# Periodic Functions Worksheets

When we have something that occurs in a regular and predictable manner, like a swing on a swing set, we refer to the movement as periodic. There are many things that occur in nature that are periodic like our heartbeat and breathing. If we model this process then we can understand where these process are in there trajectory at any point in time. There are many different practical uses for this math in the real world. These worksheets can help you learn to bring phenomena that repeat in regular intervals to life on paper.

### Aligned Standard: HSF-TF.B.6

- Periodic or Not Step-by-step Lesson - You can use a graph or visualize it yourself. It's up to you!
- Guided Lesson - Is that one of the longest multiple choice questions you have seen in your life?
- Guided Lesson Explanation - I personally like to take the time to draw the graph. Guess I don't have much of an imagination.
- Practice Worksheet - This is one very long worksheet.
- Matching Worksheet - Match the graphs to the data tables and analyze the outcome.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Periodic behavior follows a consistent pattern. It's a maybe, it's a certainty!

- Homework 1 - Any phenomena that has a behavior or pattern that repeats over time; in a somewhat predictable cyclic manner is referred to as periodic.
- Homework 2 - The following tabled values show the height above the ground of a point on a bicycle wheel as the bicycle is wheeled along a flat surface.
- Homework 3 - )The horizontal line that the wave is only above and is called the principal axis.

### Practice Worksheets

The answer keys are huge, but necessary.

- Practice 1 - We will need to make four scatter plots and see if there is a repetitive pattern in any of the graph.
- Practice 2 - Is the data periodic? i) The equation of the principal axis ii) The period iii) The amplitude
- Practice 3 - For each set of data, draw a scatter plot and decide whether or not the data exhibits approximately periodic behavior.

### Math Skill Quizzes

These quizzes will take a good bit of time.

- Quiz 1 - Does this follow a pattern of any kind?
- Quiz 2 - The data will be classified as periodic if it follows a cyclic and somewhat predictable pattern.
- Quiz 3 - There can be some outliers and a pattern can still exist.

### What are Periodic Phenomena?

Do you feel like math is getting trickier for you, and you're unsure of what term means what? Don't worry; we will make it easier for you to understand and retain what might seem difficult for you. Let's start, shall we? In general terms, a periodic phenomenon refers to a phase in an event that is repeated at regular intervals. This means that if you can chart out the changes that occur, you will be able to accurately predict where and when a phenomenon is within its progression and a fixed point in time. Periodic phenomenon is observed in various fields, including science, such as oscillatory motion, sound waves, and many more. Just like science, periodic phenomenon in math to refers to a periodic function, which repeats its values at regular intervals or periods. There are many examples related to periodic functions. The most important are the trigonometric functions. Trigonometric functions repeat over intervals of 2π radians. In the real world it could something as simple as determining the position of a rocking chair at a point in time since those chairs work at focused points in time. It could also be something much more complex like the position of comet in our solar system at a point in time.

### Why Do We Model Periodic Phenomena?

We model just about anything to be able to understand more about it. When something is considered to be periodic, it is predictable. This means that if we create an accurate model of it, we will know where it is within its progress at any point in time. This is how we understand the location of things in solar system without being able to touch and feel them. One thing that is not often talked about is the fact that the world is constantly getting hit with asteroids. Meaning space debris is making landfall. In fact over one thousand people worldwide die each year from the direct or indirect impact of asteroids. NASA has an entire team evaluating the impact of these things constantly. Guess what type of math is involved in their daily routine?