# Thread: sin&cos

1. ## sin&cos

I am given a graph and asked:

let f(x)=sin(2pi x) and g(x)= cos(2pi x). Find a possible formula in terms of f or g for the graph.

the graph: cos function
period=1
midline=-3
amp=2

the top of the wave starts at -1 and drops down to -5

im not sure what the question is asking?

2. Originally Posted by Kate182
I am given a graph and asked:

let f(x)=sin(2pi x) and g(x)= cos(2pi x). Find a possible formula in terms of f or g for the graph.

the graph: cos function
period=1
midline=-3
amp=2

the top of the wave starts at -1 and drops down to -5

im not sure what the question is asking?
OK, if the function is a cos graph, it's of the form

$\displaystyle y = a \cos(bx) + c$,

Where $\displaystyle a$ is the amplitude, $\displaystyle b = \frac{2\pi}{Period}$ and $\displaystyle c$ is the mean value.

So $\displaystyle a = 2, b = 2\pi, c = -3$

Which means the function is

$\displaystyle y = 2 \cos (2\pi x) -3$.

Do you see that $\displaystyle g(x)$ is contained in that graph?

So we can write the graph in terms of $\displaystyle g(x)$.

$\displaystyle y = 2g(x) - 3$.

3. Originally Posted by Prove It
OK, if the function is a cos graph, it's of the form

$\displaystyle y = a \cos(bx) + c$,

Where $\displaystyle {\color{red}|}a{\color{red}|}$ is the amplitude, $\displaystyle {\color{red}|}b{\color{red}|} = \frac{2\pi}{Period}$ and $\displaystyle c$ is the mean value.

So $\displaystyle a = 2, b = 2\pi, c = -3$

Which means the function is

$\displaystyle y = 2 \cos (2\pi x) -3$.

Do you see that $\displaystyle g(x)$ is contained in that graph?

So we can write the graph in terms of $\displaystyle g(x)$.

$\displaystyle y = 2g(x) - 3$.
....