Question 464893: I need to determine an amplitude, period and shift phase for each function. and I half to graph one period of the function. y=sin(x - PI/2)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! I need to determine an amplitude, period and shift phase for each function. and I half to graph one period of the function. y=sin(x - PI/2).
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Standard form for the sine function: y=Asin(Bx-C), with A=amplitude, Period=2π/B, and Phase-shift=C/B.
For given sine function, y=sin(x - PI/2)
Amplitude=1
B=1
Period=2π/1=2π
1/4 Period=2π/4=π/2
Phase-shift=C/B=(π/2)/1=π/2 (to the right)
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Graphing:
On the x-axis, starting from 0, make tick marks at π/2, π, 3π/2, 2π, 5π/2 Note the marks are (1/4) period apart. At these tick marks, y=0, 1, 0, -1, 0 respectively. You now have the following (x,y) coordinates to plot the given sin function: (π/2,0), (π,1), (3π/2,0), (2π,-1), (5π/2,0) (This covers one period of the shifting sine curve.)
To complete the graph, extend the curve back to the origin where y=-1 (y-intercept)
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