SOLUTION: Hello Could you please help me with this. And this is going to be word for word, ok In this problem you will determine the equation of a sin function. And the following is all

Question 611857: Hello
Could you please help me with this. And this is going to be word for word, ok
In this problem you will determine the equation of a sin function.
And the following is all of the info you will have on the function.
Amplitude is 3
period is 6. (note the period is not 6π )
phase shift is 2 (again no mention of π)
and graph 2 periods of the function.
Thank for your efforts
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Amplitude is 3
period is 6. (note the period is not 6π )
phase shift is 2 (again no mention of π)
and graph 2 periods of the function.
**
Equation for sin function: y=Asin(Bx-C), A=amplitude, Period=2π/B, C/B=phase shift
For given sin function:
Amplitude=3
Period=6=2π/B
1/4 period=6/4=3/2=1.5
B=2π/6=π/3
Phase shift=2=C/B=C/(π/3) (2 units to the right)
C=2π/3
Equation of given sin function: y=3sin(πx/3-2π/3)
..
Graphing function for two periods:
I don't have the means to draw a graph, but I will develop the coordinates with which you can draw the graph yourself.
On an (x,y) coordinate system with the x-axis scaled in radians:
Coordinates of basic sin function with amplitude 1 and no phase shift as follows:
y=sin(πx/3)
(0,0), (1.5,1), (3,0), (4.5,-1), (6,0), (7.5,1), (9,0), (10.5,-1), (12,0)
..
With amplitude=3
y=3sin(πx/3)
(0,0), (1.5,3), (3,0), (4.5,-3), (6,0), (7.5,3), (9,0), (10.5,-3), (12,0)
..
With Phase Shift 2 units to the right (final configuration)
y=3sin(πx/3-2π/3)
(2,0), (3.5,3), (5,0), (6.5,-3), (8,0), (9.5,3), (11,0), (12.5,-3), (14,0)
..
One more point to consider:
y-intercept
set x=0
y=3sin(-2π/3)≈2.6
..
The final coordinates of the graph:
(0,2.6), (2,0), (3.5,3), (5,0), (6.5,-3), (8,0), (9.5,3), (11,0), (12.5,-3), (14,0)

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