Sketch 2 cycles of the function. Plot and label at least 5 points.
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What is the topic of this assignment - "transformation" or "graphing" or something else?
Next, given that it is a sine-function, let's look at just
y = sin(x)
the range of 'x' for the above function for 2 cycles would be 0<= x <= 4*(pi)
Given that you have to plot 2 cycles, of
y=2sin(pi/3x)+1
what would be the range of 'x' for the function above - for 2 cycles?
Here is a PDF file of the homework i'm working on. I believe it is a transformation assignment, but I'm not sure.
Dr.Peterson
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If you're taking a course, the place to start might be to follow an example from your textbook, or steps they might recommend. Do you have anything like that?
It is common in my experience for this topic (graphing trig functions) to be taught after teaching transformations of general functions, but to teach some aspects in a slightly different way. If that is true of you, you might start with transformations. Do you see two vertical transformations (a stretch and a shift/translation)? Do you also see a horizontal transformation caused by replacing x with (pi/3)x?
I'd like to see you apply whatever you have learned to whatever parts you can handle, so we can focus on the parts that are new to you.
I believe the range would be [-1,3]
I read the textbook and can do amplitude, phase shift, and range, but I can't do this last part.
Dr.Peterson
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I take it you mean the pi/3 part.
Here are several ways to think about it, any one of which your textbook may teach (or several):
First, there is a formula: the period of [MATH]\sin(Ax)[/MATH] is [MATH]\frac{2\pi}{A}[/MATH]. So if [MATH]A = \frac{\pi}{3}[/MATH], the period is [MATH]\frac{2\pi}{\frac{\pi}{3}} = \frac{2\pi}{1}\cdot\frac{3}{\pi} = 6[/MATH].
Second, for any function [MATH]f[/MATH], the function [MATH]g(x) = f(Ax)[/MATH] is stretched horizontally by a factor of [MATH]\frac{1}{A}[/MATH] (that is, stretched if this is greater than 1, compressed if it is less than 1). Since the period of the sine is [MATH]2\pi[/MATH], and [MATH]A = \frac{\pi}{3}[/MATH], the graph is compressed by a factor of [MATH]\frac{1}{A} = \frac{3}{\pi}[/MATH], so that its period is 6.
Third, the sine is 0 at [MATH]0, \pi, 2\pi, \dots[/MATH], so your function is 0 when [MATH]\frac{\pi}{3}x = 0, \pi, 2\pi, \dots[/MATH]. Solving for x, this is when x = 0, 3, 6, ... .
Fourth, one cycle is when the argument of the sine goes from 0 to [MATH]2\pi[/MATH], that is, [MATH]0\le\frac{\pi}{3}x\lt2\pi[/MATH]; solve for x and a period of your function is [MATH]0\le x\lt6[/MATH].
Does one of those methods work for you?
D