Where do the trigonometric ratios come from?

This video describes where the three trigonometric ratios of sine, cosine and tangent come from. It discusses why trigonometry is important as well as some of the great achievements of this important branch of mathematics; one of which is Joseph Fourier's discovery that non-sinusoidal waves can be constructed using sine waves. The video then proves the simplest of all trigonometric identities (sin / cos = tan). It then discusses how a calculator calculates these ratios and ends with a simple way to calculate the value of pi using Madhava's simple series pi = 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - ... including a simple implementation of this series in the Python programming language.