A unit circle is placed at the origin. At any point along the circle we can draw a tangent line and calculate its slope. Then we can plot (x-coordinate, slope). It seems to make this nice curved X shape. Can we make an equation for it?

Your task is to find an equation, without trigonometry.

Note: As interesting as it was to try drawing the shape on a whiteboard, I had to fight the urge to use trig for this equation. In fact, I think it has a nice parametric form using trig, so you could also find that. Or whatever you like. We were just playing around with some math.

What am I missing here?  The domain of the desired solution/plot should be -1 to 1 for a unit circle.  The range should be +- infinity, with the two infinities associated with x= +-1?  Not sure how the posted plot can have the values it has?

Edited on February 19, 2024, 5:33 pm

Posted by Kenny M on 2024-02-19 17:26:21