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Thread: sin&cos

  1. #1
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    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?
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  2. #2
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    Quote Originally Posted by Kate182 View Post
    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 $\displaystyle g(x)$.


    $\displaystyle y = 2g(x) - 3$.
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Prove It View Post
    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 $\displaystyle g(x)$.


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