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Maths help Please
Topic Started: Jun 7 2006, 06:05 AM (414 Views)
***musical princess***
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HOLY CARP!!!
If i have a trigonal function of x and i want to transform it, what step comes first?

Say, i start with f(x)=sinx and i want to transform it into f(x)=3sin(2x-30degrees), do i stretch it in the y axis first, in the x axis first or do i shift the whole graph first?

Because, depending on which you do first, it has an impact on what the final translation looks like and i don't know which stage you are supposed to do first....???

Anyone?

x
x Caroline x
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Aqua Letifer
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ZOOOOOM!
What do you mean by "transforming" it?
I cite irreconcilable differences.
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***musical princess***
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Translating it, what ever you want to call it. :P

Altering the first sin graph into the second function.

x
x Caroline x
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John D'Oh
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MAMIL
I think I understand what you're asking. You do the stuff in the brackets first, then the sine, then multiply by 3. i.e. x becomes (2x-30)
What do you mean "we", have you got a mouse in your pocket?
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Axtremus
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1. Squish the X-axis into 1/2 its original size. (This accounts for the "2x")
2. Shift the whole graph along the X-axis to the right by 30 degrees. (It's a "phase shift")
3. Stretch the Y-axis into 3 times its original size. (This takes care of the "3" multiplier)
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Aqua Letifer
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ZOOOOOM!
Well, I'm not privy to your newspeak, but yes, I can probably help. :P

Without doing any math, I can tell you that the new function should be 3 times "taller", the wavelength should be half of what is used to be (meaning the x-axis will be "shrunk up" a bit), and if memory serves me correctly, it should be slightly shifted RIGHT (because of that -30degrees business).

I cite irreconcilable differences.
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***musical princess***
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So i would compress it by 2x, then shift it by 30 degrees, THEN stretch that graph by 3?

x
x Caroline x
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***musical princess***
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Axtremus
Jun 7 2006, 03:20 PM
1. Squish the X-axis into 1/2 its original size. (This accounts for the "2x")
2. Shift the whole graph along the X-axis to the right by 30 degrees. (It's a "phase shift")
3. Stretch the Y-axis into 3 times its original size. (This takes care of the "3" multiplier)

In that order? Yes?

x
x Caroline x
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Aqua Letifer
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ZOOOOOM!
P.S. I don't know what methods you're using for this (or rather, what methods you should be using), but the easy way to see where and how far it shifts, and also the wavelength, is to solve that new function for when it's at a maximum, minimum, and 0. Then, just fill in the blanks.
I cite irreconcilable differences.
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John D'Oh
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MAMIL
***musical princess***
Jun 7 2006, 10:21 AM
So i would compress it by 2x, then shift it by 30 degrees, THEN stretch that graph by 3?

x

You compress x by 2, then shift by 30. Then sine. Then you stretch y by 3.
What do you mean "we", have you got a mouse in your pocket?
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***musical princess***
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Aqua Letifer
Jun 7 2006, 03:22 PM
P.S. I don't know what methods you're using for this (or rather, what methods you should be using), but the easy way to see where and how far it shifts, and also the wavelength, is to solve that new function for when it's at a maximum, minimum, and 0. Then, just fill in the blanks.

I'm not supposed to be differentiating, it's only supposed to be a simple shift. I know how to do all the differnt stretches and phase differences, i just don't know whether you do phase differences first, or stretches/compression.

x
x Caroline x
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John D'Oh
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MAMIL
***musical princess***
Jun 7 2006, 10:22 AM
Axtremus
Jun 7 2006, 03:20 PM
1. Squish the X-axis into 1/2 its original size. (This accounts for the "2x")
2. Shift the whole graph along the X-axis to the right by 30 degrees. (It's a "phase shift")
3. Stretch the Y-axis into 3 times its original size. (This takes care of the "3" multiplier)

In that order? Yes?

x

Yes
What do you mean "we", have you got a mouse in your pocket?
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***musical princess***
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Okay, so where would that cut the y-axis? Would it be at 1.5?

x
x Caroline x
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John D'Oh
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***musical princess***
Jun 7 2006, 10:28 AM
Okay, so where would that cut the y-axis? Would it be at 1.5?

x

Do you mean 15?

(2x15)-30 = 0.
3sin(0) = 0.
What do you mean "we", have you got a mouse in your pocket?
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Aqua Letifer
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ZOOOOOM!
Have you gotten into derivatives yet? I assume you have? Why not just use them to find some key endpoints? That'll show you the shape of the graph.

And as for which thing to do first, and which to do last, well... it's sort of all together. The graph is 3 times a high, 1/2 as wide, AND slightly shifted right, all at once. One or the other doesn't really "come first".
I cite irreconcilable differences.
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***musical princess***
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John D'Oh
Jun 7 2006, 03:31 PM
***musical princess***
Jun 7 2006, 10:28 AM
Okay, so where would that cut the y-axis? Would it be at 1.5?

x

Do you mean 15?

(2x15)-30 = 0.
3sin(0) = 0.

I proper don't get this at all.

My text book is really confusing me. :wacko:

It has the upper and lower limits at 3 and -3. It cuts the y-axis at -1.5. It doesn't have a difinte degree for the start of the sine pattern but cosine starts at 60 degrees and it has a period of 180 degrees.

What on earth is it talking about??

This is why i can't figue out which function they've done first.

x
x Caroline x
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***musical princess***
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Aqua Letifer
Jun 7 2006, 03:33 PM
Have you gotten into derivatives yet? I assume you have? Why not just use them to find some key endpoints? That'll show you the shape of the graph.

And as for which thing to do first, and which to do last, well... it's sort of all together. The graph is 3 times a high, 1/2 as wide, AND slightly shifted right, all at once. One or the other doesn't really "come first".

But in some cases, maye not this one, it does actually have an effect on the final shape of the graph.

x
x Caroline x
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John D'Oh
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MAMIL
Can you write out the full question? I don't quite understand what they're asking for.
What do you mean "we", have you got a mouse in your pocket?
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Aqua Letifer
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ZOOOOOM!
I'm just not seeing it. I mean, I don't consider these three parameters of a trig function seperate. Anyways, this is really a simple problem, but I'm not sure what methods they want you to use, or what the exercise is designed to help you do, so it's hard to give you advice on how to solve it.

That description you gave is pretty confusing to me, too. Unnecessarily so.
I cite irreconcilable differences.
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***musical princess***
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HOLY CARP!!!
(Maths deserves to burn in hell!!!)

Okay...

i) sketch the curve of the function f(x)=3sin(2x-30degrees)

ii)state the period


I thought i knew how to do it but the graph they have drawn as a solution is raelly confusing me.

x
x Caroline x
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***musical princess***
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Aqua Letifer
Jun 7 2006, 03:38 PM
I'm just not seeing it. I mean, I don't consider these three parameters of a trig function seperate. Anyways, this is really a simple problem, but I'm not sure what methods they want you to use, or what the exercise is designed to help you do, so it's hard to give you advice on how to solve it.

That description you gave is pretty confusing to me, too. Unnecessarily so.

I'm sorry. I'm trying my best to explain but i can't get my head around it. My teacher told me a while ago that it is important which order you do the things in because it can effect the shape of the graph.

x
x Caroline x
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Aqua Letifer
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ZOOOOOM!
Oh. Well not bad at all! I think each of us has said this, only in a different way (which is what makes math awesome), find your maximums, minimums, and zero values of the function. And since you know what the sine wave looks like, it'd be easy to fill in the other values after that. (This shouldn't get you into trouble with the "order" of things, because by doing this, you aren't so much starting with one point, so much as you are letting them all "fall into place". I mean, order or not, the max, min, and zeros of that function aren't going to change no matter what the heck you do first, assuming you find them correctly.)

After you get that done, you can look back at your graph and determine the period.
I cite irreconcilable differences.
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John D'Oh
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MAMIL
There's three things to consider:

since x becomes 2x, the normal period for the sine is halved (frequency doubled). This is done first.
There's then a linear phase shift of 30 degrees, AFTER the doubling of freq.
The amplitude of this curve (i.e. y) is increased by a factor of 3.

Does that help?
What do you mean "we", have you got a mouse in your pocket?
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kentcouncil
Fulla-Carp
Check out this website:

http://www.analyzemath.com/trigonometry/sine.htm

It has an interactive tutorial applet that shows you how changing the co-efficients changes the graph. It's quite good as a visual aid.
It was a confusion of ideas between him and one of the lions he was hunting in Kenya that had caused A. B. Spottsworth to make the obituary column. He thought the lion was dead, and the lion thought it wasn't.

- P.G. Wodehouse
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John D'Oh
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MAMIL
***musical princess***
Jun 7 2006, 10:40 AM
(Maths deserves to burn in hell!!!)

Bear in mind that the reason I'm trying to help, (other than my generous spirit, of course) is that this is more interesting than what I'm supposed to be doing by a factor somewhat larger than the one you're applying to your curve. Give you an idea of how great a career in engineering is? ;)
What do you mean "we", have you got a mouse in your pocket?
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