Periodic Functions: Find Fundamental Period & Graph Solution

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Homework Help Overview

The discussion revolves around determining the fundamental period of the function f(x) = sin(x)/sin(x) and exploring how to graph it. Participants are examining the implications of the function's definition and its behavior at points where sin(x) equals zero.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the nature of the function and its simplification to a constant, questioning the implications of undefined points. There is also inquiry into alternative methods for determining the period beyond graphical representation.

Discussion Status

The conversation is active, with various interpretations of the function's behavior being explored. Some participants have provided insights into the spacing of undefined points and their relation to the period, while others have expressed confusion regarding the implications of these points.

Contextual Notes

There are discussions about the function being undefined at specific points, such as multiples of π, and the implications this has on determining the period. Participants are also considering the relationship between the periods of sin(x) and cos(x).

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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