Courrey J. Alexander

 

Examine graphs of

 

y = a sin(bx + c)

 

for different values of a, b, and c.

 

 

 

 

       I have investigated the amplitude of the sine curve with both positive and negative integers while both b and c remain constant at 1.  I would like to know if I would get the same results for positive and negative decimals.  I assume that it would only make the curves closer to each other in proximity.  I will create a graph for -0.5a-0.1.

 

       Now that I have investigated the behavior of a with both positive and negative integers and decimals, I would like to see the behavior of the graph when a and c are held constant at 1 as b varies from -10 to 10.

 

       The graph shows that as the value of b approaches 0 from both sides, the sine curve behaves like a coil that expands and contracts.  The period 2P/n has the following values:

 

       The value of b apparently has something to do with the displacement of the curve (movement from left to right).  I will investigate further with b, but first, I will investigate the behavior of c in (-10,10) as a and b are held constant at 1.

 

       This graph shows that as c approaches 0 from both sides, the sine curve behaves like a wave going from left to right.  Approaching 0 from the right causes the curve to shift to the right.  Approaching 0 from the left, of course, causes the curve to shift to the left.  The value of c apparently something to do with the displacement of the curve as well.

 

       Now that I have investigated the behavior of a, b, and c one at a time as the other two remained constant at 0, I would like to see the graph as all three vary from -5 to 5.

 

       As a, b, and c vary, the sine curve behaves similarly to the graph when b varies.  As I stated earlier, variations in both b and c seemed to have affected the displacement of the sine curve.  This is because the displacement, or phase shift, is equal to .  The value of c alone affects the phase angle for the sine curve y=a sin (bx+c).

 

       If the displacement, or phase shift, has a negative value, then I need to move the sine graph to the left of its normal position (y=sin x) by . 

 

       Of course, if the phase shift has a positive value, then I need to move the sine graph to the right.

 

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