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April 3rd, 2016, 12:11 AM   #1
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sinusoidal function transformation

Find the points corresponding to (0, 0), (π/2, 1), (π, 0) when the graph of y = sin x is modified by stretching in the x-direction by a factor of 3 and in the y-direction by a factor of 2, shifting pi/2 units right and 1 unit upwards. What is the amplitude and the period of the new curve.

help i have no idea where to begin

do you apply the stretch or shift first
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 April 3rd, 2016, 04:52 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 The problem says "modified by stretching in the x-direction by a factor of 3" first, then later tells you that it is "shifting pi/2 units right". That tells you to do the stretching first and the shifting second. Starting from y= sin(x), "stretching in the x- direction by 3" makes it y= sin(3x). Then "shifting pi/2 units right" changes it to y= sin(3x- \pi/2).
April 3rd, 2016, 05:10 AM   #3
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$y=A\sin[B(x+C)]+D$

Horizontal stretch by a factor of 3 changes the period from $2\pi$ to $6\pi$ ...

$B=\dfrac{2\pi}{6\pi}=\dfrac{1}{3}$

Vertical stretch by a factor of 2 increases amplitude to 2 ... $A=2$

Horizontal shift $\dfrac{\pi}{2}$ units right ... $C=-\dfrac{\pi}{2}$

Vertical shift 1 unit up ... $D=1$

$y=2\sin\bigg[\dfrac{1}{3}\left(x-\dfrac{\pi}{2}\right)\bigg]+1$
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