Chapter 13Periodic Functions and Trigonometry

Section 13.1Exploring Periodic Data

Periodic

To be periodic Things that are periodic

Repeats on a regular basis

Repeats in the exact same manner

Can be predicted

Seasons of the year Daily classes Travel of a comet Location of the second

hand on an analog clock

Occurrence of the chorus in a song

Other examples?

It repeats a pattern of y – values at regular intervals

One complete pattern is called a cycle

The period of the function is the length of the x values to form one cycle.

Periodic Functions

1 Period or 1 Cycle

A Period can be found on a graph as being when the function is at a certain y – value, moving in a certain direction, until it is back at that same y – value, moving in the same direction.

The Maximum value of a periodic function is the greatest y – value that it achieves.

The Minimum value of a periodic function is the smallest y – value that it achieves.

The Amplitude is half the distance from the minimum value to the maximum value or it is the distance from the center to one extreme.

The Frequency of a periodic function is the reciprocal of the period.

Vocabulary

1. Identify one cycle in 2 different ways.

2. State the Period.

3. State the Frequency.

Cycles, Periods, and Frequencies

1. Identify one cycle in 2 different ways.

2. State the Period.

3. State the Frequency.

Cycles, Periods, and Frequencies

1. Identify one cycle in 2 different ways.

2. State the Period.

3. State the Frequency.

Cycles, Periods, and Frequencies

Periods and Trends

Amplitude

Today we did page 699 #1 – 13

If you want or need extra practice do pages 699 – 700 #16 – 19, 23 – 30

Extra Practice