Euler’s product formula for sine is
To visualize the convergence of the infinite product, let’s look at the error in approximating sin(πx) with the Nth partial product of the infinite product, i.e.
Here’s a plot of the partial products.
We knew before making the plot that the error had to go to zero as N increases; otherwise Euler’s product wouldn’t converge. But it’s interesting to visualize how the error goes to zero.