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

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

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

    Find the first three positive values of x for wich 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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    Hello, JOhkonut!

    f(x)\:=\:4\sin\left(\frac{\pi}{2}x\right) +2

    Find the first three positive values of x for which f(x)\:=\:5

    Solve for x\!:\;\;4\sin\left(\frac{\pi}{2}x\right) +2 \;=\;5\quad\Rightarrow\quad \sin\left(\frac{\pi}{2}x\right) \:=\:\frac{3}{4}

    . . . . \frac{\pi}{2}x \:=\:\arcsin(0.75)\quad\Rightarrow\quad x \;=\;\frac{2}{\pi}\arcsin(0.75) .[1]


    \text{Let }\theta_1 \:=\:\arcsin(0.75) \:=\:0.84806

    . . Then: . \theta_2\:=\:\pi-\theta_1,\;\;\theta_3\:=\:\theta_1 + 2\pi


    Substitute these into [1].

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