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Math Help - Solving Trigonometric Equations

  1. #1
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    Solving Trigonometric Equations

    Hello again

    I just want to know how to solve this trig equation

    The instantaneous power in a stove element is given by the equation

    Power = V(0)^2/R sin^2 wt
    where w = 100pi
    V(0) = 340 V
    t = time (sec)
    R = Resistance (ohms)

    a) Find the power for a 48 ohm stove element when t = 0.001 seconds
    b) Find the max power
    c) Find the time at whcih the max power occurs

    I'm sure a is a simple 'put a value' in but I get a wierd answer. Please help!
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  2. #2
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    P = \frac{V_0^2}{R} \sin^2(\omega t)

    a) P = \frac{340^2}{48} \sin^2(100\pi \cdot .001) \approx 230 \, \, watts

    b) max power will occur when \sin(\omega t) = 1 ...

    P_{max} = \frac{340^2}{48} \cdot 1 \approx 2408 \, \, watts

    c) the initial time that max power occurs will be when \omega t = \frac{\pi}{2}

    100\pi t = \frac{\pi}{2}

    solve for t

    note that max power will occur periodically when \omega t is equal to odd multiples of \frac{\pi}{2}
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