How to find the period of a function?

Question

Nitin · Accepted Answer

Periodic function is classified as a function that repeats its values at a certain intervals. Mainly used are sine and cosine functions.
In determining the Period of a Function, we will need to familiarize ourselves first with the equation below.
  
where,
 Amplitude
 Horizontal Phase Shift (positive to the left and negative to the right)
 Vertical Shift (positive upward and negative downward)
Having an equation, we can now easily solve for the Period using the formula,
  
So if there is a given equation of
 ,
We have,
  

Substituting it, we will get
  
  
Therefore, the period of  is .  
In some instances, a graph can given instead of an equation.
One example is this cosine curve.

To determine the period of this graph, we need to identify where does the graph repeat itself. 

By inspection, it is clear that the graph repeats itself at the span of . 
Therefore, the cosine curve has a period of .

How to find the period of a function?

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