Converting a Cartesian equation to polar form

[rdioface]

Homework Statement

Convert the following Cartesian equation to polar form.
x^2/9 + y^2/4 = 1

Homework Equations

r*cos(t)=x
r*sin(t)=y
r=Sqrt(x^2 + y^2)
y/x = Arctan(t)

The Attempt at a Solution

I get ugly looking things like r^2(cos^2(t)/9 + sin^2(t)/4) = 1 but being a simple ellipse (edit: duh) I expect a cleaner answer.

 

[Mark44]

Homework Statement

Convert the following Cartesian equation to polar form.
x^2/9 + y^2/4 = 1

Homework Equations

r*cos(t)=x
r*sin(t)=y
r=Sqrt(x^2 + y^2)
y/x = Arctan(t)

The Attempt at a Solution

I get ugly looking things like r^2(cos^2(t)/9 + sin^2(t)/4) = 1 but being a simple hyperbola I expect a cleaner answer.

It's actually an ellipse, not a hyperbola.

Multiply both sides by 36 to get rid of the fractions. After that you get
4r²cos²(t) + 9r²sin²(t) = 36

You can break up the sin² term into 4r²sin²(t) + 5r²sin²(t). Does that give you any ideas?

 

[rdioface]

That gets me to r^2(4 + 5sin^2(t))=36. Are there any further steps to be done?

 

[Mark44]

Solve for r.

 

[rdioface]

Alright thanks, it seemed like there might have been some crazy trig identity I was missing or something.