Question

Can someone please help me?

Describe the effect of changing each of the variables on the graph of y=a sin (bx-c) + d.

a-
b-
c-
d-

Answer 1

i know that one shifts, one shrinks, and one increases the graph but i can't remember which is which, please help!

Answer 2

Hi! Have you ever heard of wolframalpha.com?
It's a "computational search engine," and it's really good with math.

You can have it plot some functions, and easily compare them.

You can plot \(y=\sin(x)\) and \(y=2\sin(x)\) and \(y=5\sin(x)\) all together.

This might be a good way to learn and remember what the things do!

And you'll also want to think about \(\sf why\) it has that effect, and I can help there.

Let me set up a plot for you with the equations I mentioned earlier!

Answer 3

Check out this link, and note that the functions are color coded!
http://www.wolframalpha.com/input/?i=plot+sin%28x%29+and+2sin%28x%29+and+5sin%28x%29

Answer 4

okay checking it now!

Answer 5

Notice that this is altering the \(a\) in your general equation.
It is called the amplitude :)

Answer 6

so that determines whether the graph shrinks or grows?

Answer 7

a-increase the veritcal height by a times
c and d sihfts the graph horizontally and vertically
b shrinks
but to learn follw what @theEric suggests

Answer 8

Haha, @matricked just pointed out something that we should be specific about:
which what does the graph shrink or grow when you change \(a\)?

Answer 9

a adjusts the graph verticlly while b adjusts the graph horizontally

Answer 10

@matricked for future reference does c shift the graph horizontally while d shifts the graph vertically or is it the other way around?

Answer 11

so b doesn't shrink the graph?

Answer 12

Well, let's see what \(b\) will do!

Answer 13

c shifts the graph wrt horizontally while d vertically...
and if a <1 small then the graph shrinks as well

Answer 14

do you know co-ordinate geometry

Answer 15

no I'm not too familiar with geometry, I'm barely on trig functions in pre cal :O

Answer 16

ok
doesn't matter

Answer 17

Here's a change in \(b\). Just make sure you look at the color labels.
http://www.wolframalpha.com/input/?i=plot+sin%28x%29+and+sin%281%2F10+*x%29
http://www.wolframalpha.com/input/?i=plot+sin%28x%29+and+sin%2810+*x%29

I can show you something about the sine function that might help a bit. It is trigonometry.

Answer 18

oh wow that made the graph a lot closer together, so it does shrink it!

Answer 19

Yeah! Do you know about the "unit circle"?

Answer 20

yes i do!

Answer 21

Oh good! That's what the sine function is based on.

Answer 22

oh okay! ill make sure to look at it more when i get the chance! thank you so much for all of your help guys, i really appreciate it!! :)

Answer 23

Okay! I want to explain the things, in case you get a chance to read this.

Answer 24

thank you for taking your time to explain! my laptop is about to die and i don't have a charger with me, so i apologize if i lose connection but i will definitely check again tomorrow if i miss anything! :)

Answer 25

When considering these alterations, keep in mind what the plain old sine function is.

\(a\sin(bx+c)\)

\(\huge a\)
\(a\) multiplies this sine function. Normally, sine oscillates up and down between \(y=-1\) and \(y=1\). If you multiply it's normal value by \(a\), then every point on the graph will be \(a\) times what it would be normally.

So, \(a\sin(x)\) will oscillate between
\(y=-1a=-a\)
and
\(y=1a=a\)
So, between \(-a\) and \(a\) up and down, whatever \(a\) is.
So, that's why this function will seem stretched or shrunk vertically on a graph.
All the points are multiplied from what they would be, so they change proportionally to \(a\).
http://www.wolframalpha.com/input/?i=plot+1%2F2*sin%28x%29+and+sin%28x%29+and+2sin%28x%29

Answer 26

\(\huge b\)
\(b\) is the number that multiplies \(x\). So now we look to the unit circle!

Let's look at it in steps. Remember that \(x\) is an angle on our unit circle.
So let's move our angle from zero to about 10degrees.
Now let's move it another 10.And another 10.
Look at how high up the point on the circle is where the line meets it. That is the sine function increasing from zero, like you see for plain old \(\sin(x)\).
http://www.wolframalpha.com/input/?i=plot+sin%28x%29

But what if... we went by 20 degree changes!!!!! This is \(2\times10\).Look how much faster it changes, or oscillates! In three steps, we covered more of its wave shape. Less \(x\), more wave. We are condensing it, horizontally.

http://www.wolframalpha.com/input/?i=plot+sin%28x%29+and+sin%282x%29+and+sin%28x%2F2%29

But, what if we made changes like 5 degrees, or \(\frac12\times10\).Now it's taking many steps, or \(x\)-values, to get very far at all on it's wave. The wave will be stretched out, horizontally.