## anonymous 5 years ago Convert r=3sin(theta) into a cartesian equation.

1. anonymous

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

2. anonymous

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

3. nowhereman

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

4. anonymous

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

5. anonymous

Good point @nowhereman

6. nowhereman

a, right forgot that r

7. nowhereman

you can divide it away then

8. anonymous

In r you can put r=(√x^2+y^2)

9. anonymous

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

10. anonymous

$x^2+y^2=3y$

11. anonymous

Sorry, you got to square the right side

12. nowhereman

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

13. anonymous

Kinda abstract...

14. nowhereman

yeah, that was math is about.

15. 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

16. amistre64

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

17. amistre64

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

18. nowhereman

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

19. amistre64

well (3/2)^2 :)

20. anonymous

21. 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

22. amistre64

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

23. anonymous

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

24. amistre64

any ?s speak up ;)

25. anonymous

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

26. 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

27. amistre64

center at (0,3/2)

28. amistre64

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

29. anonymous

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

30. amistre64

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

31. 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?

32. amistre64

been wondering how to make money doing this.... got $60 left in the bank.... :/ 33. amistre64 that form is not the standard for a circle equation.... just needs dressed up a bit ;) 34. anonymous Huh? What do you mean? 35. anonymous "been wondering how to make money doing this.... got$60 left in the bank.... :/"??

36. amistre64

just broke, thats all :)

37. anonymous

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

38. amistre64

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

39. amistre64

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

40. anonymous

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

41. amistre64

thatd be good if it works out :)

42. amistre64

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

43. anonymous

44. anonymous

I mean do you really want to do it?

45. amistre64

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

46. anonymous

You are really good

47. anonymous

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

48. amistre64

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

49. anonymous

50. amistre64

lol.... just wasnt sure ;)

51. anonymous

52. amistre64

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

53. anonymous

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

54. anonymous

Bye

55. amistre64

Ciao :)