Find Phase Shift & # Squares to Move Trig Graphs

[cruisx]

Hi i was just wondering if someone could tell me how one can find the phase shift and the number of squares to move the graph over by from an equation?. We are doing cosine and sine graphs and my teacher has been away for a few days so the supply teachers haven't been really that great in teaching. I know how to get the amplitude and change the scale of the graph suchs as 2 \pi or 3\pi/2. I can also plot the base curve fine but i get stuck when i have to shift it right or left. I don't know how many number of squares to do so? I was wondering if someone would be helpfull enough to teach me so? is there an equation i can use? i would really appericiate the help.

(example of some of the examples that were on the board)
1) y = 5cos3(\vartheta-\pi)

2) y = 2cos3(x + \pi/6)

i can figure everything else out excpet for the phase shift(how many squares to shif the graph)

thanks in advance to who ever tries to help me out.

 

[tiny-tim]

Hi cruisx!

(have a theta: θ and a pi: π )

(example of some of the examples that were on the board)
1) y = 5cos3(\vartheta-\pi)

2) y = 2cos3(x + \pi/6)

i can figure everything else out excpet for the phase shift(how many squares to shif the graph)

ok, let's do 2) …

you know how to draw y = 2cos3x …

where do you put the bumpy bit in the middle?

instead of at x = 0, it'll be at (x + π/6) = 0,

in other words at x = -π/6 …

so you shift the graph π/6 to the left.