Question 561411: Can someone please help me with this question from my book?
Describe each of the following graphs of y. Give (a) its amplitude (if applicable), (b) its maximum and minimum (if applicable) and (c) its period. If it has no amplitude, maximum, or minimum, write "none" on the appropriate blank line. Be sure to review the definitions of amplitude, maximum, and minimum, in answering these questions.
1. y=tan 2x
2. y=3 sin1/3x
Thanks
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Give (a) its amplitude (if applicable), (b) its maximum and minimum (if applicable) and (c) its period. If it has no amplitude, maximum, or minimum, write "none" on the appropriate blank line. Be sure to review the definitions of amplitude, maximum, and minimum, in answering these questions.
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The formula used for graphing tan functions with no phase shift: y=tan Bx, period=π/B
1. y=tan 2x
B=2
Period=π/B=π/2
1/4 period=π/8
For one period on an (x,y) coordinate system with the x-axis scaled in radians:
Coordinates are: (-π/4,-∞), (-π/8,-1), (0,0), (π/8,1), (π/4,∞)
You now have the information you need to plot given tan function. Note that it will have the same shape as the basic tan function except its period is π/2 instead of π.
Amplitude, maximum, or minimum: none
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The formula used for graphing sin functions with no phase shift: y=AsinBx, period=2π/B, A=amplitude
2. y=3 sin1/3x
B=(1/3)
Period: 2π/(1/3)=6π
1/4 period=6π/4=3π/2
Amplitude=3
maximum=3
minimum=-3
For one period on an (x,y) coordinate system with the x-axis scaled in radians:
Coordinates are: (0,0), (3π/2,3), (3π,0), (9π/2,-3), (6π,0)
You now have the information you need to plot given sin function. Note that it will have the same shape as the basic sin function except its period is 6π instead of 2π.
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