Sinusoidal Functions

Chapter 6

Periodic Motion

Graphs of motion with repeating patterns

Think of yourself on a Ferris Wheel

Your height above ground fluctuates as you ride around on the Ferris Wheel over timeThis is periodic motion that repeats itself at equal intervals of time.

Period:The interval needed for the function to repeat itself.

Cycle:One period is one cycle. Cycles repeat themselves over and over.

Peak:The highest point(s) on the graph.

TroughThe lowest point(s) on a graph.

AmplitudeThe distance (or height) from the center line of the function to the maximum or minimum point.

Periodic behavior is everywhere!

• Moon phases• Tides• Temperatures• Daylight length• Electricity usage• Heartbeats• Traffic Lights

Which graphs are periodic functions?

What is the period of this graph?

What is the amplitude of this graph?

Where are the peaks and troughs?

What is the period and amplitude?

Extrapolating

• Estimating a value that is beyond the range of the given data

Interpolating

• Estimating a value that is between elements in given data

A few questions to try...

• Pg 331 # 5,6