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anonymous

  • one year ago

Quick graphing question, thanks for helping! I posted the graph in the comments. I need to write the a coordinate in polar form, but make the radius a positive value. I also need to write point B in polar form as well. Thank You, this topic is really confusing. :P

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  1. anonymous
    • one year ago
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    @mathstudent55 @Nnesha @thomaster @sammixboo @pooja195 @freckles @inkyvoyd @k_lynn @mathmath333 @ybarrap @AkashdeepDeb @tanya123

  2. anonymous
    • one year ago
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    yup

  3. ybarrap
    • one year ago
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    Using Euler's Identity: $$ \large Ae^{i\theta}=A(\cos \theta +i \sin \theta ) $$ |dw:1434408079892:dw| Assuming each ring is 1 unit. Does this make sense?

  4. anonymous
    • one year ago
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    Isn't that B?

  5. ybarrap
    • one year ago
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    Yes, that's right

  6. anonymous
    • one year ago
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    ah cool.

  7. anonymous
    • one year ago
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    So for A it would be: -4(cos(5pi/6)+isin(5pi/6))

  8. anonymous
    • one year ago
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    ?

  9. ybarrap
    • one year ago
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    Close. The radius is always positive. It's just the distance of the ring to the center. In this case it's 4, not -4. Also, write in polar form. What you have is almost correct, but keep in the exponential format. The right side of the equation is rectangular coordinates. Polar: $$ e^{i\theta} $$ Rectangular $$ \cos \theta +i \sin \theta $$ One is equal to the other.

  10. anonymous
    • one year ago
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    What exactly does it look like then?

  11. ybarrap
    • one year ago
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    |dw:1434408649310:dw| See the rectangle I drew above. That is point B in Polar form.

  12. ybarrap
    • one year ago
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    See - https://en.wikipedia.org/wiki/Euler%27s_identity#Explanation

  13. anonymous
    • one year ago
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    I thought polar form was cos theta + isin theta. I thought rectangular was the coordinates (r, theta)?

  14. ybarrap
    • one year ago
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    The other way around. The first is called rectangular because cosine is the x value and sine is the y value |dw:1434409158978:dw|

  15. ybarrap
    • one year ago
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    Technically: $$ (r\cos\theta,r\sin\theta) $$ is the rectangular coordinates $$ (r,\theta) $$ Is Polar

  16. ybarrap
    • one year ago
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    $$ r\exp^{i\theta}=r\left(\cos\theta+i\sin\theta \right) $$

  17. anonymous
    • one year ago
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    Should I write it as (r, theta)? I never formally learned e^i theta

  18. ybarrap
    • one year ago
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    Yes, that is also in Polar form

  19. anonymous
    • one year ago
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    Thanks! That was helpful!

  20. ybarrap
    • one year ago
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    $$ \text{Rectangular: }(r\cos\theta,r\sin\theta)\\ \text{Polar: }(r,\theta) $$

  21. anonymous
    • one year ago
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    Gotcha, thanks for clearing that up! :)

  22. anonymous
    • one year ago
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    I gave you a medal

  23. ybarrap
    • one year ago
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    It was helpful that you knew the basics!

  24. anonymous
    • one year ago
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    Oh wait, one last question

  25. anonymous
    • one year ago
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    Should I write it as (4, 5pi/6), since r has to be positive? And if I were to graph (-3, pi/3) would it be on the -3 mark or the 3 mark?

  26. ybarrap
    • one year ago
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    If the second is in Polar form, it would be invalid because r > 0.

  27. anonymous
    • one year ago
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    That is odd, my worksheet says to graph it. Should I just write it in the -3 area?

  28. ybarrap
    • one year ago
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    The second one only makes sense if it is rectangular coordinates because r MUST always be positive. Imagine a circle. Can it ever have a negative radius?

  29. anonymous
    • one year ago
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    That is true. Do you think they mean that it should be graphed on the 3 mark?

  30. ybarrap
    • one year ago
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    (-3,pi/3) only makes sense if x=-3 and y=pi/3. Although, it is very unusual to specify a y-value using pi. But it is definitely NOT polar because of the -3.

  31. ybarrap
    • one year ago
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    Here's is the plot of that point - http://www.wolframalpha.com/input/?i=plot+%28-3%2Cpi%2F3%29

  32. ybarrap
    • one year ago
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    Here is that same point in Polar form - http://www.wolframalpha.com/input/?i=convert+%28-3%2Cpi%2F3%29+to+polar+form

  33. anonymous
    • one year ago
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    I think wolfram turned it into a complex number. I'll just graph it on 3 and see what my teacher says. Thanks for the help! I learned a lot!

  34. anonymous
    • one year ago
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    Part 1 should be (4, 5pi/6) right?

  35. ybarrap
    • one year ago
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    Yes it's right for point A That's what rectangular actually means, but you won't realize that until later. (x,y) is the same as (\(r\cos\theta,r\sin\theta\)) is the same as \( r(\cos\theta+i\sin \theta)\) plus that exponential format, which you haven't studied yet.

  36. anonymous
    • one year ago
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    Alright, thanks!

  37. ybarrap
    • one year ago
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    You're welcome

  38. anonymous
    • one year ago
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    :)

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