Graphs of Sine and Cosine

## Easy Problem

Graph the function f(x)=cos+3

The addition of 3 has the effect of moving the parent function up 3 units.  Notice that the graph to the left has been moved up until the sinusoidal axis is located at 3.

## Medium Problem

Graph the Function f(x)=cos(x+11)-9

The addition of 11 in the inside of the parenthesis moves the graph 11 units to the left.

The subtraction of 9 outside the parenthesis moves the graph down 9 units, making the sinusoidal axis at -9 instead of at 0.

## Challenge Problem

Graph the Function f(x)=3cos1/3(x+1)+4

First, lets start with the 1/3 in front of the parenthesis.  To find the period of a cosine graph, take the B value, which is 1/3, and divide 2π by it.  Therefore, the period of this graph is 2π/(1/3) which is 6π.

Next, lets take the 3 from the front.  This 3 increases the amplitude of the graph to 3, instead of 1.  Notice how the graph goes from a maximum of 7 (3 above the sinusoidal axis) to a minimum of 1 (3 below the sinusoidal axis).

Lastly, the 1 added from inside the parenthesis moves the graph to the left 1 unit.  And the addition of 4 outside the parenthesis moves the graph up 4 units, putting the sinusoidal axis at 4.

## Real-World Problem

Now that you know how to graph the cosine function, try out this real-world problem all by your self.

A man dives off of a diving board with a height of 12 ft.  Using the equation f(x)=8cos2x+12, graph his trajectory into, and out of the water.  Did the man hit the bottom of the pool if the pool is 6 ft. deep?

To look at some more examples of graphing sine and cosine, go to http://www.youtube.com/watch?v=s_NI50p-pcg