Question

Can anyone help me parametrize sin(x)*e^y=0?

Answer 1

The solution is Pi

Answer 2

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

Answer 3

Check this out. http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn.aspx

Answer 4

You mean, you want the parametric equations?

Answer 5

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

Answer 6

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

Answer 7

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.

Answer 8

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.

Answer 9

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

Answer 10

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."

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

I dont think you can parametrise, end of story

Answer 15

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

Answer 16

i do

Answer 17

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.

Answer 18

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

Answer 19

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

Answer 20

can you tell me how?

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

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.

Answer 25

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.

Answer 26

wait so what is the vector?

Answer 27

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).

Answer 28

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>

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

and that's for a general level curve?

Answer 33

so what is the parametric eqn for z=0?

Answer 34

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

Answer 35

yeah, thx for your help!

Answer 36

most ppl here dont know multivariable calc though

Answer 37

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.

Answer 38

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.

Answer 39

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

Answer 40

*parametric equations

Answer 41

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)

Answer 42

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?

Answer 43

where did you go?

Answer 44

i lost the post, this is moving so fast

Answer 45

hahaha, scroll down a bit more

Answer 46

computer wont let me

Answer 47

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?

Answer 48

yeah

Answer 49

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

Answer 50

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?

Answer 51

right, we dont know what will happen in the future

Answer 52

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

Answer 53

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

Answer 54

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

Answer 55

but there arent any real laws. or permanent

Answer 56

everything changes

Answer 57

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

Answer 58

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

Answer 59

no i mean, aside from god

Answer 60

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

Answer 61

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

Answer 62

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?

Answer 63

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

Answer 64

oh i hope i didnt contradict myself

Answer 65

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

Answer 66

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

Answer 67

well then science will just have to modify things a bit

Answer 68

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

Answer 69

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

Answer 70

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

Answer 71

hence, quantum mechanics and the such