Changing polar equations to rectangular equations?

[steener]

changing polar equations to rectangular equations?

Can somebody please explain to me, how I would convert:

?=?/2 into a rectangular equation?

Along with: r=sin?, r=6cos+sin?, r(squared)sin2?=2


Your help would be greatly appreciated!

 

[malawi_glenn]

Ask in the home-work section, not here.

This thread will be moved, so don't make a new one.

 

[HallsofIvy]

Can somebody please explain to me, how I would convert:

?=?/2 into a rectangular equation?

Along with: r=sin?, r=6cos+sin?, r(squared)sin2?=2


Your help would be greatly appreciated!

Unfortunately your "special characters" just show up as "?" to me. I would guess that the ? in the last three are "theta": $\theta$ in LaTex, but I have no idea what the "?" in ?= ?/2 are- I presume they are different or the equation is trivial.

I presume that you know (or else you wouldn't be attempting these problems) that $x= r cos(\theta)$ and $y= r sin(\theta)$. Looking at the first one, my thought would be to multiply both sides by r: $r^2= r sin(\theta)$ which, since $r^2= r^2(cos^2(\theta)+ sin^2(\theta)= x^2+ y^2$, is just $x^2+ y^2= y$, the equation of a circle.

For $r= 6cos(\theta)+ sin(theta)$, same thing: multiply both sides by r to get $r^2= 6r cos(\theta)+ r sin(\theta)= x^2+ y^2= 6x+ y$, again the equation of a circle.

For $r^2 sin(2\theta)= 2$, use the fact that $sin(2\theta)= 2sin(\theta)cos(\theta)$.