Trigonometric Graphs... help D: (1 Viewer)

[LC14199]

Ok so basically here's my issue down to the simplest possible statement: I'm having trouble graphing these because I don't understand the method we're being taught.

More Depth:

Our teacher used this website as an example for graphing: http://www.purplemath.com/modules/grphtrig3.htm (Pages 2 and 3 were used).

The issue I'm having is, when period is modified, normally there would be more crests and more troughs in the same length. However, the mathomat (it's a plastic stencil, used to keep things neat and easy to draw) only has the one curve size (For cosine it has 2 troughs and 1 crest, for sine it has 1 crest and 1 trough). How can I use the mathomat to keep my graphs looking nice, but still keep them accurate? I don't think it's possible tbh.

Cheers,
LC

EDIT: An example of a question I'm having an issue doing this with: f(x) = 3Cos(4x)

EDIT 2: Also forgot to mention, we were told to renumber the axis to make amplitude a non-issue, so that's not where I'm having a problem.

 

[Nailgun]

Ok so basically here's my issue down to the simplest possible statement: I'm having trouble graphing these because I don't understand the method we're being taught.

More Depth:

Our teacher used this website as an example for graphing: http://www.purplemath.com/modules/grphtrig3.htm (Pages 2 and 3 were used).

The issue I'm having is, when period is modified, normally there would be more crests and more troughs in the same length. However, the mathomat (it's a plastic stencil, used to keep things neat and easy to draw) only has the one curve size (For cosine it has 2 troughs and 1 crest, for sine it has 1 crest and 1 trough). How can I use the mathomat to keep my graphs looking nice, but still keep them accurate? I don't think it's possible tbh.

Cheers,
LC

EDIT: An example of a question I'm having an issue doing this with: f(x) = 3Cos(4x)

EDIT 2: Also forgot to mention, we were told to renumber the axis to make amplitude a non-issue, so that's not where I'm having a problem.

its easy
basically like you renumbered the y-axis to make amplitude a non-issue
renumber the x-axis to make the period a non-issue

 

[Drongoski]

Ok so basically here's my issue down to the simplest possible statement: I'm having trouble graphing these because I don't understand the method we're being taught.

More Depth:

Our teacher used this website as an example for graphing: http://www.purplemath.com/modules/grphtrig3.htm (Pages 2 and 3 were used).

The issue I'm having is, when period is modified, normally there would be more crests and more troughs in the same length. However, the mathomat only has the one curve size (For cosine it has 2 troughs and 1 crest, for sine it has 1 crest and 1 trough). How can I use the mathomat to keep my graphs looking nice, but still keep them accurate? I don't think it's possible tbh.

Cheers,
LC

EDIT: An example of a question I'm having an issue doing this with: f(x) = 3Cos(4x)

By re-labelling. For f(x) = 3cos (4x), where you had 1 for graph of y = cos x, replace the Y-values 1 with 3 and -1 with -3; for the x-axis, where you previosly had labels -pi, -pi/2, 0, pi/2, pi etc, replace ith -pi/4, -pi/8, 0, pi/8. pi/4 etc.

 

[LC14199]

But if I use the mathomat to draw the Cos(x) curve and then renumber the x-axis, that still doesn't solve the problem of it not having the correct number of crests and troughs.

Here's what it should look like:

http://www.wolframalpha.com/input/?i=Graph+3Cos(4x)+in+Domain+0+<=+x+<=+2π

And here's what it would look like using the mathomat (without the renumbered x-axis) (The mathomat has a Cos(2x) stencil on it)

http://www.wolframalpha.com/input/?i=Graph+3Cos(2x)+in+Domain+0+<=+x+<=+2π

 

[Nailgun]

But if I use the mathomat to draw the Cos(x) curve and then renumber the x-axis, that still doesn't solve the problem of it not having the correct number of crests and troughs.

what do you mean by the correct number of crests and troughs?
the number will depend on how much of the curve you are drawing

 

[LC14199]

Apologies, I forgot to mention the Domain requirement. (I edited my previous post with links to what I'm talking about).

 

[Nailgun]

Apologies, I forgot to mention the Domain requirement. (I edited my previous post with links to what I'm talking about).

are you graphing them on the same graph?
I don't see why you can't just make a longer line for the x-axis

 

[LC14199]

Because, my book is only so long in its width.

 

[InteGrand]

To sketch y = f(4x), take the graph of y = f(x) and compress it horizontally by a factor of 4.

So if you have a graph of y = 3.cos(x), then squeeze this horizontally by a factor of 4. So before the positive zeros were at pi/2, 3pi/2, 5pi/2, 7pi/2, … .

Now, they'll be at one-quarter of each of these values, i.e. pi/8, 3pi/8, 5pi/8, 7pi/8 … .

In other words, you can draw the same shape as a typical y = cos(x) curve and just label the axial intercepts appropriately to make it y = 3.cos(4x) graph.

 

[Nailgun]

Because, my book is only so long in its width.

either go freehand or go get a new book

 

[Nailgun]

To sketch y = f(4x), take the graph of y = f(x) and compress it horizontally by a factor of 4.

So if you have a graph of y = 3.cos(x), then squeeze this horizontally by a factor of 4. So before the positive zeros were at pi/2, 3pi/2, 5pi/2, 7pi/2, … .

Now, they'll be at one-quarter of each of these values, i.e. pi/8, 3pi/8, 5pi/8, 7pi/8 … .

In other words, you can draw the same shape as a typical y = cos(x) curve and just label the axial intercepts appropriately to make it y = 3.cos(4x) graph.

the issue is he wants to draw it in the domain 0 < x < 2pi, by using the same cos(x) curve shape, on the same axis length
something has to give somewhere

 

[LC14199]

the issue is he wants to draw it in the domain 0 < x < 2pi, by using the same cos(x) curve shape, on the same axis length
something has to give somewhere

Correct. I guess I'm going to have to go free hand, and just try to scale it manually myself.

 

[leehuan]

Correct. I guess I'm going to have to go free hand, and just try to scale it manually myself.

For starters, the HSC prefers your graph to be 1/3 page, whilst the mathomat only does it to about the size of 1/8 (though I don't think most examiners care).

Then, a TON of people go in to the exam without their mathomat anyway.

 

[LC14199]

For starters, the HSC prefers your graph to be 1/3 page, whilst the mathomat only does it to about the size of 1/8 (though I don't think most examiners care).

Then, a TON of people go in to the exam without their mathomat anyway.

My mathomat gives a cartesian plane of 10cm in each direction. On an A4 page, 10cm height and width is about a third.

EDIT: It's almost exactly a third. A4 is 21cm (width) x 29.7cm (height)

 

[leehuan]

My mathomat gives a cartesian plane of 10cm in each direction. On an A4 page, 10cm height and width is about a third.

EDIT: It's almost exactly a third. A4 is 21cm (width) x 29.7cm (height)

The mathomat itself can be used a ruler so it can be used to draw a "Cartesian plane" the size of one full A4 page.

I've never heard of the sine graph being any more than 4cm though

 

[LC14199]

True. Well I guess I'll have to free hand it as best I can, and just go with it I guess.

 

[leehuan]

I can admit that free-handing a sine graph can look appreciably worse (at least, to yourself) than almost any other graph out there. But you can't achieve perfection with just the mathomat alone.

Unless you could somehow meld plastic in the exam room within a matter of seconds, but you know.

 

[Drongoski]

Your mathomat is no help if you need to draw y = cos x and y = 3cos(4x) on the same axes. You will need to learn how to draw sine and cosines curves by hand. I'm a real expert at doing this but unfortunately I don't know how to upload a video of myself drawing such graphs (beautifully, if I might add).

 

[LC14199]

We're not drawing these curves on the same axis. I'm only drawing 3Cos(4x), but I'm trying to use the SHAPE of Cos(x) because it's on my mathomat, and is therefore able to be drawn perfectly.

But since this apparently isn't do-able, I'll just free-hand it.

 

[leehuan]

We're not drawing these curves on the same axis. I'm only drawing 3Cos(4x), but I'm trying to use the SHAPE of Cos(x) because it's on my mathomat, and is therefore able to be drawn perfectly.

But since this apparently isn't do-able, I'll just free-hand it.

You can always change the scale of your graphs.

But if you wanted an explicit visual comparison between the two then no, you have to free-hand.