Re: parametric: x = cos(t), y = sin(t)

Wed, 5 Dec 2007 23:39:34 +0100 (CET) from Daniel C. Bastos 
<dbast0s@[EMAIL PROTECTED]
>:
> In ``Calculus'' by James Stewart, 4th edition, chapter 11, section 1 (if
> I recall correctly), there's the argument that the pair of equations
> above describes a circle because ~``we can eliminate t by noticing that
> 
>                   x^2 + y^2 = cos^2(t) + sin^2(t) = 1;
> 
> But I was hoping for an algebraic construction from the pair of the
> equations that would reach
> 
>                              x^2 + y^2 = 1,
> 
> which gives me a clear elimination of t; but I only have my argument
> above, if correct. 

*If* correct?  It pretty clearly *is* correct, and is the standard 
way of reducing those particular equations to Cartesian form.

Do you find it unsatisfying because there's an element of inspiration 
involved? I agree, the first time you look at this problem it's not 
exactly routine, but then neither is factoring x^2-y^2 the very first 
time.

-- 
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
                                  http://OakRoadSystems.com/
"If there's one thing I know, it's men. I ought to: it's
been my life work."  -- Marie Dressler, in /Dinner at Eight/