April 3rd, 2016, 12:11 AM  #1 
Newbie Joined: Apr 2016 From: australia Posts: 1 Thanks: 0  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 xdirection by a factor of 3 and in the ydirection 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 
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 xdirection 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 
Math Team Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1587 
$y=A\sin[B(x+C)]+D$ 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 ... $D=1$ $y=2\sin\bigg[\dfrac{1}{3}\left(x\dfrac{\pi}{2}\right)\bigg]+1$ 

Tags 
function, sinusoidal, transformation, trig functions 
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