# Find the period of the function

• arif112
In summary: This thread is for summaries of conversations only. Thank you!In summary, the function sin(4 pi t)+cos(7 pi t) repeats itself when t = ½, similar to when two clocks with hands, one turning 4 rounds while the other turns 7 rounds, meet in their starting position. To find the period of this function, one can use the identity sin((a+b)t) = sin(at)cos(bt) + cos(at)sin(bt) and determine the period of the individual functions sin(4 pi t) and cos(7 pi t). It is recommended to follow the guidelines for asking questions, including providing the full question and showing an honest attempt at a solution.
arif112
sin(4 pi t)+cos(7 pi t)

arif112 said:
sin(4 pi t)+cos(7 pi t)

sin(0) = sin(2π), so as for the function sin(4πt) it will repeat itself when t = ½.

Think of when the function sin(4πt)+cos(7πt) will repeat itself.

Say you have two clocks with hands, one clock turning 4 rounds while the other turns 7 rounds.

You start the clocks simultaniously at a starting point = 0.

Now, how many rounds will the hand of clock A have to turn before the hands of both clocks meet in the starting position?

arif112 said:
sin(4 pi t)+cos(7 pi t)
What question do you about this? Write it in terms of sin(x) and cos(x)? Determine its period and amplitude?

(Ah- the title of this thread says "find the period". It's always a bit iffy not to put the question in the body of the thread- careless people like me might not see it!)

Last edited by a moderator:
arif112 said:
sin(4 pi t)+cos(7 pi t)
Hello arif112. Welcome to PF.

I see that you're new here.

In the future, use the template that is provided for you when you start a new thread. Don't erase it, but fill it in.

Also, familiarize yourself with the rules for this forum. How to Ask for Homework Help

Include the entire question in the body of your initial post, It's not sufficient to post part (or all) of the question in the title and then leave that part out of the body .

You need to make an attempt at a solution.
Make an honest attempt. Show what you've tried. Discuss what you know about the problem and where you're stuck.

So, ...
For your problem, what is the period of each of the functions that you a given -- individually ?

A useful identity: sin((a+b)t)= sin(at)cos(bt)+ cos(at)sin(bt)

## 1. What is the period of a function?

The period of a function is the distance between two consecutive points on the graph of the function that have the same value. In other words, it is the length of the repeating pattern of the function.

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

To find the period of a function, you need to identify the pattern of the function. If it is a trigonometric function, you can use the formula 2π/b, where b is the coefficient of the variable. If it is a polynomial function, you can find the distance between two consecutive x-intercepts or peaks on the graph.

## 3. Can a function have multiple periods?

Yes, a function can have multiple periods. If the function has a repeating pattern, each of the patterns can be considered as a period. However, there is always one shortest period that contains all the other periods.

## 4. What does the period tell us about the function?

The period of a function can tell us about the frequency or the time it takes for the function to repeat itself. For example, if the period is 2π, it means that the function will repeat itself every 2π units on the x-axis. It can also tell us about the symmetry of the function.

## 5. Can the period of a function be negative?

No, the period of a function cannot be negative. It is always a positive value as it represents a distance on the x-axis. However, the function itself can have negative values as it is a representation of the relationship between the input and output values.

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