```Question 499205
Describe how the graph of the function y=1.5sin(4x) is related to the graph of y=sinx.
Questions:
What is the amplitude,period of the fuction y=1.5sin(4x)?
Graph the two periods of the function y=1.5sin(4x).
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Standard form of equation for sin function: Asin(Bx-C), A=amplitude, Period=2&#960;/B, Phase shift=C/B
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y=1.5sin(4x) and  y=sinx are sin functions with different periods and different amplitudes.
The former has a period of &#960;/2 and amplitude=1.5; the latter a period of 2&#960; and amplitude=1.
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For given sin function, y=1.5sin(4x):
Amplitude=1.5
B=4
Period=2&#960;/B=2&#960;/4=&#960;/2
1/4 Period=&#960;/8
Phase shift: none
Graphing.
On the x-axis make tick marks at 0, &#960;/8, 2&#960;/8, 3&#960;/8, 4&#960;/8, 5&#960;/8, 6&#960;/8, 7&#960;/8 and 8&#960;/8. (For clarity I left these fractions as 8th's, but they should be reduced in the final graph). Plug these values into given sin function and you will get the following respective points to graph the function:
(0,0), (&#960;/8,1.5), (&#960;/4, 0), (3&#960;/8,-1.5) (&#960;/2,0), (5&#960;/8,1.5), (3&#960;/2,0), (7&#960;/8,-1.5), and (&#960;, 0)
See graph below as a visual check on the graph:
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{{{ graph( 300, 300, 0,  4, -2, 2, 1.5sin(4x)) }}}```