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Trigonometric functions ->sine function EASY!

  1. May 2, 2013 #1
    Trigonometric functions -->sine function EASY!

    1. The problem statement, all variables and given/known data
    Consider the trigonometric function f(t)=-1+4sin(0.5π(t-1)).
    (a) What is the amplitude of f(t)?
    (b) What is the period of f(t)?
    (c) What are the maximum and minimum values attained by f(t)?


    2. Relevant equations

    Period: 2π/b

    3. The attempt at a solution

    The amplitude is 4.
    The period is 2π/b = 2π/0.5 = 4π.

    How do you find the maximum and minimum values?

    Any help would be appreciated!
     
  2. jcsd
  3. May 2, 2013 #2

    Dick

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    sin(x) varies between +1 and -1, right?
     
  4. May 2, 2013 #3

    SammyS

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    That period looks wrong to me.
     
  5. May 2, 2013 #4

    Dick

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    Good point. b is 0.5π, right?
     
  6. May 3, 2013 #5
    How do we find the y intercept for this equation?

    f(t)= -1+4sin(0.5π(t-1))
    0=-1+4sin(0.5π(t-1))
    1=4sin(0.5π(t-1))

    How do I do the rest?

    I know the y intercept is -5 but I'd like to know how you get there if you try to find it by hand.
     
  7. May 3, 2013 #6
    How is it 0.5π?
     
  8. May 3, 2013 #7

    HallsofIvy

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    "b" was, in the first post, the coefficient of t in the general form.

    Yes, "b" is [itex]0.5\pi[/itex] so the period is [itex]2\pi/0.5\pi= 4[/itex], not "[itex]4\pi[/itex]".
     
  9. May 3, 2013 #8

    Dick

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    That's not really a 'y-intercept', you are finding the zeros of f(t). And since it's periodic there will be lots of them. For the rest you've got (1/4)=sin(0.5π(t-1)). Try and figure out where sin(x)=1/4. Set 0.5π(t-1) equal to those values.
     
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