Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

Good point @nowhereman

Answer 6

a, right forgot that r

Answer 7

you can divide it away then

Answer 8

In r you can put r=(√x^2+y^2)

Answer 9

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

Answer 10

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

Answer 11

Sorry, you got to square the right side

Answer 12

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

Answer 13

Kinda abstract...

Answer 14

yeah, that was math is about.

Answer 15

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

Answer 16

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

Answer 17

it should end up as:

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

Answer 18

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

Answer 19

well (3/2)^2 :)

Answer 20

Amistre, what was your process for getting that answer?

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

any ?s speak up ;)

Answer 25

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

Answer 26

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

Answer 27

center at (0,3/2)

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

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?

Answer 32

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

Answer 33

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

Answer 34

Huh? What do you mean?

Answer 35

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

Answer 36

just broke, thats all :)

Answer 37

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

Answer 38

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

Answer 39

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

Answer 40

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

Answer 41

thatd be good if it works out :)

Answer 42

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

Answer 43

Are you serious about it?

Answer 44

I mean do you really want to do it?

Answer 45

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

Answer 46

You are really good

Answer 47

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

Answer 48

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

Answer 49

I have your email address, did you forget?

Answer 50

lol.... just wasnt sure ;)

Answer 51

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

Answer 52

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

Answer 53

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

Answer 54

Bye

Answer 55

Ciao :)