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Helping without trig (Posted on 2024-02-19) Difficulty: 3 of 5
A very bright young student of mine who has not learned trigonometry presented me with this question she came up with.

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.

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  Subject Author Date
Puzzle AnswerK Sengupta2024-02-19 22:29:43
re(2): solutionCharlie2024-02-19 18:17:47
re: solutionKenny M2024-02-19 17:26:21
SolutionsolutionCharlie2024-02-19 13:44:47
Some ThoughtsDoing some algebraLarry2024-02-19 12:06:12
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