If the period is PI - Mathematics

Question

How would I calculate whether a period is PI? Is there an equation? I have a question on an assignment which asks to find out where the period is equalled to PI. 

Answer 1

Hi Gaby,

 

You can find this from Trigonometry section from either Alg 2 or Precalculus.

 

You will see Trigonometric Graphs of sin, cos, tan, csc, sec, cot.  Take a look into sin or cos graphs.  Here is an image of it:

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b is the inside of sin, cos, tan function.

 

So, basically you have to see have many 1-full cycle of each graph is in 2π (for sin & cos) and π (for tan & cot).   Here is an example from sin:

 

y= sin 2x 

 

Let's compare to y = sin x.  This graph has a period of 2π but y = sin 2x has a period of π (2/2).  Here is the graph:

 

 

You can see sin x has 1-full cycle and sin 2x has 2-full cycles when it reaches 2π or 360.  Therefore sin x has a period of 2π and sin 2x has period of π.

 

 

From this sin graphs, you can see that brown one has completed only 1/2 cycle and it takes 4π to make 1-full cycle.  Therefore, sin (1/2)x will have a period of 4π  (2 ÷ 1/2).

Cosine functions will work same way as sine.  Only difference will be the shift.

 

I hope you got what you need for your assignment.  Good luck to you.