Euler’s product formula for sine is

To visualize the convergence of the infinite product, let’s look at the error in approximating sin(π*x*) with the *N*th 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.