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Determining Sin wave horizontal shift 'C' value

  1. May 20, 2014 #1
    Find the equation of a sine function with its first positive maximum point at (pi/5,8) and its next minimum point at (7pi/10,-2).

    With the sin form as y=a*sin[b*(x-c)] + d

    I found:

    a=[max-min]/2 = 5
    b= 2pi/period= 2pi/(2*[max-min])=2
    d=max+min/2=3

    I am having troubles determining the value for c.

    How I am thinking about is that the point of reference for sin when it hits its first maximum is at pi/2. The difference between the pi/2 and pi/5 would be my phase shift however the answer is not right. The value for c should be pi/20.

    Can someone explain what I have done incorrectly here?
     
  2. jcsd
  3. May 20, 2014 #2

    SammyS

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    sin(x) has its first max at x = π/2 -- basically when its argument is π/2 .

    What is the argument of the sine function appearing in your expression?
     
  4. May 20, 2014 #3
    My arguement is 2(x+3pi/10)
     
  5. May 20, 2014 #4

    SammyS

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    So, you've found c ?
     
  6. May 20, 2014 #5
    Yes, but the correct answer for the argument is 2(x+pi/20)
     
  7. May 20, 2014 #6
    Ahh I think I got it... so what I am supposed to do is set the argument at pi/5 equal to pi/2 and solve for c like this...

    2(pi/5 -c) = pi/2

    Thanks for your help!
     
  8. May 20, 2014 #7

    SammyS

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    So the argument is 2(x - c) .

    That should equal π/2 at the first maximum. Right?

    You know the x value at the first max., so plug that in & solve.
     
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