Parametrization of the Circle

[AuSmith]

The most common parametrization of the circle is

[unparseable or potentially dangerous latex formula]

Though, this is not rational (sin(t) and cos(t) cannot be expressed as a quotient of two polynomials). Find a rational parametrization. I.e. one with

[unparseable or potentially dangerous latex formula]

where [unparseable or potentially dangerous latex formula] are all polynomials.

[suchenzang]

I read an article on this a while back regarding the parametrization of a unit circle. The author parametricized a circle by using (-1,0) as a reference point and then expressing the line that contained the point on the circle, (x,y), and (-1,0) using m (namely [unparseable or potentially dangerous latex formula] where m is the slope of the line). He then proceeded to solve for x using the pythagorean theorem ([unparseable or potentially dangerous latex formula] or [unparseable or potentially dangerous latex formula]) giving you [unparseable or potentially dangerous latex formula]. Solving for x in the second part of that equation you get [unparseable or potentially dangerous latex formula] and then solving for y from [unparseable or potentially dangerous latex formula] you get [unparseable or potentially dangerous latex formula].