will someone please teach me how to convert rectangular equations to polar and vice versa ... my test is 2mm and its already 2 AM ):

Question

will someone please teach me how to convert rectangular equations to polar and vice versa ... my test is 2mm and its already  2 AM ):

dumbcow · Answer

well there are 4 identities you will use:
$$x^2 + y^2 = r^2$$
$$x = r \cos \theta$$
$$y =r \sin \theta$$
$$\tan \theta = \frac{y}{x}$$
the converting involves multiple substitutions

dumbcow · Answer

Here is example:
$$y = 4x +3$$
convert to polar
$$r \sin \theta = 4r \cos \theta +3$$
solve for r
$$r = \frac{3}{\sin \theta - 4 \cos \theta}$$