Help Graphing Sine Function

1. Feb 27, 2012

theintarnets

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. Feb 27, 2012

theintarnets

Ohhhhhhhhhhhhhhhhhhhhhhhhhh, I scale it by ∏/30 don't I? Cue facepalm.

3. Feb 28, 2012

HallsofIvy

Staff Emeritus
No, you don't. $3x- \pi/5= 3(x- \pi/15)$.