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anonymous

  • 5 years ago

Convert the equation to polar form. 5x=5y AND x^2+y^2=16

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  1. anonymous
    • 5 years ago
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    x=r cosƟ, y=r sinƟ, x^2+y^2=r^2.

  2. anonymous
    • 5 years ago
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    I don't get the second one. x^2+y^2=r^2

  3. anonymous
    • 5 years ago
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    No, not really. Trig and I don't get along at all

  4. myininaya
    • 5 years ago
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    ok loco do you have that picture i drawed you where I graph (x,y) and called the angle between the initial ray and I guess we can call it the vector with endpoints at the origin and at the point (x,y)

  5. anonymous
    • 5 years ago
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    yeah, it's open in my pdf

  6. myininaya
    • 5 years ago
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    k and I put inside a circle i called the radius of that circle r

  7. myininaya
    • 5 years ago
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    that trangle is a right triangle so we can use Pythagorean them to find what r is in terms of x and y

  8. myininaya
    • 5 years ago
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    r=sqrt(x^2+y^2)

  9. myininaya
    • 5 years ago
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    or like anwar said before x^2+y^2=r^2

  10. anonymous
    • 5 years ago
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    yeah, i don't this equation? what do i use it for?

  11. myininaya
    • 5 years ago
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    we want to convert x^2+y^2=16 to a polar equation so that means we want it in terms of r and pheta but what is x^2+y^2=.....?

  12. myininaya
    • 5 years ago
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    loco, do you know what to fill that blank with?

  13. anonymous
    • 5 years ago
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    5x^2+5y^2=16

  14. myininaya
    • 5 years ago
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    if we are doing 5x^2+5y^2=16 then we can factor out 5 so we have 5(x^2+y^2)=16 but what does x^2+y^2=----?

  15. anonymous
    • 5 years ago
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    does it equal r?

  16. myininaya
    • 5 years ago
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    right!

  17. anonymous
    • 5 years ago
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    sorry, if i take too long, trying to figure this out

  18. myininaya
    • 5 years ago
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    5r=16 is the polar equation of the cartesian equation 5x^2+5y^2=16

  19. myininaya
    • 5 years ago
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    these equations give the same graph using a little different way of graphing

  20. myininaya
    • 5 years ago
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    these are equations are equivalent

  21. myininaya
    • 5 years ago
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    polar is in the form (r,pheta) Cartesian is in the form (x,y)

  22. anonymous
    • 5 years ago
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    what do u mean equivalent? = to what? 16

  23. myininaya
    • 5 years ago
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    no to each other

  24. anonymous
    • 5 years ago
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    so 5x=5y, is that what u mean?

  25. myininaya
    • 5 years ago
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    5r=16 is equivalent to 5x^2+5y^2=16 because they are the same graph

  26. anonymous
    • 5 years ago
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    oh ok...

  27. myininaya
    • 5 years ago
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    so you want to convert 5x=5y to polar equation?

  28. anonymous
    • 5 years ago
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    yes

  29. myininaya
    • 5 years ago
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    so remember polar has (r,pheta) form so x=rcos(pheta) and y=rsin(pheta) 5rcos(pheta)=5rsin(pheta) we could divide both sides by 5 so we have rcos(pheta)=rsin(pheta) rcos(pheta)-rsin(pheta)=0 r(cos(pheta)-sin(pheta))=0 so we have r=0 and cos(pheta)-sin(pheta)=0

  30. anonymous
    • 5 years ago
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    wow... um.. let me try to figure all this out

  31. anonymous
    • 5 years ago
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    ok

  32. anonymous
    • 5 years ago
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    There?

  33. myininaya
    • 5 years ago
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    hey i was talking to my hubby. hes gonna be home soon so I'm going to leave soon but we were done with writing 5x=5y to a polar equation

  34. anonymous
    • 5 years ago
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    yes

  35. myininaya
    • 5 years ago
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    so did you have a question or something?

  36. anonymous
    • 5 years ago
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    this might sound arrogant but, how do i set it up and how do i get the answer

  37. myininaya
    • 5 years ago
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    how you have to do is place x^2+y^2 with r and replace x with rcos(pheta) and y with rsin(pheta) and usually I tried to simplified like I did above

  38. myininaya
    • 5 years ago
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    all not how

  39. myininaya
    • 5 years ago
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    write with no x and no y

  40. myininaya
    • 5 years ago
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    your goal is to write with r and pheta

  41. anonymous
    • 5 years ago
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    ok

  42. myininaya
    • 5 years ago
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    x^2+y^2 with r^2*

  43. myininaya
    • 5 years ago
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    do you see my mistake way up there? i forgot r^2 when i wrote 5r^2=16 is equivalent to 5x^2+5y^2=16

  44. anonymous
    • 5 years ago
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    so it would be 5^2+5^2=

  45. myininaya
    • 5 years ago
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    ?

  46. myininaya
    • 5 years ago
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    where did you get x=5 and y=5?

  47. anonymous
    • 5 years ago
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    oh.. crap. i got them from the original equation

  48. myininaya
    • 5 years ago
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    hey anwar is going to come back and help you i have to leave k?

  49. anonymous
    • 5 years ago
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    ok thank you very much for all ur help though :)

  50. myininaya
    • 5 years ago
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    i think you are over thinking this stuff

  51. anonymous
    • 5 years ago
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    i tend to do that a lot :P

  52. myininaya
    • 5 years ago
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    i hope you get it

  53. anonymous
    • 5 years ago
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    thank you

  54. anonymous
    • 5 years ago
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    i got the whole night, don't worry i'll get it

  55. anonymous
    • 5 years ago
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    Just gimme a minute. I'll help you when I finish with another question if you still need help.

  56. anonymous
    • 5 years ago
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    ok

  57. anonymous
    • 5 years ago
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    I don't know where you have reached. But I'll start by these formula in polar coordinates: \[x=r \cos \theta .... (1)\] \[y=r \sin \theta .... (2)\] \[x^2+y^2=r^2 .... (3)\]

  58. anonymous
    • 5 years ago
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    We're trying to convert the given equations that are in terms of x and y to an a form in terms of r and theta, which is called polar coordinates. Is that clear so far?

  59. anonymous
    • 5 years ago
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    Good, Now consider the first equation: 5x=5y. Divide both sides by 5 you get: \[x=y\] But we can substitute fot x with equation (1) and for y with equation (2). That's: \[x=y \implies r \cos \theta=r \sin \theta\]

  60. anonymous
    • 5 years ago
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    ok

  61. anonymous
    • 5 years ago
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    Is is clear so far?

  62. anonymous
    • 5 years ago
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    Is it*

  63. anonymous
    • 5 years ago
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    For the 2nd equation: \[x^2+y^2=16\] we will just apply directly the third formula, since x^2+y^2 is just r^2. Then: \[x^2+y^2=16 \implies r^2=16\]

  64. anonymous
    • 5 years ago
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    is this the answer

  65. anonymous
    • 5 years ago
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    Yep. You can simplify it more, but this is OK.

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