Precalculus 1/27/10

Sinusoidal functions - day 2

Today we learned how to move the graph of sine up and down. This is called vertical shift. What's important about this is that you drawn in what's called a sinusoidal axis to help you graph the function. Here's an example...







As you might expect, the graph is translated up 2 units. We say this has a vertical shift upward of 2. The range of this graph is [0,2]








Here's another example where the graph is translated in a different way.










This graph is moved pi/2 to the right.

This is an example of phase shift of positive pi/2. If the graph is translated to the left, the phase shift would be negative.









Some very helpful hints...

If you have the general sinusoidal equation y = Asin(Bx+C)+D...

1. A is the amplitude
2. The period of the function can be calculated by



3. The Phase shift can be calculated by




4. The vertical shift is D

Hope this helps. You can find more notes on Mr. Corn's webpage here.