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agentx5

  • 2 years ago

Yikes, need to find the area and the name for these parametric equations: x(t) = a cos(t) (2 cos(2 t)+1) y(t) = a sin(t) (2 cos(2 t)+1) What is...? I don't even...? How? I'll draw the graph....

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  1. agentx5
    • 2 years ago
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    Cartesian? Check me please? x^6+3 x^4 (y^2-3)+3 x^2 y^2 (y^2+2)+y^6 = y^4 |dw:1342133559037:dw|

  2. agentx5
    • 2 years ago
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    It looks like of like a D-orbital from chemistry, but it's got little lobes on the vertical, so that means it's probably more like some weird F-orbital. :-D Help?

  3. agentx5
    • 2 years ago
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    \[x^6+3 x^4 (y^2-3)+3 x^2 y^2 (y^2+2)+y^6 = y^4\]

  4. agentx5
    • 2 years ago
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    I just chose some arbitrary "a" constant to sub.

  5. mahmit2012
    • 2 years ago
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    |dw:1342133866479:dw|

  6. agentx5
    • 2 years ago
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    Is that \(\tan t\) @mahmit2012 ? Ty in advance btw, you always seem to be the one who's here to help when I get stuck on these challenge problems :D

  7. mahmit2012
    • 2 years ago
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    |dw:1342133990522:dw|

  8. mahmit2012
    • 2 years ago
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    |dw:1342134107025:dw|

  9. mahmit2012
    • 2 years ago
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    |dw:1342134151837:dw|

  10. agentx5
    • 2 years ago
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    \(x^2 + y^2 = \text{radius}^2\)

  11. mahmit2012
    • 2 years ago
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    |dw:1342134219662:dw|

  12. mahmit2012
    • 2 years ago
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    so a=1

  13. asnaseer
    • 2 years ago
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    you can see a graph of this using wolfram, e.g.: http://www.wolframalpha.com/input/?i=plot+%7Bx%3Da*cos%28t%29%282cos%282t%29%2B1%29%2C+y%3Da*sin%28t%29%282cos%282t%29%2B1%29%7D+when+a%3D3 your graph is correct :)

  14. agentx5
    • 2 years ago
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    \(\text{Area} = 3 \pi a^2\), correct ?

  15. agentx5
    • 2 years ago
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    Whoa cool link there, @asnaseer I didn't know you could do that with Wolfram, that's some pretty fancy syntax :D

  16. agentx5
    • 2 years ago
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    Does this graph actually have a name though? It's not as if I can just Google the image lol

  17. mahmit2012
    • 2 years ago
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    |dw:1342134548532:dw|

  18. mahmit2012
    • 2 years ago
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    |dw:1342134699157:dw|

  19. mahmit2012
    • 2 years ago
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    |dw:1342134862828:dw|

  20. mahmit2012
    • 2 years ago
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    |dw:1342134931824:dw|

  21. agentx5
    • 2 years ago
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    *reading & taking notes* :-3

  22. mahmit2012
    • 2 years ago
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    origin build with 1+cos2t=0 _> x=0 , y=0 common term between x , y

  23. mahmit2012
    • 2 years ago
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    |dw:1342135079515:dw|

  24. mahmit2012
    • 2 years ago
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    |dw:1342135156538:dw|

  25. mahmit2012
    • 2 years ago
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    is it clear?

  26. mahmit2012
    • 2 years ago
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    for exactly drawing d/dt=0 for x , y give you some critical points

  27. agentx5
    • 2 years ago
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    Clear, you are finding the polar lines, basically, where r = 0.

  28. mahmit2012
    • 2 years ago
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    |dw:1342135317896:dw|

  29. agentx5
    • 2 years ago
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    We just touched on polar stuff today, this question was from the "challenge" section of the written homework. The other curves have names that we discussed in the lecture like "carotid", "ellipse", and "circle" which are kind of obvious which is which.

  30. agentx5
    • 2 years ago
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    Yep! That looks like the other questions where we were asked to find the vertical and horizontal tangents

  31. agentx5
    • 2 years ago
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    dy/dt = 0 is for horizontal I believe

  32. mahmit2012
    • 2 years ago
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    |dw:1342135476935:dw|

  33. mahmit2012
    • 2 years ago
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    |dw:1342135505524:dw|

  34. mahmit2012
    • 2 years ago
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    interesting problem !

  35. agentx5
    • 2 years ago
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    Does this funky thing have a name though? :-D

  36. mahmit2012
    • 2 years ago
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    No! it has a nice shape .

  37. agentx5
    • 2 years ago
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    It just asks me to type in the "area" in the one text field. Which was correct yay! And then it has a text box under it for "name of curve". The others were easy, but this one I haven't got a clue. Maybe it's in the text, somewhere amidst all its pages but it's not easy to find.

  38. agentx5
    • 2 years ago
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    It kind of looks like... one of those things when you roll a circle within a circle

  39. mahmit2012
    • 2 years ago
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    Try to solve one by yourself then think it's so easy and sure after that enjoy with the figure.

  40. agentx5
    • 2 years ago
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    Well I'm not going to sweat it, the hard part is done. Who cares about the name, you're right :-D

  41. mahmit2012
    • 2 years ago
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    |dw:1342136059673:dw|

  42. mahmit2012
    • 2 years ago
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    first thing attracted me to math was figuring out the shape of equation.

  43. agentx5
    • 2 years ago
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    dx = 3 sin(3t) dt dy = 2 cos(t)-3 cos(3t) dt

  44. mahmit2012
    • 2 years ago
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    Are you solving mine?