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Math Help - Voltage output sinusoidal function problem

  1. #1
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    Voltage output sinusoidal function problem

    The voltage output (in volts) of an electrical circuit at time t seconds is given by the following function.

    V
    (t) = 22 sin(5πt − 3π) + 1

    (e) During the first second, determine when the voltage output of the circuit is 3 volts. (Enter your answers as a comma-separated list. Round your answers to four decimal places.)

    My approach is to
    1. set the function equal to 3
    3=22sin(5∏t-3∏)+1

    2. take the natural log to get rid of the exponent
    ln3=(2sin(5∏t-3∏)+1)ln2
    [SUP]
    (ln3/ln2)-1=2sin(5∏t-3∏)

    [(ln3/ln2)-1]/2=sin(5∏t-3∏)

    arcsin ([(ln3/ln2)-1]/2)=5∏t-3∏

    t= (arcsin([ln3/ln2)-1]/2) + 3∏) / 5∏

    t=0.6189


    I don't know if I'm on the right track so far, and I have no idea where to go from here? Any help would be soooooo great!! Thanks.
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  2. #2
    Member dokrbb's Avatar
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    Re: Voltage output sinusoidal function problem

    Quote Originally Posted by UWstudent View Post
    The voltage output (in volts) of an electrical circuit at time t seconds is given by the following function.

    V
    (t) = 22 sin(5πt − 3π) + 1

    (e) During the first second, determine when the voltage output of the circuit is 3 volts. (Enter your answers as a comma-separated list. Round your answers to four decimal places.)

    My approach is to
    1. set the function equal to 3
    3=22sin(5∏t-3∏)+1

    2. take the natural log to get rid of the exponent
    ln3=(2sin(5∏t-3∏)+1)ln2
    [SUP]
    (ln3/ln2)-1=2sin(5∏t-3∏)

    [(ln3/ln2)-1]/2=sin(5∏t-3∏)

    arcsin ([(ln3/ln2)-1]/2)=5∏t-3∏

    t= (arcsin([ln3/ln2)-1]/2) + 3∏) / 5∏

    t=0.6189


    I don't know if I'm on the right track so far, and I have no idea where to go from here? Any help would be soooooo great!! Thanks.
    I can suggest you that there is something you miss between these steps:

    [(ln3/ln2)-1]/2=sin(5∏t-3∏)

    arcsin ([(ln3/ln2)-1]/2)=5∏t-3∏, and you final result will be something like 0.06s , so sounds reasonable since you get a time during the first second
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  3. #3
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    Re: Voltage output sinusoidal function problem

    Hi
    As the index is raised to the power 2 you need to take logs to this base.

    Then log to base2 of 3 = ln3/ln2

    This is a standard result from the laws of logs.
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