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What am I missing in eliminating variables from parametric equations? [res]

Hi,

I just signed up to try out Mathematica Online. I'm trying to work through some examples to learn how to use it.

To experiment with eliminating variables in parametric equations, I tried the following standard example:

eqn={x==rCos[t],y==rSin[t]}

Eliminate[eqn,{r,t}]

Using "Convert To" -> "InputForm" in the function menu on the righthand side of the input screen for the 2nd line, I got this output:

InverseFunction[rSin, 1, 1][y] == InverseFunction[rCos, 1, 1][x]

(I don't know how to paste the program's actual output into this post editor.)

I expected to get the standard equation of a circle:

x^2 + y^2 = r^2

What am I missing?

Thanks!

POSTED BY: Alan Feuerbacher
2 Replies

Well, white space for one thing. The product r*Cos[t], which may be written r Cos[t], is definitely not the same thing as rCos[t] (notice lack of a space).

Then there is the problem that you can only eliminate one variable if given two equations. In attempting to eliminate two of them, Eliminate might not select the one you really want.

This may be more to your liking.

`eqn = {x == r Cos[t], y == r Sin[t]}
Eliminate[eqn, {t}]

Out[695]= {x == r Cos[t], y == r Sin[t]}

During evaluation of In[695]:= Eliminate::ifun: Inverse functions are being used by Eliminate, so some solutions may not be found; use Reduce for complete solution information. >>

Out[696]= r^2 - y^2 == x^2`
POSTED BY: Daniel Lichtblau

Thank you!

The white space was my main problem, followed by a bit of a brain glitch. Various other test examples work now.

POSTED BY: Alan Feuerbacher
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