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 -0.5£a£-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.