anonymous
  • anonymous
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....
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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|
anonymous
  • anonymous
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?
anonymous
  • anonymous
\[x^6+3 x^4 (y^2-3)+3 x^2 y^2 (y^2+2)+y^6 = y^4\]

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anonymous
  • anonymous
I just chose some arbitrary "a" constant to sub.
anonymous
  • anonymous
|dw:1342133866479:dw|
anonymous
  • anonymous
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
anonymous
  • anonymous
|dw:1342133990522:dw|
anonymous
  • anonymous
|dw:1342134107025:dw|
anonymous
  • anonymous
|dw:1342134151837:dw|
anonymous
  • anonymous
\(x^2 + y^2 = \text{radius}^2\)
anonymous
  • anonymous
|dw:1342134219662:dw|
anonymous
  • anonymous
so a=1
asnaseer
  • asnaseer
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 :)
anonymous
  • anonymous
\(\text{Area} = 3 \pi a^2\), correct ?
anonymous
  • anonymous
Whoa cool link there, @asnaseer I didn't know you could do that with Wolfram, that's some pretty fancy syntax :D
anonymous
  • anonymous
Does this graph actually have a name though? It's not as if I can just Google the image lol
anonymous
  • anonymous
|dw:1342134548532:dw|
anonymous
  • anonymous
|dw:1342134699157:dw|
anonymous
  • anonymous
|dw:1342134862828:dw|
anonymous
  • anonymous
|dw:1342134931824:dw|
anonymous
  • anonymous
*reading & taking notes* :-3
anonymous
  • anonymous
origin build with 1+cos2t=0 _> x=0 , y=0 common term between x , y
anonymous
  • anonymous
|dw:1342135079515:dw|
anonymous
  • anonymous
|dw:1342135156538:dw|
anonymous
  • anonymous
is it clear?
anonymous
  • anonymous
for exactly drawing d/dt=0 for x , y give you some critical points
anonymous
  • anonymous
Clear, you are finding the polar lines, basically, where r = 0.
anonymous
  • anonymous
|dw:1342135317896:dw|
anonymous
  • anonymous
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.
anonymous
  • anonymous
Yep! That looks like the other questions where we were asked to find the vertical and horizontal tangents
anonymous
  • anonymous
dy/dt = 0 is for horizontal I believe
anonymous
  • anonymous
|dw:1342135476935:dw|
anonymous
  • anonymous
|dw:1342135505524:dw|
anonymous
  • anonymous
interesting problem !
anonymous
  • anonymous
Does this funky thing have a name though? :-D
anonymous
  • anonymous
No! it has a nice shape .
anonymous
  • anonymous
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.
anonymous
  • anonymous
It kind of looks like... one of those things when you roll a circle within a circle
anonymous
  • anonymous
Try to solve one by yourself then think it's so easy and sure after that enjoy with the figure.
anonymous
  • anonymous
Well I'm not going to sweat it, the hard part is done. Who cares about the name, you're right :-D
anonymous
  • anonymous
|dw:1342136059673:dw|
anonymous
  • anonymous
first thing attracted me to math was figuring out the shape of equation.
anonymous
  • anonymous
dx = 3 sin(3t) dt dy = 2 cos(t)-3 cos(3t) dt
anonymous
  • anonymous
Are you solving mine?
anonymous
  • anonymous
|dw:1342136471144:dw|
anonymous
  • anonymous
|dw:1342136508456:dw|