What is the tangent function?
I'm not asking what it does, and I'm not looking for "tan(angle)=opposite leg/adjacent leg". I'm asking what the actual function is. For instance, using degrees (not radians) tan(22.5)=20.5 - 1. What equation is 22.5 plugged into to get approximately 0.4142? tan(45)=1. What equation is 45 plugged into to get 1? I tried searching this on google but of course everything was "The tangent function is used for...." or "the tangent function equals the opposite over adjacent...." so I figured my best bet was here. Thanks!
PS: I'm pretty sure it uses integrals so it would be nice if you explained how those specific ones work out. Thanks again!