Assignment 1

by

Allison McNeece

**Exercise: **Examine graphs of y = a sin (bx + c) for different values of a, b, and c.

Lets begin with the simple case of a, b, c = 1

playing around with the values of a,b,c will give us a visual of how they change the graph:

Let us first vary a but keep b and c fixed at 1:

a = 2

a = 3

a = -2

a = -3Notice how a affects the y values of the graph. Also negative values of a will invert the graph across the x-axis.

Observe the animation below has a varying from -5 to 5:

Now let's vary b but keep a and c fixed at 1:

b = 2

b = 3

b = -2

b = -3Below is the animation of b varying from -5 to 5:

Finally lets vary c and keep a and b fixed at 1:

c = 2

c = 3

c = -2

c = -3And again we have an animation of c varying from -5 to 5:

Just for funsies look at this crazy graph with a=7, b=45, c=0: