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Math Help - period two product of sin, cos

  1. #1
    jut
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    period two product of sin, cos

    how does one find the period of this function

    y(x)=sin\frac{8\pi x}{9} cos\frac{3\pi x}{4}
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  2. #2
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by jut View Post
    how does one find the period of this function

    y(x)=sin\frac{8\pi x}{9} cos\frac{3\pi x}{4}
    Try using the identity \sin A \cos B = \frac {\sin (A-B) + \sin (A+B)} 2

    and see where that takes you.
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  3. #3
    jut
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    Ah yes.

    <br /> <br />
sin\frac{8\pi x}{9} cos\frac{3\pi x}{4}=  \frac {\sin (-7 x \pi /20) + \sin (17 x \pi /20)} 2<br /> <br />

    So the frequency of each sine wave can be found...

    <br />
f_1=7/40<br />

    <br />
f_2=17/40<br />

    And to find the fundamental frequency...

    <br />
f_o=GCD(7/40,17/40)=1/40<br />

    Which gives a period of...

    <br />
T_o=40<br />

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