According to http://mathworld.wolfram.com/SawtoothWave.html the sawtooth function can be plotted as
$$ f(x)=1/2-tan^{-1}[cot\frac{\pi x}{2L}] $$
and they add that $[x]$ is the floor function.
But when I plot $1/tan(cot(pi*floor(x)))$ for simplicity in Kalgebra, this is what I see. What am I missing?
The formula $tan^{-1}$ does not denote $1/\tan$. It denotes the inverse tangent function, also known as "arctan" (i.e., the function that takes a number $t$ and tells you what angle (between $-\pi/2$ and $\pi/2$) has $t$ as its tangent. Thus $\arctan(1) = \pi/4$, for instance.
Also: if you use "floor", you get the wrong picture; what's probably wanted is the "fractional part", which is $x - floor(x)$. See this desmos plot:
As you'll notice (perhaps), I left out the "cot"; that gives as a result an actual "curved" saw-tooth. TO get an ordinary sawtooth, $$ y=\frac{1}{2}-\arctan\left(\cot\left(\pi x\right)\right) $$ suffices, as this plot shows. Note that no "floor" function is needed.