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

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In summary, The conversation discusses the difficulty of a homework question and the use of cross-sections to sketch a graph of the function f(x,y) = sin(y). It also mentions the practice of only providing answers to odd numbered problems in textbooks.
  • #1
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.
 
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  • #2
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
 
  • #3
okie dokie, so would that mean that the sine curve would be coming "out of the page"
 
  • #4
Correct.

cookiemonster
 
  • #5
oh yeah! thanks! you know, cookiemonster and elmo were always my favorites.
 
  • #6
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 :frown:
 
  • #7
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
 
  • #8
You should be thankful you get answers! Most textbooks don't, or at best they have 'hints'.
 
  • #9
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
 
  • #10
haha that's something to look foward to...
 
  • #11
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.
 

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

What is the purpose of sketching functions?

The purpose of sketching functions is to visually represent a mathematical relationship between two variables. It allows us to gain a better understanding of the behavior and characteristics of a function.

How do I determine the domain and range of a function?

The domain of a function is the set of all possible input values that the function can take. It is typically represented on the x-axis of a graph. The range, on the other hand, is the set of all possible output values of the function and is typically represented on the y-axis of a graph. To determine the domain and range, you can look at the inputs and outputs of the function and identify any restrictions or patterns.

What are the key features to look for when sketching a function?

Some key features to look for when sketching a function include: the x and y intercepts, any asymptotes, increasing and decreasing intervals, and any extrema (maximum or minimum points). It is also important to consider the overall shape and behavior of the function, such as whether it is linear, quadratic, exponential, etc.

How do I determine the slope of a function?

The slope of a function represents the rate of change between two points on the graph. It can be determined by calculating the rise over run, which is the change in the y-values divided by the change in the x-values. Alternatively, you can also use the derivative of the function to determine the slope at a specific point.

Can a function have more than one representation on a graph?

Yes, a function can have multiple representations on a graph. For example, a quadratic function can be represented as a parabola, a linear function can be represented as a straight line, and an exponential function can be represented as a curve. However, each of these representations should still follow the rules and characteristics of the original function.

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