## Modeling Periodic Phenomena with Trigonometric Functions

#### Aligned To Common Core Standard:

**High School** - HSF-TF.B.6

What is 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. 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. These worksheets can help you learn to bring phenomena that repeat in regular intervals to life on paper.

### Printable Worksheets And Lessons

- 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.

#### 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.