1

I need to compute the slope (m) of the nine points of a circumference divided in equal parts. But a circumference is not a function.

I make a Geometric approach but I am not satisfied with it.

Do anyone know how to solve it analytically.

enter image description here

Haizum Skallah
  • 653
  • 1
    That should be $\tan \frac{2k\pi}{9}$, $0\le k\le 8$. – Hagen von Eitzen Aug 03 '13 at 14:00
  • 1
    Parametrize your shape, here a circle, as in $x=r\cos t, y=r\sin t$ and then differentiate that set of equations. – Maesumi Aug 03 '13 at 14:01
  • I can do the differentiation there. But, I do not know how to Parametrize the shape... I am in my first course of calculus in my first year. Can you help me understand the parametrization process? Where can I have more information? – Haizum Skallah Aug 03 '13 at 14:15
  • I am not sure why you are not satisfied with a geometric approach. It is much more suitable for this problem. – Tunococ Aug 04 '13 at 00:16
  • It is only because this problem is a part of something else. I am trying to solve it in a formal way. I need to make it a computable process. If knowing this you have an opinion I will be very glad to hear it. – Haizum Skallah Aug 04 '13 at 03:26

2 Answers2

1

Here is the equation for a circle, placed at the origin with a radius $ r $: $ x^2+y^2=r^2 $. Solve for $y$, making it the function of $ x $: $y (x)=\pm \sqrt{r^2-x^2}$. Now differentiate with respect to $ x $ and plug in the $ x $-values of the points in question into the expression you got.

Constantine
  • 1,429
1

From the equation of a circle, you can get $y^2=r^2-x^2 \implies y=\pm \sqrt{r^2-x^2}$. Now you can use implicit differentiation. It involves using the chain rule in order to differentiate. This is a technique taught in Calculus I, so hopefully you know it.

Check this link out as well- it is exactly what you are doing: https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/implicitdiffdirectory/

Sujaan Kunalan
  • 10,944