Search for a tool
Period of a Function

Tool to compute the period of a function. The period of a function is the lowest value t such that the function repeats itself: f(x+t)=f(x-t)=f(x), that is the case for trigo functions (cos, sin, etc.)

Results

Period of a Function -

Tag(s) : Functions

Share
Share
dCode and more

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!


Please, check our community Discord for help requests!


Thanks to your feedback and relevant comments, dCode has developed the best 'Period of a Function' tool, so feel free to write! Thank you!

Period of a Function

Period of a Function Calculator



Tool to compute the period of a function. The period of a function is the lowest value t such that the function repeats itself: f(x+t)=f(x-t)=f(x), that is the case for trigo functions (cos, sin, etc.)

Answers to Questions

What is a period of a function? (Definition)

The period $ t $ of a periodic function $ f(x) $ is the value $ t $ such that $$ f (x+t) = f(x) $$

Graphically, its curve is repeated each period, by translation. The function is equal to itself all the lengths $ t $ (it presents a pattern which is repeated by translation).

The value of the period $ t $ is also called the periodicity of the function.

How to find the period of a function?

To find the period $ t $ of a function $ f(x) $, demonstrate that $$ f(x+t)=f(x) $$

Example: The trigonometric function $ \sin(x + 2\pi) = \sin(x) $ so $ \sin(x) $ is periodic of period $ 2\pi $ function-period

Trigonometric functions are usually periodic period, to guess the period, try multiples of pi for value $ t $.

If the period is equal to 0, then the function is not periodic.

How to find the value f(x) of a periodic function?

Any periodic function of period $ t $ repeats every $ t $ values. To predict the value of a periodic function, for a value $ x $ calculate $ x_t = x \mod t $ (modulo t) and find the known value of $ f(x_t) = f(x) $

Example: The function $ f(x) = \cos (x) $ has a period of $ 2\pi $, the value for $ x = 9 \pi $ is the same as for $ x \equiv 9 \pi \mod 2\pi \equiv \pi \mod 2\pi $ and therefore $ \cos(9\pi) = \cos(\pi) = -1 $

How to find the amplitude of a periodic function?

The amplitude is the absolute value of the non-periodic part of the function.

Example: $ a \sin(x) $ has for amplitude $ | a | $

How to prove that a function is not periodic?

If $ f $ is periodic, then it exists a real not null such as $$ f(x+t)=f(x) $$

Demonstration consists in proving that it is impossible. For example with a reductio ad absurdum or performing a calculation that leads to a contradiction.

What are usual periodic functions?

The most common periodic functions are trigonometric functions based on sine and cosine functions (which have a period of 2 Pi).

FunctionPeriod
Sine $ \sin(x) $$ 2\pi $
Cosine $ \cos(x) $$ 2\pi $
Tangent $ \tan(x) $$ \pi $

Source code

dCode retains ownership of the online 'Period of a Function' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Period of a Function download for offline use on PC, tablet, iPhone or Android !

Need Help ?

Please, check our community Discord for help requests!

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developed the best 'Period of a Function' tool, so feel free to write! Thank you!


Source : https://www.dcode.fr/period-function
© 2021 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
Feedback