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

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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.)

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 \( t \).

The value of the period found is also called the periodicity of the function.

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 \( \tan(x) \) | \( \pi \) |

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