Modify tan(x) function to be sharper On the right is `-tan(x) + Pi/2` function. On the left is a function i am trying to create which is a "sharper" version of the function on the right. !1 Any idea how to get the left function ? It doesn't have to be a modified version of `tan` but i think it is easier this way, i could be wrong.

This function should go through the points $(-1,\pi), (0, \frac\pi2), (1,0)$. It is quite easy to see why. It is also just $\tan$ scaled and translated, so the general shape is the same.

$$f(x)=(\tan(1)-\tan(x))\frac{\pi}{2\tan(1)}$$