## Sine Curves

## by

## Bradley Johnson

In this exploration we will examine functions of the form y = a*sin(bx + c). We intend to examine how the parameters a, b, and c change how the sine curve looks.

Beginning with a = b = 1 and c = 0 we see the sine wave has an amplitude of 1 as pictured below.

We will now look at the changes of the graph for different values of b. Below we see graphs with b = 2 ; b = 4 ; b = 5 ; b = 7 respectively.

It is clear that changing the parameter b effects the frequency of which the oscilations occur in the sine wave. This is also known as a change is period. For larger values of b the period becomes smaller. For small values of b ( less than 1) the period of the function becomes larger. The graphs below show b = 1/2 ; and b = 1/5 respectively.

We next examine the changes that occur for changing values of c. The graphs shown below are for a = b = 1 and varying c. Respectively those shown are c = 0 ; c = 1; c = 3 ; c = 4

The graphs appear to be translating to the left as the value of c increases. For values of c less than zero we would see a translation of the graph to the right.