Periodic Functions: Find Fundamental Period & Graph Solution

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.
  • #1
Ujjwal28
32
0

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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  • #2
What exactly do you mean? f(x) = sinx/sinx is a constant function without the points for which sinx = 0.
 
  • #3
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
 
  • #4
what is cosx/cosx equal to?
 
  • #5
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.
 
  • #6
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?
 
  • #7
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 .
 
  • #8
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
 
  • #9
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.
 

Related to Periodic Functions: Find Fundamental Period & Graph Solution

1. What is a periodic function?

A periodic function is a type of mathematical function where the pattern of the function repeats itself at regular intervals. This means that the output values of the function repeat after a certain input value, known as the fundamental period.

2. How do you find the fundamental period of a periodic function?

The fundamental period of a periodic function can be found by identifying the smallest interval at which the function repeats itself. This can be done by looking at the graph of the function or by using mathematical formulas, depending on the type of function.

3. What is the importance of finding the fundamental period of a periodic function?

Knowing the fundamental period of a periodic function is important because it helps in understanding the behavior and properties of the function. It also allows us to accurately graph the function and make predictions about its future values.

4. How do you graph a periodic function and find its solution?

To graph a periodic function, you need to first determine the fundamental period and then plot points on the graph by substituting different input values. The solution of the function can be found by analyzing the graph and identifying the values of the function at different input points.

5. Can all functions be considered periodic?

No, not all functions can be considered periodic. A function can only be considered periodic if it repeats itself at regular intervals. Functions that do not have a repeating pattern are called non-periodic functions.

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