agentx5 Group Title 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.... 2 years ago 2 years ago

1. agentx5 Group Title

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 Group Title

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 Group Title

$x^6+3 x^4 (y^2-3)+3 x^2 y^2 (y^2+2)+y^6 = y^4$

4. agentx5 Group Title

I just chose some arbitrary "a" constant to sub.

5. mahmit2012 Group Title

|dw:1342133866479:dw|

6. agentx5 Group Title

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 Group Title

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8. mahmit2012 Group Title

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9. mahmit2012 Group Title

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10. agentx5 Group Title

$$x^2 + y^2 = \text{radius}^2$$

11. mahmit2012 Group Title

|dw:1342134219662:dw|

12. mahmit2012 Group Title

so a=1

13. asnaseer Group Title

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 Group Title

$$\text{Area} = 3 \pi a^2$$, correct ?

15. agentx5 Group Title

Whoa cool link there, @asnaseer I didn't know you could do that with Wolfram, that's some pretty fancy syntax :D

16. agentx5 Group Title

Does this graph actually have a name though? It's not as if I can just Google the image lol

17. mahmit2012 Group Title

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18. mahmit2012 Group Title

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19. mahmit2012 Group Title

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20. mahmit2012 Group Title

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21. agentx5 Group Title

22. mahmit2012 Group Title

origin build with 1+cos2t=0 _> x=0 , y=0 common term between x , y

23. mahmit2012 Group Title

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24. mahmit2012 Group Title

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25. mahmit2012 Group Title

is it clear?

26. mahmit2012 Group Title

for exactly drawing d/dt=0 for x , y give you some critical points

27. agentx5 Group Title

Clear, you are finding the polar lines, basically, where r = 0.

28. mahmit2012 Group Title

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29. agentx5 Group Title

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 Group Title

Yep! That looks like the other questions where we were asked to find the vertical and horizontal tangents

31. agentx5 Group Title

dy/dt = 0 is for horizontal I believe

32. mahmit2012 Group Title

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33. mahmit2012 Group Title

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34. mahmit2012 Group Title

interesting problem !

35. agentx5 Group Title

Does this funky thing have a name though? :-D

36. mahmit2012 Group Title

No! it has a nice shape .

37. agentx5 Group Title

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 Group Title

It kind of looks like... one of those things when you roll a circle within a circle

39. mahmit2012 Group Title

Try to solve one by yourself then think it's so easy and sure after that enjoy with the figure.

40. agentx5 Group Title

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

41. mahmit2012 Group Title

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