The correct parametric equations are: $x = 2\cot (t), y = 2\sin^2(t)$

I originally called Texas Instruments for help because I was getting the wrong graph on my TI-84 but could get the right graph on the Desmond website.

The TI-calculator doesn't have a $\cot$ key but does have a $tan^{-1}$ key, while the Desmond site does accept $\cot$ as an argument.

So, on the TI-84 I entered the equations as: $x = 2\tan^{-1}(t), y = 2\sin(t)^2$ (note that $\sin^2$ cannot be entered, so the exponent is applied to the variable)

But that gives a curve quite different than the actual "Witch of Agnesi".

TI told me I had to enter the equations on the calculator as: $x = 2(1/tan(t)), y = 2\sin(t)^2$ And it worked! But they couldn't explain why.

Does anyone have any idea why this should be the case? Because, it appears the $\tan^{-1}(t)$ can never be used for $\cot(t)$. It has to be $\dfrac{1}{tan(t)}$. And, apparently, they aren't the same.