# Parametric equation to cartesian

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1. Oct 5, 2014

### Mrencko

1. The problem statement, all variables and given/known data
I have this equation and i need to find the cartesian equation, so i apreciate your help

2. Relevant equations
X=cost ' y=2sin2t

3. The attempt at a solution
I am usign this

Sin2t=2costsint
So x+y/2=cost+2costsint
But i dont know what to do after,
I also try to solve that this way
Y/2=sin2t
Y/2=2costsint then sint=y/(4cost)
Y/2=2((x)y/4x)
When i isolate y i get y/y=3x-2

2. Oct 6, 2014

### Staff: Mentor

So y = 4sin(t)cos(t). What is y/x?

Ideally, you want to get something that involves sin2(t) + cos2(t), which equals 1, and eliminates the parameter t.

3. Oct 6, 2014

### Mrencko

Thanks for the help i juts figure out how to get rid of that parameter 1-cos alll div by 2

4. Oct 6, 2014

### Staff: Mentor

I doubt that will work.

5. Oct 6, 2014

### Mrencko

y=4xsint==>y^2=16x^2(1(cost)^2)=y^2=16x^2(1-x^2)

6. Oct 6, 2014

7. Oct 6, 2014

### Staff: Mentor

With one correction, that works. Where you have y2 = 16x2(1(cost)^2), it should be y2 = 16x2(1 - cos2(t)). Otherwise, what you ended with is the same as I got.

8. Oct 6, 2014

### Mrencko

Thanks thats it Sorry pal i have anoter problem i am doing x=sect y=tant
So what i need to do use the 1+tan^2=sec^2
Or use the sin/cos=tan and 1/cos = sec? I can get the solution

9. Oct 6, 2014

### LCKurtz

Using $1 + \tan^2\theta = \sec^2\theta$ is the obvious choice. But you should post new questions in new threads if you don't want to have your hand slapped by a moderator.

10. Oct 6, 2014