SOLUTION: I have to write a comparison of these two periodic functions: f(x)= 3sin(piX/4)-2 and g(x)= -2sin(12piX/5)+7. - I need to discuss amplitude

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Question 880989: I have to write a comparison of these two periodic functions: f(x)= 3sin(piX/4)-2 and g(x)= -2sin(12piX/5)+7.
- I need to discuss amplitude - relate it to verticle dilation, verticle shift and its relationship to the line of equilibrium.
- mention any other transformations.
what i have figured out so far is that both have no phase shifts and both cross the line of equilibrium halfway between a peak and a trough. I'm just not sure if i'm right and haven't fully answer the question. I'll be really happy to get some help. thank you!
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
I have to write a comparison of these two periodic functions:
f(x)= 3sin(piX/4)-2
amp = 3
vertical shift: 2 units down
horizontal shift: none
period: (2pi)/(pi/4) = 8
eqilibrium when 3sin(piX/4)-2 = 0
Solve::sin(piX/4) = 2/3
piX/4 = arcsin(2/3) = 0.7297
X = 4(0.7297)/pi = 0.9291
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g(x)= -2sin(12piX/5)+7
amp = 2
vertical: reflection in x-axis
vertical shift: 7 up
horizontal shift: none
period: (2pi)/(12pi/5) = 5/6
equilibrium when -2sin(12piX/5) + 7 = 0
Solve: sin(12piX/5)= 7/2
sin cannot be more than 1
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Cheers,
Stan H.
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SOLUTION: I have to write a comparison of these two periodic functions: f(x)= 3sin(piX/4)-2 and g(x)= -2sin(12piX/5)+7. - I need to discuss amplitude - relate it to verticle dilation, ver