Periodic Functions: Find Fundamental Period & Graph Solution

[Ujjwal28]

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

 

[member 587159]

What exactly do you mean? f(x) = sinx/sinx is a constant function without the points for which sinx = 0.

 

[Ujjwal28]

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

 

[member 587159]

what is cosx/cosx equal to?

 

[RUber]

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.

 

[Ujjwal28]

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?

 

[SammyS]

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 .

 

[Ujjwal28]

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

 

[Ujjwal28]

Okay another question.. What is the lcm of pi, 2pi and pi/3?

 

[RUber]

Lowest common multiple can't be smaller than the largest member of the group. Check that one first.