## anonymous 5 years ago Can anyone help me parametrize sin(x)*e^y=0?

1. anonymous

The solution is Pi

2. anonymous

i want to find a parametrization though. You know, x^2+y^2=1, the parametrization is x=cos(t) y=sin(t)

3. anonymous
4. anonymous

You mean, you want the parametric equations?

5. anonymous

so you mean parametrize z= e^(y)sin(x)

6. anonymous

yes chaguanas, i just cant seem to find a relation between x and y, or such. and im checking the link now, murph. thx

7. anonymous

the thing is, the link tells you more about how to reverse a parametric eqn than how to make one. Right now, I can't find a relation; i.e. I can't parametrize in polar coordinates nor in spherical coordinates.

8. anonymous

ok, the whole question is: find parametric eqns for the three level curves of the function W(x,y)=sin(x)e^y which pass throught the points... well, I found one level curve z at z=0 to be sin(x)e^y=0, so I need to parametrize it.

9. anonymous

You need to post the whole question. Because you are not giving us enough info, and even misinterpreting the question.

10. anonymous

ok, "find parametric eqns for the three level curves of the function W(x,y)=sin(x)e^y which pass throught the points P=(0,1), Q=(pi/2,0) and R=(pi/6,3). Also compute the vectors of the gradient vector field W at the points P, Q, and R."

11. anonymous

I know how to find the gradients, so im more concerned with the first part.

12. anonymous

I think you find the dell or gradient, which is a vector, and use that vector in conjunction with the points to find parametric eq

13. anonymous

but the gradient only shows change, how can it help me parametrize?

14. anonymous

I dont think you can parametrise, end of story

15. anonymous

well, it is a homework question. i don't think the books wrote all that for nothing

16. anonymous

i do

17. anonymous

Be careful with the word parametrise, that was your previous lesson. The gradient are normal to the level curve. You want to find the parametric eq.

18. anonymous

i still don't understand, how is the gradient going to help me?

19. anonymous

It is going to give you a vector. The vector is used in conjunction with the points to find the parametric eq.

20. anonymous

can you tell me how?

21. anonymous

Partial derivative in relation to x, partial in relation to y

22. anonymous

yes i know, what do you do with the gradient after that?

23. anonymous

let's say the vector is <1,2> and point P (0,1). Parametric eq is x=0 + 1t, or x=t y=1+2t

24. anonymous

ok, so the vector at (0,1) comes out to <e,0>. so parametric is x=e*t, y=1? That doesn't come out right.

25. anonymous

Don't solve for the vector at (0,!). Just get the vector from the partial fractions. You are anticipating and reading too much into the question.

26. anonymous

wait so what is the vector?

27. anonymous

Just find the partial derivative in relation to x, partial in relation to y. You already said you know how to do it. In fact, you have already done it. But apparently you made an extra step and put in (0,1).

28. anonymous

yeah, but im supposed to somehow use that to parametrize? ok, so i got the gradient and it's <cos(x)e^y, sin(x)e^y>

29. anonymous

For the rest of your life, don't use the word parametrize. You are not parametrizing. You are finding the parametric equations.

30. anonymous

sorry. ok, so how do you use <cos(x)e^y, sin(x)e^y> to find the parametric equations?

31. anonymous

$x =t e ^{y} \cos x$$y =1+te ^{y}\sin$

32. anonymous

and that's for a general level curve?

33. anonymous

so what is the parametric eqn for z=0?

34. anonymous

Post your question again, as a new post, this time the whole question; so you can get a fresh perspective from some other guys.

35. anonymous

36. anonymous

most ppl here dont know multivariable calc though

37. anonymous

One or two of them do. There is someone named Lokisan who comes on at odd hours and goes through all pass questions and sends a response.

38. anonymous

I think I got it. plug in values for P in your original eq. I think it gives your 0. So one of your level curve is sinxe^y=0. Do it for the other two points. Then find parametric eq of each.

39. anonymous

yes, that was exactly my original question, which was "find the parametric equation of sin(x)e^y=0", but I just couldn't find a parameter that satisfies the equation

40. anonymous

*parametric equations

41. anonymous

Finding parametric equations is a very simple process. Use partial fractions to get a vector, and with that vector and the point find values of x and y, (the answers include t)

42. anonymous

you did that for me before, but so what is the vector? I got the gradient, so what do you want me to do with it?

43. anonymous

where did you go?

44. anonymous

i lost the post, this is moving so fast

45. anonymous

hahaha, scroll down a bit more

46. anonymous

computer wont let me

47. anonymous

listen, im not trying to take sides because I don't even worship a god. However, i'm just saying that everything happens for a reason. If something happens, don't look to god. look to another reason. That's why they got meterology and all that what not, right?

48. anonymous

yeah

49. anonymous

whats this about worshipping the laws of nature. we dont even know the laws of nature are permanent

50. anonymous

physics? yes, it is. are you saying that gravity is not permanent, that it does not equal 9.8m/s^2 when close to Earth's surface?

51. anonymous

right, we dont know what will happen in the future

52. anonymous

there is no reason to prevent gravity from ceasing, mass will cease, etc , in the next instant

53. anonymous

just because our "laws" have described nature in the past, who is to say what will happen in the future

54. anonymous

science works until it stops working, so to speak. and then we try something else

55. anonymous

but there arent any real laws. or permanent

56. anonymous

everything changes

57. anonymous

yes, i suppose that if god decides to change the laws of physics, then he will. however, for now, earthquakes will always occur when a tectonic plate happens to accidentally brush up against another one, and fires will keep on reacting as long as there is oxygen to fuel it, and babies cannot be magically lifted into the air without any physics behind it

58. anonymous

nothing can be done, nor should be done, to change that. or else there will be devastating consequences

59. anonymous

no i mean, aside from god

60. anonymous

even if god doesnt exist, the laws of nature can spontaneously change. what is there to provent that?

61. anonymous

actually, god's existence could be arguably a reason that gravity will not cease. he is there to prevent it. but i dont see any evidence for god. so we are truly floating blindly in space , and our laws have no permanence

62. anonymous

that's philosophy. out of my range, out of the range of mathematics too, within which we are posting =D but, science has worked for hundreds of thousands of years, and it doesn't seem to be changing now, so why should it?

63. anonymous

why should it not . actually there is a reason why it should. empirically everything changes

64. anonymous

oh i hope i didnt contradict myself

65. anonymous

if you can find one, (outside of quantum mechanics, and any other science that is still developing) I should like to know it

66. anonymous

can find what? an example of a law changing, oh

67. anonymous

well then science will just have to modify things a bit

68. anonymous

the only reason why science works in the first place is because there is consistency in the universe, regularity, repeatability. if we lose this regularity (doesnt matter what it is), then science wont work . you cant frame a law of nature if there is nothing for it to express , if nothing is predictable

69. anonymous

youre right though, this is outside the scope of math problems

70. anonymous

if we lose a regularity, then we search further, because we can always assume there is a regularity in the universe. Even "regularity" cannot be strictly defined. what occurs often is regularity, sometimes things that are irregular in the beginning become regular as we understand it more

71. anonymous

hence, quantum mechanics and the such