Question

How would I find the equation of this graph?

Answer 1

i dont understand that

Answer 2

The graph?

Answer 3

yeah :(

Answer 4

Ok

Answer 5

you know how to work it ?

Answer 6

No, that is why I posted this.

Answer 7

lol thanks for trying

Answer 8

First, please identify the function graphed here. Hint: Note that y is not zero when x = 0.

Answer 9

You mean like cosine?

Answer 10

im not sure whats really going on y'all , im just trying to find out how it works or the answer

Answer 11

Yes, this is the graph of a cosine function.
What does the word "period" mean in this context?
What does the word "amplitude" mean in this context?

Answer 12

Isn't period that difference, and amplitude is how high it goes from the middle? I don't know exactly.

Answer 13

My apologies , i thought this was my problem that i posted lol , i just realized it wasnt

Answer 14

Oh, no problem! I was confused on what you were talking about.

Answer 15

Regarding "Isn't period that difference?" Please elaborate on your question. It's not clear.

Answer 16

the* and I am not sure exactly what it is, that is why I'm asking for some help

Answer 17

Regarding "amplitude is how high it goes from the middle?" That's a lot better. Note that amplitude is always a positive quantity.

The cosine function is "periodic." Explain in your own words what that means.

Answer 18

I don't know...

Answer 19

Maybe that it repeats?

Answer 20

I'm happy to help, but not to start an explanation from scratch. Please look up "period of the sine function" on the Internet and tell me what you learn from that. yes, repeating itself is the primary definition of "periodic."

Answer 21

That it has a period of 2pi

Answer 22

Since the Sine repeats itself every 2pi

Answer 23

Right. See, you knew this pretty well already and were able to find more info through an Internet search. Good for you. Now take a look at the graph and determine what the period of this cosine function is.

Answer 24

2pi?

Answer 25

Yes. The cosine function repeats itself every 2pi radians.

When we're finished here, we'll have an equation that looks like this:

y = a*cos b*x.

Very important rule: Dividing 2pi by b (b coming from that equation, above, results in our obtaining the period of the function.

Here we already know tht the period is 2pi. Find the value of b, please.

Answer 26

How do I find b? Sorry I don't know

Answer 27

As I said before, the period is \[Period=\frac{ 2\pi }{ b }.\] If we know the Period, we can find the corresponding value of a.


If P=(2pi)/a, and we multiply both sides of this equation by a, what do we get?

Answer 28

Do you want me to find a or b?

Answer 29

So sorry. My mistake.

If P=(2pi) / b, multiply both sides of this equation by 'b' to eliminate fractions.

Answer 30

Both sides? Would it be 2pi?

Answer 31

Thanks :(

Answer 32

If P = (2pi) / b, and we multiply both sides by b, we get 2*b=2pi.

Solve this equation for b, please.

What do you think the value of a is?

Write out the function now: y = a * cos b*x, substituting the values of a and b we've found.