8 3 modeling periodic behavior

8.3 Modeling Periodic Behavior

Objectives:

1. Write equations of/graph translated sine and cosine curves

2. Use trig functions to model periodic behavior

Translations ReviewRemember:y = f(x – h) is a horizontal shift righty = f(x + h) is a horizontal shift lefty = f(x) + k is a vertical shift upy = f(x) – k is a vertical shift down

Examples:

Examples:

Example 1:Give an equation of the sine wave

shown:

“Axis of the wave”

Example 2:

Write an equation of the graph shown using cosine.

Example 3:

Graph

You Try!

Graph

Trigonometric Models

Many real life problems use trig functions to model periodic behavior.

The variable won’t always represent an angle.

For example, might use sin t or cos t where t is time.

Example:The depth of water at the end of a pier

varies with the tides. Today the high tide was at 4:15 am with depth 5.2 m. Low tide was at 10:27 am with depth 2.0 m.

Find an equation that models the depth t hours after midnight.

1. Make a sketch

Find the depth of the water at noon.

A large boat needs at least 3 m of water to dock. During what time after noon can it safely dock?