A Visual Guide to Trigonometric Functions and their Reciprocals
Sine, Cosine and Tangent (AKA sin, cos and tan) are trigonometric functions we learn at school to solve angles and sides of a triangle using some infamous and quirky acronyms “SOHCAHTOA!”. Although it very much helps us interrogate a triangle and sketch out waves, we lose so much understanding of the origin of these functions and they simply remain as a BlackBox of understanding in our minds as to what does sin, cos and tan do when given a number? Furthermore, we lose any explanation as to where they come from? (other than being those exciting buttons on your calculator!)
There are several ways to explain what sin, cos and tan are but the unit circle method provides one to perfectly visually demonstrate where these fundamental and ubiquitous functions come from without having to get bogged down into the details of its math or a mention of pi! So let’s see how they come about all using a simple unit circle of the form x²+y² =1 in an animated and visual fashion. This can be then further extended to understand where the inverse trigonometry functions secant, cosecant and cotangent (AKA sec, cosec and cot) come from.
