How do I sketch the graph of f(x, y) = sin(y) using x, y, and z cross sections?

[phy]

ok, can anyone please help me with this question? my textbook is pathetic; it gives the easiest examples and the homework questions are hard; on top of that, they only have the answers to the odd numbered questions which are easier than the even numbered questions; if that wasn't bad enough, my professor just copies the examples from the textbook and shows them during the lectures; he's a nice guy but get some other examples! ok, without any further adew, here's the question: sketch the graph of the function f(x, y) = sin(y); i know that i have to use x, y and z cross sections but i don't quite understand how to use them. if you could provide me with the steps to do this question it would be perfect! thanks.

 

[cookiemonster]

f(x,y) = sin(y)

hold x constant and we get

f(c,y) = sin(y)

So the cross-section (the yz plane) at location c is the sine function.

Then we note that the constant c is arbitrary and has no effect on the cross section, so every cross section we get by holding x constant will be the sine function. So what we have is the union of all lines parallel to the x-axis passing through the sine function in the yz-plane.

cookiemonster

 

[phy]

okie dokie, so would that mean that the sine curve would be coming "out of the page"

 

[cookiemonster]

Correct.

cookiemonster

 

[phy]

oh yeah! thanks! you know, cookiemonster and elmo were always my favorites.

 

[gazzo]

Phy what textbook have you got that only gives answers to odd numbers? I've got a calc book by james stewart that does the same.

does it save that much paper? why don't they just make the font smaller

 

[cookiemonster]

It's standard practice to give answers only to odd problems. It allows instructors to assign even problems so the students can't just copy the answers out of the back of the book.

cookiemonster

 

[Lonewolf]

You should be thankful you get answers! Most textbooks don't, or at best they have 'hints'.

 

[cookiemonster]

Yeah, and eventually they just stop giving you problems, too. So not only do you have to solve the problems, you have to make them up, too!

cookiemonster

 

[gazzo]

haha that's something to look foward to...

 

[phy]

gazzo, i have the calc book by james stewart too. i have the solution manual as well but it only covers up to chapter 8. it has absolutely nothing on graphing and that could have been helpful.