Question

sketch the curve with the given polar equation by first sketching the graph of r as a function of theta in Cartesian coordinates. r=2+sin(theta)

Answer 1

Hey big money, so what's going on?
We gotta sketch some stuff?

Answer 2

Sketching it in polar isn't too bad.
You just need to draw it out carefully and pay attention to each coordinate point.

To graph it in Cartesian though.. hmm thinking..
I guess we could multiply both sides by r,\[\Large\bf\sf r^2=2r+r \sin \theta\]Then move the 2r to the other side,\[\Large\bf\sf r^2-2r=r \sin \theta\]And complete the square on the r's,\[\Large\bf\sf r^2-2r+1=r \sin \theta+1\]\[\Large\bf\sf (r-1)^2=r \sin \theta + 1\]Hmmm does this work? Thinking..

Answer 3

Oh oh oh I misunderstood the question, sorry about that :(
They didn't want us to `convert` it to Cartesian,
they just want it graphed in Cartesian, as Ravi showed in his first picture.

Answer 4

You remember what the sine function looks like when graphed?
Your function here is the same just the entire thing is shifted up 2 units.

Answer 5

yea

Answer 6

how would i draw the other graph though?

Answer 7

Here is a layout we can use to help us.
I've labeled some rings to help us easier draw out our radial distances.

Answer 8

We want to graph a bunch of coordinate pairs.
So for each of these special angles we'll try to find the radius that corresponds to it.