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Solving Trigonometric Equations

  1. Nov 17, 2011 #1
    1. The problem statement, all variables and given/known data

    1) When a pendulum 0.5m long swings back and forth, its angular displacement Ɵ from rest position, in radians is given by Ɵ=1/4sin((pi/2)t), where t is the time, in seconds. At what time(s) during the first 4 s is the pendulum displaced 1 cm vertically above its rest position? (assume the pendulum is at its rest position at 0).

    2) the current in a household appliance varies according to the equation A=5sin120pit, where A is the current in amperes, and t is the time, in seconds. at what rate is hte current changing at t=1s?





    3. The attempt at a solution
    1) i'm not sure how to approach/solve this question

    2) i got 0, can anyone confirm?
     
  2. jcsd
  3. Nov 17, 2011 #2

    Mark44

    Staff: Mentor

    Start by sketching a graph. At what points on the graph is the height above the starting position 1 cm?
    Show us how you got 0.
     
  4. Nov 17, 2011 #3
    a=(5sin120pi(1))-(5sin120pi(0.999))/(1-0.999)
    =0?? doesn't make sense though
     
  5. Nov 17, 2011 #4
    What you have calculated here is the current at t = 1. Is the question not asking for the rate of change at t = 1?
     
  6. Nov 17, 2011 #5
    so would it be
    a=(5sin120pi(1.001))-(5sin120pi(0.999))/(1.001-0.999)
     
  7. Nov 17, 2011 #6
    Yes, that's a pretty close approximation and will give you an answer within 2.35 % of the exact answer. Question, have you ever done any calculus before? (and yes, I do realize this is the precalculus section)
     
  8. Nov 17, 2011 #7
    no, i have it second semester.

    and the answer is STILL 0 :/
     
  9. Nov 17, 2011 #8
    I assure you the answer is not zero, make sure your calculator is in radian mode, and make sure you keep track of your negatives.
     
  10. Nov 17, 2011 #9
    the maximum of this graph is 0.25 :/


    i got the answer as a=-328.365.
     
  11. Nov 17, 2011 #10
    For the pendulum, think in terms of trigonometric functions. If you set the rest position to (0, 0) and you know the radius is 0.5 m, for what values of [itex]\theta[/itex] will the height be 1 cm? Once you figure that out, you can find the times fairly easily.

    Ok so:

    [tex] m = \frac{5 \sin{120\pi 1.001} - 5 \sin{120\pi 0.999}}{0.002}[/tex]
    [tex] m = 2500(\sin{120.12 \pi} - \sin{119.88 \pi}) [/tex]

    where [itex]\sin{120.12 \pi} \approx 0.368[/itex] and [itex] \sin{120\pi 0.999} \approx -0.368 [/itex]. I think if you try again you'll get the right answer.
     
  12. Nov 17, 2011 #11
    i still don't understand to be honest :/
     
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