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Need help with trigonometry

  1. May 27, 2013 #1
    A sinusoidal voltage is represented by the formula v = 6sin (314t + pi/2). Sketch the graph on the graph paper provided for values of t from 0.0s to 0.04s and show on the graph the values of
    • the amplitude
    • the time period

    and show how the frequency of the waveform may be determined from the graph.



    can i have a small hint on finding the amplitude and the time period?
     
  2. jcsd
  3. May 27, 2013 #2
    If you know calculus, the amplitude will be the value of v at the time ##t_0## such that ##\left.\frac{dv}{dt}\right|_{t_0}=0##.

    If you don't know calculus, what's the maximum value of the sine function and what does that imply about the magnitude of ##6\sin(\xi)##?
     
    Last edited: May 27, 2013
  4. May 27, 2013 #3

    LCKurtz

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    No. The amplitude is not a value of ##t##.

    In other words, the amplitude.

    @will.i.am2: You are required to show an attempt at solving the problem to receive help.
     
  5. May 27, 2013 #4
    Sorry. I misspoke. The amplitude will be the value of v at ##t_0##. I fixed my post.
     
  6. May 27, 2013 #5
    v = 6sin (314t + π/2)
    v = 6sin (314(0) + 3.14 /2)
    v = 6sin (0 + 1.57)
    v = 6sin(1.57)
    v = 0.16

    v = 6sin (314t + π/2)
    v = 6sin (314(0.01) + 3.14 /2)
    v = 6sin (3.14 + 1.57)
    v = 6sin(4.71)
    v = 0.49

    v = 6sin (314t + π/2)
    v = 6sin (314(0.02) + 3.14 /2)
    v = 6sin (6.28 + 1.57)
    v = 6sin(7.85)
    v = 0.81

    v = 6sin (314t + π/2)
    v = 6sin (314(0.03) + 3.14 /2)
    v = 6sin (9.42 + 1.57)
    v = 6sin(10.99)
    v = 1.14

    v = 6sin (314t + π/2)
    v = 6sin (314(0.04) + 3.14 /2)
    v = 6sin (12.56 + 1.57)
    v = 6sin(14.13)
    v = 1.46
     
  7. May 27, 2013 #6
    i think maximum value of sin is 6 but i don't know what's it implying on the amplitude of 6sin.
     
  8. May 27, 2013 #7

    Dick

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    I think the maximum of sin is 1. Try graphing it. And set your calculator to radians, not degrees.
     
  9. May 27, 2013 #8
    i have done it in rads only. & how can it's be 1?
     
  10. May 27, 2013 #9
    What does the value of y = sin(x) look like. What max/min values does it have ? What about y = psin(x) where p is some real number. What are it's max/min values ? How does this relate to the equation you were given ?
     
  11. May 27, 2013 #10

    Dick

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    If you take sin(1.57) in radians, you should get very close to 1. 1.57 is almost pi/2.
     
  12. May 27, 2013 #11
    why have you taken sin of half pi? I still didn't get it.
     
  13. May 27, 2013 #12

    Dick

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    I'm trying to tell you v=0.16 isn't right because your calculator isn't in radian mode. sin(1.57) should round off to 1.00, so 6*sin(1.57) should be 6.
     
  14. May 27, 2013 #13
    This is in the wrong forum. This is neither calculus nor beyond. It's pre-calculus.
     
  15. May 28, 2013 #14
    How did you arrive at this value... Let's try it

    we have

    [tex] v = 6sin(314t + \frac{\pi}{2}} [/tex]

    verbally stated v = 6 times the sin of 314t + [itex]\frac{\pi}{2}[/itex] radians.

    So at time t = 0 we have..

    [tex] v = 6sin(314(0) + \frac{\pi}{2}) [/tex]

    which gives

    [tex] v = 6 sin( \frac{\pi}{2}) [/tex]

    In other words to get v at t=0 we have to multiply the sine of [itex]\frac{\pi}{2}[/itex] radians by 6.

    [itex] \frac{\pi}{2} [/itex] radians in degrees is 90 degrees, the sine of which is 1 . So what then happens when you then multiply 1 by 6 to get the final result for v ?

    Your calculations are screwed up. As someone else pointed out, you appear to be using a calculator set to degrees but you are providing radians. Either switch the calculator to radians or, convert the radians to degrees and then compute the sine.
     
  16. May 28, 2013 #15
    ^^

    yes, you guys are absolutely right & my mistake I wasn't doing in rad.

    it is equal to 6 then the amplitude would be 6 - (-6) / 2 = 6
     
  17. May 28, 2013 #16

    verty

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    Given that -1 <= sin(x) <= 1, it follows that -6 <= 6 sin(x) <= 6 (just multiply each part by 6).

    PS. It helps to learn all you can about these trig functions.
     
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