By Brooke Norman

 

 

Is it just scribble or does it have meaning?

 

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Looking at the graphs of sine and cosine can sometimes just look like wavy lines that have no meaning.  Lets take a more in depth look to see what all this scribble is about.

 

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Lets take a look at the graph of the equations: y=sin(x) and y= cos(x).  Look to see where they cross the x- and y-axis.

 

 

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Now lets look at the equations of y= a cos(bx+c) and y=a sin(bx+c), and look at different values of a, b, and c.

 

For each graph, we are going to see what is happening as the graphs cross the x- and y- axis and what the minimum and maximum values for w and y are.  This means, what changes are occurring due to the value changes of a, b, and c.

 

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Lets look at the sine graph first.

 

Here we are going to look at the graph as the value of a is changed, letting b=1 and c=0.

Purple: y=1/2 sin(x)

Red: y= sin(x)

Blue: y= 3 sin(x)

Green: y = 5 sin(x)

 

 

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Here we are going to look at the graph as the value of b is changed, letting a=1 and c=0.

Purple: y=sin(1/2 x)

Red: y=sin(x)

Blue: y=sin(3x)

Green: y= sin (5x)

 

 

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Here we are going to look at the graph as the value of c is changed, letting a=1 and b=1.

Purple: y=sin(x)

Red: y=sin(x+1/2)

Blue: y=sin(x+3)

Green: y=sin(x+5)

 

 

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Now, lets look at the cosine graph.

 

Here we are going to look at the graph as the value of a is changed, letting b=1 and c=0.

Purple: y=1/2 cos(x)

Red: y= cos(x)

Blue:y= 3 cos(x)

Green: y = 5 cos(x)

 

 

 

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Here we are going to look at the graph as the value of b is changed, letting a=1 and c=0.

Purple: y=cos(1/2 x)

Red: y=cos(x)

Blue: y=cos(3x)

Green: y= cos (5x)

 

 

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Here we are going to look at the graph as the value of c is changed, letting a=1 and b=1.

Purple: y=cos(x)

Red: y=cos(x+1/2)

Blue: y=cos(x+3)

Green: y=cos(x+5)

 

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Lets combine the graphs of asin(bx+c) and acos(bx+c). 

 

Here is both of them when we vary a

Y=asin(x) and y=acos(x)

 

 

Purple:  y=sin(x)

Red: y=3sin(x)

Blue: y=cos(x)

Green: y= 3cos(x)

 

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Here is both of them when we vary b

Y=sin(bx) and y=cos(bx)

 

 

Purple: y=sin(x)

Red: y= sin(3x)

Blue: y=cos(x)

Green: y=cos(3x)

 

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Here is both of them when we vary c

Y=sin(x+c) and y=cos(x+c)

 

 

Purple: y=sin(x)

Red: y=sin(x+3)

Blue: y= cos(x)

Green: y=cos (x+3)

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Here is what all the graphs look like when they are combined?

 

 

 I guess its more than scribble, huh?

 

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