For Assigment One, I chose to investigate
the equation: y= a sin(bx +c). While on the surface this seems
to be a rather simple equation, changes made in the values of
the variables: a, b, c greatly affect the graphs that are produced.
I will begin by examining the equation at its simpliest form,
This equation creates a graph of a sin function
that passes through the orgin with a maximum of 1 and a minimum
I will now experiment with changing the values,
begining with the variable a, increasing the value to 2, 3 and
As we can see, changing the variable a, changes
the height of the graph. Let us now look at the variable b.
Variable b causes the sine wave to shorten
the length between its maximums and minimums. Finally we will
look at variable c.
Variable c changes the x-axis intercept of
Note that the value of the x intercept is
the value that makes the part of the equation (x+1) equal to zero.
So therefore a positive value for the variable c will shift the
graph to the left, while a negative value will shift it to the