Lesson 67 of 1524
Periodic Functions
Periodic functions repeat after a given value.
Practice this chapterPeriodic functions repeat after a given value. In the general formula for a sinusoidal function, the period is P = 2 π | B |
In the general formula for a sinusoidal function, | A | represents amplitude.
periodic function — a function f ( x ) that satisfies f ( x + P ) = f ( x ) for a specific constant P and any value of x. function cos x — even, so its graph is symmetric about the y -axis. function sin x — odd, so its graph is symmetric about the origin. sinusoidal function — any function that can be expressed in the form f ( x ) = A sin ( B x - C ) + D or f ( x ) = A cos ( B x - C ) + D.
Worked example
What does “periodic function” mean in Periodic Functions?
- 1Use the wording this chapter gives for periodic function.
- 2The book says: a function f ( x ) that satisfies f ( x + P ) = f ( x ) for a specific constant P and any value of x.
- 3Do not use the meaning of function cos x. That term means even, so its graph is symmetric about the y -axis.
Result: a function f ( x ) that satisfies f ( x + P ) = f ( x ) for a specific constant P and any value of x
Why. That is the meaning this chapter gives for periodic function.
Do not swap periodic function and function cos x. periodic function means a function f ( x ) that satisfies f ( x + P ) = f ( x ) for a specific constant P and any value of x. function cos x means even, so its graph is symmetric about the y -axis.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.