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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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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|
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?
\[x^6+3 x^4 (y^2-3)+3 x^2 y^2 (y^2+2)+y^6 = y^4\]

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