Is there a simple way to graph trig functions that aren't "regular"? Like f(t) = sin(t) is regular, but g(t) = 2sin(3(t-pi/3)) has different amplitude (2 instead of 1), a different period (pi instead of 2pi), and a phase shift (starting at pi/3 instead of at 0). It's complicated!!

- stapel_eliz
**Posts:**1628**Joined:**Mon Dec 08, 2008 4:22 pm-
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In finding the phase shift, the amplitude, and the period, you've actually already done the hard part!Is there a simple way to graph trig functions that aren't "regular"?

Now draw the "regular" graph, but draw it "lightly", with the markings (like the t- and y-axes) in pencil. Draw lines for the amplitude (or tick-marks on the axis, if that's what your instructor prefers), and mark off the "regular" period "important" points; at the very least, mark off 0, pi/2, pi, 3pi/2, and 2pi. Do this for at least an extra half-period on either "end" of the "regular period".

Now re-label. Instead of the amplitude line being labelled as y = 1, re-label as y = 2. Instead of the period markings being 0, pi/2, etc, contract by labelling as 0, pi/4, etc (to account for the period being half as long as "regular"). Since this function is shifted pi/3 to the right, move all those labels by pi/3: 0 is relabelled as pi/3 (that is, you'll need to move the y-axis line

Now draw the shifted lines in darker, and erase the lines you don't need. You're done!

Eliz.

Oh. Thats **way** easier! But what about for shifting up and down? Do you do the same as you said before, but then redo the t-axis up or down too?

- stapel_eliz
**Posts:**1628**Joined:**Mon Dec 08, 2008 4:22 pm-
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