Cosine Functions

In the following examples, follow these steps:

1. Draw the XY-axis with your EZ Graphing slide case.
2. Graph the parent function.
3. Now add to your graph Reflection, Dilation and Translation in this order.
4. Finally, click on the problem to check the solution.

General Form for Cosine Curves

$\large&space;y=AcosB(x+C)+D$

A = Amplitude; in a way, this is the y-dilation of the curve
B = Frequency; in a way, this is the x-dilation of the curve. This important value helps you find the period of the cosine curve:

$\small&space;Period=\frac{2\pi&space;}{B}\;&space;or\;&space;\frac{360^o}{B}$

C = Translation in the x-axis; also known as the phase shift

D = Translation in the y-axis

Translation

Example 1

$\large&space;y=cos(x)-1$

Example 2

$\large&space;y=cos(x-2)$

Dilation

Example 3

$\large&space;y=2cos(x)$

Example 4

$\large&space;y=\frac{1}{2}cos(x)$

Example 5

$\large&space;y=cos\left&space;(&space;\frac{1}{3}x\right&space;)$

Reflection

Example 7

$\large&space;y=-cos(x)$

Example 8

$\large&space;y=cos(-x)$

Put it all together

Example 9

$\large&space;y=cos(x-2)-1$

Example 10

$\large&space;y=-2cos(3x)+1$

Try the next function