How to find period of a graph

Some functions (like Sine and Cosine) repeat forever
and are called Periodic Functions.

The Period goes from one peak to the next (or from any point to the next matching point):

The Amplitude is the height from the center line to the peak (or to the trough).

Or we can measure the height from highest to lowest points and divide that by 2.

 

The Phase Shift is how far the function is shifted horizontally from the usual position.

The Vertical Shift is how far the function is shifted vertically from the usual position.

All Together Now!

We can have all of them in one equation:

y = A sin(B(x + C)) + D

• amplitude is A
• period is 2π/B
• phase shift is C (positive is to the left)
• vertical shift is D

And here is how it looks on a graph:

Note that we are using radians here, not degrees, and there are 2π radians in a full rotation.