Trigonometric identities happen to be invented for triangles: sin, cosine and through them tangent.
Later at school I learnt that they are periodic and have wave appearance. Than in University I came across a new topic, the Fourier series that depends on sin and cosine. At the end I was exposed to Fourier transform and how than DFT and how central it is to the communication theory.
--> My question is this, and I REALLY want a big answer to it since I have thought about it for some years. If mankind had not developed trigonometric ratios for triangles, we would not have fourier series and fourier transform (originally a method for the heat differential equation) and thus not have concept of frequency spectrum. Would it also mean that the wave equation would not exist? In terms of the advancement mankind has made e.g through frequency analysis, communication systems and radars, telephones and internet and much more. Would all this not have developed if trigonometric rations did not exist?