Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.
Section 12.12 : Cylindrical Coordinates
5. Convert the following equation written in Cylindrical coordinates into an equation in Cartesian coordinates.
\[4\sin \left( \theta \right) - 2\cos \left( \theta \right) = \frac{r}{z}\]Show All Steps Hide All Steps
Start SolutionThere really isn’t a whole lot to do here. All we need to do is to use the following \(x\) and \(y\) polar conversion formulas in the equation where (and if) possible.
\[x = r\cos \theta \hspace{0.5in}y = r\sin \theta \hspace{0.5in}{r^2} = {x^2} + {y^2}\] Show Step 2To make the conversion a little easier let’s multiply the equation by \(r\) to get,
\[4r\sin \left( \theta \right) - 2r\cos \left( \theta \right) = \frac{{{r^2}}}{z}\] Show Step 3Now let’s use the formulas from Step 1 to convert the equation into Cartesian coordinates.
\[\require{bbox} \bbox[2pt,border:1px solid black]{{4y - 2x = \frac{{{x^2} + {y^2}}}{z}}}\]