SOLUTION: Sketch on a graph 2 periods of y=150sin(4x-Pi)in radians

Question 534597: Sketch on a graph 2 periods of y=150sin(4x-Pi)in radians
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Sketch on a graph 2 periods of y=150sin(4x-π)in radians
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Equation used to graph sin function: y=Asin(Bx-C), A=amplitude, Period =2π/B, C/B=Phase shift
For given sin function:
A=150
B=4
Period: 2π/B=2π/4=π/2
1/4 period=π/8
Phase shift:C/B=π/4 (shift to right)
..
Graphing: (For 2 periods)
Let us first graph the basic sin function for 2 periods
On the x-axis make tick marks at π/8, π/4, 3π/8, π/2, 5π/8, 3π/4, 7π/8, π, representing 2 periods.
This will give you the following points:
(0,0), (π/8,1), (π/4,0), (3π/8-1), (π/2,0), (5π/8,1), (3π/4,0), (7π/8,-1), (π,0)
multiply the y-coordinates by 150
(0,0), (π/8,150), (π/4,0), (3π/8-150), (π/2,0), (5π/8,150), (3π/4,0), (7π/8,-150), (π,0)
add π/4 to the x-coordinates (shifting the curve π/4 to the right)
(π/4,0), (3π/8,150), (π/2,0), (5π/8,-150), (3π/4,0), (7π/8,150), (π,0), (9π/8,-150), (5π/4,0)
y-intercept
set x=0
0=150(sin (-π))=0
y-intercept=0
You now have all these points and the y-intercept with which you can graph the function. The graph should start from the origin. So the following is the final configuration:
(0,0), (π/8,-150), (π/4,0), (3π/8,150), (π/2,0), (5π/8,-150), (3π/4,0),(7π/8,150), (π,0), (9π/8,-150), (5π/4,0)
The x-coordinates are numbers(radians) with decimals; ie, π/8≈.3927, 3π/8≈1.1781, etc. Use π=3.14
Note that the period of given sin function=π/2
A phase shift of π/4 shifts the curve half a period to the right
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