Table of Contents
Periodic Function
A periodic function is a function that repeats its values at fixed intervals. The intervals between the repetitions are called periods.
Fundamental Period of a Function
The fundamental period of a function is the time required for the function to repeat its value. The period can be found by taking the reciprocal of the function’s frequency.
Period of Trigonometric Functions -Mathematics
The period of a trigonometric function is the length of time it takes for the function to repeat its values. For example, the period of the sine function is 2π, because it takes 2π radians for the function to repeat its values. The period of the cosine function is π, because it takes π radians for the function to repeat its values.
How to Find the Period of a Function?
The period of a function is the distance between two corresponding points on the graph of the function. To find the period of a function, use the distance formula to find the distance between two points on the graph of the function.
If a function repeats over at a constant period we can call it a periodic function.
The sine function repeats every 360° or 2π.
The cosine function repeats every 360° or 2π.
According to periodic function definition the period of a function is represented like f(x) = f(x + p), p is equal to the real number and this is the period of the given function f(x).
If x = a is a point on the graph of a function f(x), then
f(x) = f(a + p)
for all real numbers p.
Period can be defined as the time interval between the two occurrences of the wave.
The period of a wave is the time it takes for one complete wave to pass a given point.
Periodic functions examples and Questions to be solved :
1. Find the equation of the function that has the following graph.
The equation of the function is y = 2×3 − x.
2. Find the equation of the function that has the following graph.
The equation of the function is y = x3 − 3x.
3. Find the equation of the function that has the following graph.
The equation of the function is y = x3 + 3x.
4. Find the equation of the function that has the following graph.
The equation of the function is y = x3 − 6x.
5. Find the equation of the function that has the following graph.
The equation of the function is y = x3 − 9x.
6. Find the equation of the function that has the following graph.
The equation of the function is y = x3 − 12x.
7. Find the equation of the function that has the following graph.
The equation of the function is y = x3 − 15x.
8. Find the equation of the function that has the following graph.
The equation of the function is y = x3 − 18x.
9. Find the equation of the function that has the following graph.
The equation of the function is y = x3 − 21x.
