How would I change this rsin(theat)=3 into rectangular coordinate, do I just solve for r and then plug it into to y=rsin(theta) and x=rcos(theta)?

Question

anonymous · Answer

Start by multiplying both sides of rsin(theta)=3 by r

anonymous · Answer

$$rsin(\theta)=3 $$
$$r^2\sin(\theta)=3r$$
but $$r^2=x^2+y^2$$ and $$r=\sqrt(x^2+y^2)$$
and $$\sin(\theta)=y/r$$
So $$r^2\sin(\theta)=3r $$ BECOMES
$$(x^2+y^2)(y/\sqrt(x^2+y^2))=3\sqrt(x^2+y^2)$$
Simplify and this becomes,
y=3

beginnersmind · Answer

krystabell's answer is nice, but I think the simplest solution is in your question.

"How would I change this ****rsin(theat)=3**** into rectangular coordinate, do I just solve for r and then plug it into to ****y=rsin(theta)**** and x=rcos(theta)? "

beginnersmind · Answer

For the record I only saw it after I read through krystabell's solution :)

anonymous · Answer

Hehehe yes oh those formula's they sure do make you do what you did in the last problems...i didn't address that. so you don't want to solve directly for r because you would be left with r=3/sin(theta) and this would get you nowhere...Thanks beginnersmind for pointing this out!!!