anonymous one year ago Thanks for helping! This question is really weird :( r=-6sin theta I need to multiply both sides of the equation by r and use r^2=x^2+y^2 to rewrite the equation in terms of x and y.

1. anonymous

@Ashleyisakitty @jim_thompson5910 @zepdrix @Nnesha @e.mccormick @wio @sammixboo @kropot72 @mathmate

2. Astrophysics

Ok so you want to convert it to rectangular, it's good you notice we have to multiply r and use $r^2 = x^2+y^2$ we know the ratio for sin theta is the following $\sin \theta = \frac{ y }{ r }$ so we have $r = - 6\left( \frac{ y }{ r } \right)$ can you finish it off?

3. anonymous

I'm not sure I understand where to go from there

4. Astrophysics

$r^2 = - 6y$

5. Astrophysics

What's next?

6. anonymous

square - 6y?

7. Astrophysics

Why? Look at what we know, and we want to "get rid" of the polar coordinates.

8. anonymous

x^2?

9. Astrophysics

I don't know what that means

10. anonymous

11. Astrophysics

Hint: $r^2 = x^2+y^2$

12. anonymous

-6y=x^2+y^2?

13. Astrophysics

Yes, that looks good :)

14. Astrophysics

You can rearrange it and what not if you wish

15. anonymous

That is it in terms of x and y?

16. anonymous

I'm asked to complete the square to produce another equation in my worksheet. Should I do it from this form?

17. Astrophysics

You may complete the square

18. Astrophysics

Ah, yes we have to complete the square, you know how to do that right?

19. Astrophysics

When you have it as such $-6y=x^2+y^2$ it's always best to complete the square as it will be in terms of x and y.

20. anonymous

I know how to do it in regular form, but I'm sort of confused about this one

21. Astrophysics

$-6y = x^2+y^2 \implies x^2+y^2 + 6y = 0$

22. anonymous

Oh, I thought it was when you added (b/2)^2 to both sides or something like that

23. Astrophysics

I didn't complete the square...I put in a form so you can complete the square.

24. anonymous

Oh, okay gotcha

25. Astrophysics

So we don't need to worry about the x^2, now complete the square for y^2+6y

26. Astrophysics

When you have $x^2+ax \implies x^2+ 2 \frac{ ax }{ 2 } + \left( \frac{ a }{ 2 } \right)^2-\left( \frac{ a }{ 2 } \right)^2$ to complete the square.

27. anonymous

Wouldn't that make it remain the same?

28. anonymous

Sorry, I suck at pre calc :(

29. Astrophysics

You should try it, otherwise me doing everything is not going to help you :P

30. anonymous

very true

31. anonymous

But when plugging in y^2+6y in, it cancels back to y^2+6y, no?

32. Astrophysics

Mhm, no you don't do that, we don't plug in anything I just put if you have the form y^2+6y you do the following -> .....etc

33. Astrophysics

$x^2+ax \implies x^2+ 2 \frac{ ax }{ 2 } + \left( \frac{ a }{ 2 } \right)^2-\left( \frac{ a }{ 2 } \right)^2$ $x^2+ ax \implies y^2+6y$ in your question

34. anonymous

y ^2+6x+9-9?

35. anonymous

wait, no

36. Astrophysics

|dw:1434416994934:dw| now we just factor

37. Astrophysics

|dw:1434417167196:dw|

38. Astrophysics

So now we have $x^2+y^2+6y+9 = -9$ one step away from completing it

39. Astrophysics

You were right, but you put 6x instead of 6y :P

40. anonymous

Now I factor?

41. Astrophysics

That should be = 9 not -9, yes you want it to look as such $\huge x^2+(y+3)^2 = 9$ that's your final answer

42. anonymous

x^2+(y+3)^2-9=0

43. Astrophysics

Good!

44. anonymous

oh whoop, same thing ha ha

45. anonymous

Thanks for the help!

46. anonymous

That really helped

47. Astrophysics

No problem, it makes sense now? :)

48. anonymous

Yea a lot more!

49. Astrophysics

Awesome, glad to hear it, make sure you go over it again!

50. anonymous

Of course :), have a good day

51. Astrophysics

You to, bye :)

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