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anonymous

  • 4 years ago

find a polar representation for the curve: x^2 + y^2 = 9

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  1. myininaya
    • 4 years ago
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    do you remember that \[r^2=x^2+y^2\]

  2. anonymous
    • 4 years ago
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    yeah so r = 3

  3. myininaya
    • 4 years ago
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    satellite I having a moment here doesn't r=3 include the equation r=-3?

  4. myininaya
    • 4 years ago
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    you know when we are talking about polar equations?

  5. myininaya
    • 4 years ago
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    i would include r=-3 just in case because i'm having a memory issue right now

  6. anonymous
    • 4 years ago
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    i think it is just \[r=9\]

  7. myininaya
    • 4 years ago
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    \[r^2=9 => r=\pm 3\]

  8. anonymous
    • 4 years ago
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    r is the radius, always non negative. you want \[r=f(\theta) but here r is constant

  9. anonymous
    • 4 years ago
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    \[r=f(\theta)\]

  10. myininaya
    • 4 years ago
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    you only need r=3

  11. anonymous
    • 4 years ago
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    right i lunched it is \[r=3\]

  12. anonymous
    • 4 years ago
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    \[x=rcos \theta\] \[y=rsin \theta\] r=3\[r ^{2}\cos ^{2}\theta+r ^{2}\sin ^{2}\theta=9\]

  13. anonymous
    • 4 years ago
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    yeah i got that far

  14. anonymous
    • 4 years ago
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    yeah but this says \[r=3\]

  15. anonymous
    • 4 years ago
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    how do i simplify that?

  16. anonymous
    • 4 years ago
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    too much work. r is the radius. it is a constant since you have a circle of radius 3

  17. myininaya
    • 4 years ago
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    factor out r^2

  18. anonymous
    • 4 years ago
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    did that

  19. myininaya
    • 4 years ago
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    cos^2(theta)+sin^2(theta)=1

  20. anonymous
    • 4 years ago
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    \[\cos ^{2}\theta+\sin ^{2}\theta=1\]

  21. anonymous
    • 4 years ago
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    okay

  22. myininaya
    • 4 years ago
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    you don't have to do it that way the easiest is just recalling \[r^2=x^2+y^2\]

  23. anonymous
    • 4 years ago
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    you shouldn't think that hard! it is true that \[\cos ^{2}\theta+\sin ^{2}\theta=1\] but that is way too much work

  24. anonymous
    • 4 years ago
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    so it's just r = 3 as my answeR?

  25. myininaya
    • 4 years ago
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    yes

  26. anonymous
    • 4 years ago
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    yes a circle looks like \[r= number\]

  27. myininaya
    • 4 years ago
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    r=3 will include all points from the center that have distance 3 from it

  28. anonymous
    • 4 years ago
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    in polar coordinates a circle is just r = a number?

  29. anonymous
    • 4 years ago
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    yes that is correct

  30. anonymous
    • 4 years ago
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    r after all stands for "radius" and circle is a figure where the radius is constant

  31. anonymous
    • 4 years ago
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    okay thank you!

  32. anonymous
    • 4 years ago
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    http://www.wolframalpha.com/input/?i=r+%3D+3+

  33. anonymous
    • 4 years ago
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    here is one where r is not constant http://www.wolframalpha.com/input/?i=r+%3D+1%2Bsin%28theta%29

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