graphing with phase shift, non-2pi period, amplitude change,  TOPIC_SOLVED

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graphing with phase shift, non-2pi period, amplitude change,

Postby anonmeans on Sat Jan 24, 2009 7:24 pm

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!! :shock:
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Postby stapel_eliz on Sat Jan 24, 2009 7:41 pm

anonmeans wrote:Is there a simple way to graph trig functions that aren't "regular"?

In finding the phase shift, the amplitude, and the period, you've actually already done the hard part! :wink:

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 back by pi/3 units), pi/4 is relabelled as pi/4 + pi/3 = 7pi/12, and so forth.

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

Eliz.
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Re: graphing with phase shift, non-2pi period, amplitude change,  TOPIC_SOLVED

Postby anonmeans on Sat Jan 24, 2009 11:03 pm

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?
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Postby stapel_eliz on Sun Jan 25, 2009 12:17 am

anonmeans wrote:...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?

Exactly! :thumb:

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Re: graphing with phase shift, non-2pi period, amplitude change,

Postby anonmeans on Mon Jan 26, 2009 1:27 pm

Thanks!
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