Parametric to Cartesian Conversion: Troubleshooting and Identifying Mistakes

[autre]

I have the parametric function x(t) = (1-t^2)/(1+t^2), y(t) = 2t/(1+t^2) and need to eliminate the parameter and find a Cartesian equation.

I've tried to substitute t = tan u, then x(t) = cos(2u) and y(t) = tan(2u). From that I get y = sin(2x)/x. However, when I entered the original parametric function into a grapher, I get an entirely different graph. Where did I go wrong?

 

[eumyang]

I've tried to substitute t = tan u, then x(t) = cos(2u) and y(t) = tan(2u).

I'm not getting that for the y(t) equation. I think it's because you got your identity confused.
$$\frac{2\tan u}{1 - \tan^2 u} = \tan 2u$$
(minus in the denominator)

But here we have:
$$y(t) = \frac{2\tan u}{1 + \tan^2 u} = \frac{2\tan u}{\sec^2 u} = ...$$