8 3 modeling periodic behavior
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TRANSCRIPT
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?