# Find a cartesian equation

• Apr 19th 2010, 02:01 PM
DarthPipsqueak
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)

• Apr 19th 2010, 02:03 PM
dwsmith
Quote:

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
• Apr 19th 2010, 02:23 PM
DarthPipsqueak
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.
• Apr 19th 2010, 02:29 PM
skeeter
Quote:

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)

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