## 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....

1. agentx5

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

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

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

4. agentx5

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

5. mahmit2012

|dw:1342133866479:dw|

6. agentx5

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

|dw:1342133990522:dw|

8. mahmit2012

|dw:1342134107025:dw|

9. mahmit2012

|dw:1342134151837:dw|

10. agentx5

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

11. mahmit2012

|dw:1342134219662:dw|

12. mahmit2012

so a=1

13. 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 :)

14. agentx5

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

15. agentx5

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

16. agentx5

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

17. mahmit2012

|dw:1342134548532:dw|

18. mahmit2012

|dw:1342134699157:dw|

19. mahmit2012

|dw:1342134862828:dw|

20. mahmit2012

|dw:1342134931824:dw|

21. agentx5

22. mahmit2012

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

23. mahmit2012

|dw:1342135079515:dw|

24. mahmit2012

|dw:1342135156538:dw|

25. mahmit2012

is it clear?

26. mahmit2012

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

27. agentx5

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

28. mahmit2012

|dw:1342135317896:dw|

29. agentx5

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

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

31. agentx5

dy/dt = 0 is for horizontal I believe

32. mahmit2012

|dw:1342135476935:dw|

33. mahmit2012

|dw:1342135505524:dw|

34. mahmit2012

interesting problem !

35. agentx5

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

36. mahmit2012

No! it has a nice shape .

37. agentx5

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

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

39. mahmit2012

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

40. agentx5

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

41. mahmit2012

|dw:1342136059673:dw|

42. mahmit2012

first thing attracted me to math was figu