Help Graphing Sine Function

  1. 1. The problem statement, all variables and given/known data
    I have to graph this function without a calculator, and I'm not sure how to scale the x axis.
    y = 2 - sin(3x - ∏/5)

    2. Relevant equations
    y = Asin(Bx + C)
    Period = 2∏/B
    Phase Shift = -C/B

    3. The attempt at a solution
    I know that the graph will be reflected across the x axis
    Amplitude: 1

    Period: 2∏/3
    Period divided by four = ∏/6

    Phase Shift: (∏/5)/3 = ∏/15

    My professor had told us to graph with a phase shift, you add the period/4 four times like this:

    ∏/15 + ∏/6 = 7∏/30
    7∏/30 + ∏/6 = 12∏/30 or 2∏/5
    12∏/30 + ∏/6 = 17∏/30
    17∏/30 + ∏/6 = 21∏/30 or 11∏/15

    I'm supposed to start the graph at the phase shift, ∏/15, but I don't know how to scale the rest of the x-axis. How do I get to 7∏/30 on the numberline from ∏/15? Gosh I feel so dumb ):
     
  2. jcsd
  3. Ohhhhhhhhhhhhhhhhhhhhhhhhhh, I scale it by ∏/30 don't I? Cue facepalm.
     
  4. HallsofIvy

    HallsofIvy 40,306
    Staff Emeritus
    Science Advisor

    No, you don't. [itex]3x- \pi/5= 3(x- \pi/15)[/itex].
     
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