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.)

Period of a Function - dCode

Tag(s) : Functions

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*!

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.)

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 $.

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

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.

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.

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

Function | Period |
---|---|

Sine $ \sin(x) $ | $ 2\pi $ |

Cosine $ \cos(x) $ | $ 2\pi $ |

Tangent $ \tan(x) $ | $ \pi $ |

dCode retains ownership of the source code of the script Period of a Function online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Period of a Function script for offline use on PC, iPhone or Android, ask for price quote on contact page !

period,function,periodic,cos,sin,trigonometric,periodicity

Source : https://www.dcode.fr/period-function

© 2019 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback

▲