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Math Help - Common Period

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    Common Period

    If I am asked to find all solutions to 3 decimals of a trig function, and I know how to get each functions period, how to I get a common period so that I have the distance?

    Thanks
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    Quote Originally Posted by qbkr21 View Post
    If I am asked to find all solutions to 3 decimals of a trig function, and I know how to get each functions period, how to I get a common period so that I have the distance?

    Thanks
    Can I just take a moment to say:

    Huh?

    Perhaps you could post the actual problem?

    -Dan
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    Re:

    For instance if I had:

    2sin(3x)= cos(x)


    I know that 2sin(3x) has a period of \frac{2\pi}{3}


    and that cos(x) has a period of just 2\pi

    but when I writing it in terms of what I get from graphing it on my calc and then putting at the end k\pi what would be the average or how could I find the k\pi?


    I want to know how to do this for future reference...simply solving the equation won't help

    Thanks so Much!!!
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by qbkr21 View Post
    For instance if I had:

    2sin(3x)= cos(x)


    I know that 2sin(3x) has a period of \frac{2\pi}{3}


    and that cos(x) has a period of just 2\pi

    but when I writing it in terms of what I get from graphing it on my calc and then putting at the end k\pi what would be the average or how could I find the k\pi?


    I want to know how to do this for future reference...simply solving the equation won't help

    Thanks so Much!!!
    I see what you're up to. In this case both of the functions (sin(3x) and cos(x)) are periodic on  [0, 2 \pi) so any solutions will also have a period of 2 \pi. (See the graph below.)

    If you have something like
    2 sin(x/2) = cos(x)
    then we have to note that both functions are periodic on  [0, 4 \pi) so the solutions will have a period of 4 \pi.

    -Dan
    Attached Thumbnails Attached Thumbnails Common Period-trig.jpg  
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