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Math Help - Periodic Function- find the first three positive values of x...

  1. #1
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    Periodic Function- find the first three positive values of x...

    f(x)=4sin[(pi/2)x]+2

    Find the first three positive values of x for f(x)=5.

    I was able to get one of the answers(0.54) and another on by adding the period (4+0.54=4.54), but i couldnt get the one in between.
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  2. #2
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    Quote Originally Posted by JOhkonut View Post
    f(x)=4sin[(pi/2)x]+2

    Find the first three positive values of x for f(x)=5.

    I was able to get one of the answers(0.54) and another on by adding the period (4+0.54=4.54), but i couldnt get the one in between.
    Tell us why it is not \pi-x_1, where x_1 is the first solution greater than zero.

    RonL
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  3. #3
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    f(x)=4sin(pi/2*x)+2=5
    so we have
    sin(pi/2*x)=3/4

    so pi*x/2=arcsin(3/4) --> x=2arcsin(3/4)/pi

    and T=2pi/(pi/2)=4 so T/2=2

    we have
    x1=2arcsin(3/4)/pi
    x2=T/2-x1=2-2arcsin(3/4)/pi
    so we have

    x(2k+1)=2arcsin(3/4)/pi +kT=2arcsin(3/4)/pi+4k k=0.1.2.3.4...
    x(2k)=2-2arcsin(3/4)/pi+kT=2-2arcsin(3/4)/pi+4k k=1.2.3.4...
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