Periodic Functions: Find Fundamental Period & Graph Solution

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SUMMARY

The fundamental period of the expression f(x) = sin(x)/sin(x) is established as π radians. This function simplifies to a constant value of 1 except at points where sin(x) equals zero, resulting in undefined values at x = nπ. The spacing between these undefined points indicates the periodic nature of the function, confirming that the period is indeed π. Additionally, the period of cos(x)/cos(x) is also π, reinforcing the consistency of periodic functions in trigonometry.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine and cosine.
  • Knowledge of periodic functions and their definitions.
  • Familiarity with graphing techniques for mathematical functions.
  • Basic algebraic manipulation of functions and equations.
NEXT STEPS
  • Research the properties of periodic functions in trigonometry.
  • Learn how to graph rational functions with undefined points.
  • Explore the concept of limits and discontinuities in functions.
  • Study the least common multiple (LCM) of trigonometric periods.
USEFUL FOR

Students studying trigonometry, mathematics educators, and anyone interested in understanding the behavior of periodic functions and their graphical representations.

Ujjwal28
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Homework Statement


What is the fundamental period of the expression sinx/sinx.can you guys please illustrate how to make its graph?

Homework Equations


Okay I know drawing graph can give me the period.Can the period be found by any other method?

The Attempt at a Solution


I'm told that the answer is pi. That is pi radians.I don't know how to sketch it's graph
 
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What exactly do you mean? f(x) = sinx/sinx is a constant function without the points for which sinx = 0.
 
It's period is pi that's all I know about it and here is a key the period of cosx/cosx is also pi
 
what is cosx/cosx equal to?
 
The definition of a period is the smallest number n such that f(x+n) = f(x), right?
If you look at ##f(x) = \frac{\sin x}{\sin x}## you should see what Math_QED was referring to...for all points where this function is defined, it can be simplified to a constant. However, there are places where the denominator is equal to zero and so f(x) at these points is undefined.
You will notice that there is a regular spacing between these holes in the function. Use that as your period.
 
Okay so you mean y=sinx/sinx will be equal to one but holes will appear at x=0 and pi, 2pi... npi?
And the spacing bw these holes gives me the period as 1? And same for cos? It will be undefined at npi/2?
 
Ujjwal28 said:
Okay so you mean y=sinx/sinx will be equal to one but holes will appear at x=0 and pi, 2pi... npi?
And the spacing bw these holes gives me the period as 1? And same for cos? It will be undefined at npi/2?
No. It gives a period of π .
 
Yeah I got it. It was a typo. Thanks guys and I really loved RUber's answer that made it crystal clear to me thanks bro
 
Okay another question.. What is the lcm of pi, 2pi and pi/3?
 
  • #10
Lowest common multiple can't be smaller than the largest member of the group. Check that one first.
 

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