(3)

ans = 1.2246e-16

Use sinpi to calculate the same values. In this case, the results are exact.

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