S3E37. Sine as an infinite product and its three applications

In this episode we will see why "most people" cannot handle mathematics by going over a rigorous-enough proof of the famous decomposition of the trigonometric function of sine into an infinite product, along with three popular applications of that decomposition. It takes us about 55 minutes, give or take, to develop the basic workable product and when you think that we are done that is when the real mathematics kicks in, we roll up the sleeves and go to work. The three popular applications of the result derived in this episode are 1) the Wallis formula for pi (1:36:55), 2) the decomposition of the sibling function of cosine into an infinite product (1:40:26) and 3) the reflection formula for the Gamma function (1:47:42).