# Find cartesian equation from parametric equation

1. Mar 24, 2013

### trollcast

1. The problem statement, all variables and given/known data
A curve is defined by the parametric equations:

$$x=tan(t-1)\ \ \ \ \ \ \ y=cot^2(t+1)$$

2. Relevant equations
3. The attempt at a solution

I think rearranging the first equation for t gives:

$$t=tan^{-1}(x)+1$$

However that doesn't help me as I don't know how to simplify the equation I'd get if I sub t into the y equation?

2. Mar 24, 2013

### Staff: Mentor

Do you have to simplify the equation? You found an equation y=f(x).

3. Mar 24, 2013

### trollcast

I actually just realised that I've misread the equations so I can see how to solve it now.

The equations should be:

$$x=tan(t)-1\qquad y=cot^2(t)+1$$

So the solution would be:

$$tan(t)=x+1$$
$$y=\frac{1}{tan^2(t)}$$
$$y=\frac{1}{(x+1)^2}$$

4. Mar 24, 2013

### Dick

What happened to the '+1' in $y=cot^2(t)+1$?

5. Mar 24, 2013

### trollcast

Oops, so it should be:

$$x=tan(t)-1\qquad y=cot^2(t)+1\\ tan(t)=x+1\\ y - 1=\frac{1}{tan^2(t)}\\ y=\frac{1}{(x+1)^2} +1\\ y=\frac{(x+1)^2+1}{(x+1)^2}$$

6. Mar 24, 2013

Sure.