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Math Help - Can anyone show me how to solve this?

  1. #1
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    Can anyone show me how to solve this?

    Instantaneous value of voltage in an AC current at any gfiven time is given by:

    V = 140 sin (50 * PI * t) volts

    determine:

    a) The amplitude

    b) The frequency

    c) The period time

    d) The amplitude after 0.014s

    e) Equation of the waveform which LEADS the above waveform by PI/3

    f) Equation of the waveform which LAGS the above waveform by PI/3

    Your assistance in this problem would be greatly appreciated

    Tsar
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  2. #2
    Junior Member rubix's Avatar
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    I'm guessing you're having trouble figuring out the relationship between what you are given and what you are asked to find. I'm also assuming that once you know the relation, you know how to solve it

    a) Amplitude is pretty similar to max and min value of a function. Use the usual process (i.e. find deriv, set deriv to zero, and solove) to find critical points.

    b) frequency is # of occurance of a repeating process per unit time. Think of that in mathamatical terms.

    c) reciprocal of frequency

    d) plug 0.014s into deriv
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  3. #3
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    I believe it is the chain rule to solve and that gradient = 0 at max and min so equating the first derivative to zero will solve for 't'

    Is that assumption correct?

    I haven't done any math like this for 10 years
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  4. #4
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    Amplitude = 140 (since the max value of trigs is always 1)


    Period = divide either 2pi or 360 degrees (depending on the unit) by the angle inside the trig expression (in this case, 50pi). So period = 1/25 radian.


    Frequency = I'm not sure exactly how to solve it but I'll give you an idea. First of all, find the wavelength (distance between the peaks of two symmetric curves). I believe you do this by finding the first two values for which sinx equals 140 (its max). You can do this through calculus or just find x(50pi) = pi/2 and x(50pi) = (2pi + pi/2). Subtract the bigger x-value by the smaller x-value then, bam, you have the wavelength. Then divide the wavelength by some kind of time unit but I'm not really sure though.
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  5. #5
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    Quote Originally Posted by rubix View Post
    I'm guessing you're having trouble figuring out the relationship between what you are given and what you are asked to find. I'm also assuming that once you know the relation, you know how to solve it

    a) Amplitude is pretty similar to max and min value of a function. Use the usual process (i.e. find deriv, set deriv to zero, and solove) to find critical points.

    b) frequency is # of occurance of a repeating process per unit time. Think of that in mathamatical terms.

    c) reciprocal of frequency

    d) plug 0.014s into deriv
    Is the derivative 700*PI Cos (50*PI*t)......?
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  6. #6
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    You don't have to find the derivative...

    But the derivative is

    7000picos(50pix)
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  7. #7
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    I got that bit right then.

    So I'm a bit surprised by the question then?

    So you are saying you don't need the derivative to answer the question

    Dang! I never did understand trig! LOL
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