# Thread: Find a cartesian equation

1. ## Find a cartesian equation

So my professor isn't very good at teaching, and the book isn't very helpful with this as either. It only provides the simplest of examples, and I am still confused as to how to find Cartesian equations to these two problems:

r=4sin(theta) + 4cos(theta)

and

r=6tan(theta)sec(theta)

2. Originally Posted by DarthPipsqueak
So my professor isn't very good at teaching, and the book isn't very helpful with this as either. It only provides the simplest of examples, and I am still confused as to how to find Cartesian equations to these two problems:

r=4sin(theta) + 4cos(theta)

and

r=6tan(theta)sec(theta)

$\displaystyle x=rcos$
$\displaystyle y=rsin$
$\displaystyle x^2+y^2=r^2$

Use these identities

3. So I was able to figure out the first equation (4sin(theta) + 4cos(theta)) but I am still trying to figure out the second one. I'm working on it, but I think I'm stuck.

4. Originally Posted by DarthPipsqueak
So my professor isn't very good at teaching, and the book isn't very helpful with this as either. It only provides the simplest of examples, and I am still confused as to how to find Cartesian equations to these two problems:

r=4sin(theta) + 4cos(theta)

and

r=6tan(theta)sec(theta)

$\displaystyle r=6\tan{\theta}\sec{\theta}$
$\displaystyle r = \frac{6\sin{\theta}}{\cos^2{\theta}}$
$\displaystyle r\cos^2{\theta} = 6\sin{\theta}$
$\displaystyle r^2\cos^2{\theta} = 6r\sin{\theta}$
$\displaystyle (r\cos{\theta})^2 = 6r\sin{\theta}$
$\displaystyle x^2 = 6y$