Assignment 1Examining the graphs of y = a sin(bx + c)

Different values of a, b, and c affect the graphs of

y = a sin(bx + c) in a different way.

1. Graph of y = sinxThis is the basic sine graph and we will compare the effects of a, b, and c on y = sinx to this basic graph.

2. Graph of y = -sinxThis is just the reflection of y = sinx across the x-axis.

3. Graph of y = 2sinxThe range of the y = sinx is [-1,1]. But the range of this function is [-2,2]. In other words, the amplitude of this function is twice that of y=sinx.

4. Graph of y = 3sinxThe range of the y = sinx is [-1,1]. But the range of this function is [-3,3]. In other words, the amplitude of this function is three times that of y=sinx.

5. Graph of y = sin2xThe period of this function is half that of the function y=sinx. This means that every point on the graph of y = sin2x repeats itself twice within the same interval as that of y = sinx.

6. Graph of y = sin(3x)The period of this function is a third of that of the function y=sinx. This means that every point on the graph of y = sin3x repeats itself three times within the same interval as that of y = sinx.

7. Graph of y = sin(x+1)In this graph, there is a phase shift to the left by one point of every point on the graph of y=sinx.

8. Graph of y = sin(x-1)In this graph, there is a phase shift to the right by one point of every point on the graph of y=sinx.

9. Graph of y = 2sin(2x+1)This graph shows the effects of all the three variables on the graph of y = sinx interacting at the same time.

10. Graph of y = 2sin(2x-1)This graph shows the effects of all the three variables on the graph of y = sinx interacting at the same time. The only difference between this graph and the graph in number 9 above is the phase shift to the right. In number 9, the phase shift is to the left.

ConclusionAssume that

a,b, andcare positive real numbers. The graph of y = sinx is affected by these variables differently. In y =asinx, the range of the the function is [-a,a] and the amplitute is justa. In y = -asinx, the graph of y = sinx is reflected in the x-axis. For y = sin(bx), the period is just /b. Finally, for y =asin(bx +c), the phase shift is by-c/().