Convert r=3sin(theta) into a cartesian equation.

- anonymous

Convert r=3sin(theta) into a cartesian equation.

- jamiebookeater

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- anonymous

\[r=\sqrt (x^2+y^2)\]
\[\tan^{-1} (y/x)=\theta\]

- anonymous

Put them in place, and try simplifying, the resulting equation will be in terms of x and y

- nowhereman

No need to make it so complicated for θ. You should know that polar coordinates mean \[\sin θ = y\]

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## More answers

- anonymous

rsin(theta) = y. I just need to know how to deal with the r being on the left side of the equation basically.

- anonymous

Good point @nowhereman

- nowhereman

a, right forgot that r

- nowhereman

you can divide it away then

- anonymous

In r you can put r=(√x^2+y^2)

- anonymous

Ok so you use the equation of a circle? Not sure exactly where that's coming from...

- anonymous

\[x^2+y^2=3y\]

- anonymous

Sorry, you got to square the right side

- nowhereman

That would just be the definition of polar coordinates. \[r = 3\sinθ ⇔ r = 3ry ⇔ 1 = 3y ∨ r = 0 ⇔ y = \frac 1 3 ∨ x = y = 0\]

- anonymous

Kinda abstract...

- nowhereman

yeah, that was math is about.

- anonymous

Yeah I understand that but the pathetic American Education System doesn't go into the abstract much. So call me dumb but that's how it is. lol

- amistre64

the graph of this thing is a circle centered on the yaxis stretching from the origin to the y=3 mark...

- amistre64

it should end up as:
x^2 + (y -1/2)^2 = 3/2 if i see it right :)

- nowhereman

mmh, yeah I put the r on the wrong side... guess I'm not awake after all

- amistre64

well (3/2)^2 :)

- anonymous

Amistre, what was your process for getting that answer?

- amistre64

seeing the graph in my head really :) the algebra is this:
r = 3sin(t) ; * r
r^2 = 3rsin(t) ; r^2 = x^2 + y^2 ; and rsin(t) = y
x^2 + y^2 = 3y ; -3y
x^2 +y^2 -3y = 0 ; complete the square
x^2 +y^2 -3y + (3/2)^2 = (3/2)^2 ; clean up the square..
x^2 +(y-3/2)^2 = (3/2)^2

- amistre64

i was off by a y -1/2 the first time lol....but then again i am not right in the head ;)

- anonymous

Ok I think I'm beginning to see it. Thanks.

- amistre64

any ?s speak up ;)

- anonymous

I may come up with another one in a minute. Just digesting it right now.

- amistre64

at sin(0) we are at the origin; at sin(90) we are at 3; then we swing back to 0 on our way thru and that makes the circle that sits on the origin stretched to y=3 in my head

- amistre64

center at (0,3/2)

- amistre64

but yet i cant seem to get how to turn parametric equations into cartesian equation lol

- anonymous

I think I typed the right answer when I typed
\[x^2+y^2=3y\] didn't I?

- amistre64

iam; that was a good start yes :), just needed to turn it into the circle equation

- anonymous

I am not getting you, if we just write it as \[x^2+y^2-3 y = 0
\], then it represents a circle doesn't it?

- amistre64

been wondering how to make money doing this.... got $60 left in the bank.... :/

- amistre64

that form is not the standard for a circle equation.... just needs dressed up a bit ;)

- anonymous

Huh? What do you mean?

- anonymous

"been wondering how to make money doing this.... got $60 left in the bank.... :/"??

- amistre64

just broke, thats all :)

- anonymous

I know some methods, but those are not similar to these

- amistre64

:) I saw something today about a cat.... but it looked used up...

- amistre64

id be great if I could get a job tutoring at the college..

- anonymous

I can help you if you want to tutor people online by getting paid at the same time

- amistre64

thatd be good if it works out :)

- amistre64

i got aloooottt of time, and aloooott of math in me lol

- anonymous

Are you serious about it?

- anonymous

I mean do you really want to do it?

- amistre64

yeah, this experience here has taught me that I am actually good at it :)

- anonymous

You are really good

- anonymous

So if you are interested, I can help you start, but you got to email me when you wish to begin

- amistre64

tony031172@gmail.com is my junkmmail catcher, I check it still, but it keeps my good email from the clutter...

- anonymous

I have your email address, did you forget?

- amistre64

lol.... just wasnt sure ;)

- anonymous

I have your real email address a*******@*****.com

- amistre64

:) ill hit you up tomorrow, my borrowed time i up here at the library :/

- anonymous

Sure, I hope I am disturbing all of them who are sitting here

- anonymous

Bye

- amistre64

Ciao :)

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