# Periodic Functions: Find Fundamental Period & Graph Solution

• Ujjwal28
In summary, the conversation discusses finding the fundamental period of the expression sinx/sinx and its graph. The period can be found by looking at the regular spacing between the holes in the function, which is pi. The same applies for cosx/cosx, with a period of pi and undefined points at npi/2. The lcm of pi, 2pi, and pi/3 cannot be smaller than the largest member, so it would be 2pi.

## 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

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?

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