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Investigating the graphs of sine function

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Introduction

IB – SL Math Portfolio                                                                      Locci Jonathan

Investigating the graphs of sine  function

In this investigation, we are going to look at the different graph of y=sin x.  We are going to compare and investigate the graphs of y=A sin x, Y=sin Bx and y= sin(x+C).  We are going to look what the different value and what are the effects on the sin graph.

Part 1: Investigation of the graphs y = sin x

image00.png

image01.png

image06.png

In the graphic 5 sin x, as you can see is much stretched because the amplitude is greater in 5 sin x than 2 sin x. But you can also see that in 2 sin x, the graph is much wider the 5 sin x. So we can conclude that more the amplitude is low and more the graph is wide.

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Middle

image10.png

So, based on what I did,I saw that the value of the amplitude was 3 so a positive but  I didn’t use well the (x + 2) because I thought it would be more far to the left.

image11.png

For this graph, it was pretty hard to predict, the amplitude is 1/2 which is positive but because of +1, we will move to the left. You can see that I was right for the value B when it says sin3, I had the right period.

image12.png

This one I really had a good prediction, I knew that the amplitude would be on 0.5 and since the amplitude is a -1it would be up sat down but because of the (x-1) the amplitude start at 0.5. I knew as well that the value B in sin1/2 would be very wide period.

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Conclusion

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Like in the graph y = A sin x, if the value of x is a negative, the graph will flip up sat down.

Part 5: Investigation of the graphs y = cos x and y = sin x

image04.png

The graphs cos x is linked to the graph sin x, because it has the same curvy line but it has also the same amplitude which is 1.

 But The difference is the location of the relative along the x-axis. For cosine function, you need to think about the unit circle. At a rotation of image05.pngimage05.png /2 radians, the cosine component of the image is 0.  Another image05.pngimage05.png/2 radians, you go back to 1. A sine function it is  one rotation of image05.pngimage05.png /2 behind the cosine function. So all that's keeping them from being the same function is the difference if image05.pngimage05.png /2.

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