Applied 40S May 22, 2009

The "periodic" moments of our lives ...

orTransformations of the sine function

Sunshine Coast Panoramic by flickr user El Fotopakismo

Convert the following to radian. Write your answers using π and in decimal form to two decimal places.

105° -11° 450°

HOMEWORK

Convert the following to degrees. Write your answers rounded to the nearest degree.

7π 6

3.52 -2

HOMEWORK

What does periodic mean?

Clock photo source

Jupiter and Io photo source

What does periodic mean?

Low tide photo source

What does periodic mean?

Baby heartbeat photo source

What does periodic mean?

Heartbeat of Trees photo source

What does periodic mean?

The sine curve (graph) ...

Let's look at the weather ...Winnipeg Weather Data as of May 21, 2009 for the last year

TemperatureMonth J F M A M J J A S O N DMean -17 -14 -6 4 12 17 20 18 12 6 -4 -14

Source: Winnipeg weather statistics

Source: Winnipeg weather statistics

Month J F M A M J J A S O N DMean 120 140 178 232 277 291 322 286 189 150 95 99

Hours of Sunshine

swivel your data

Your turn ...

Properties and Transformations of the sine function ...

Let's look at some graphs ...http://fooplot.com

ƒ(x) = AsinB(x - C) + D

D is the sinusoidal axis, average value of the function, or the vertical shift.

The Role of Parameter D

D < 0 the graph shifts down D units.D > 0 the graph shifts up D units.

Generate a sinusoidal equation and sketch the graph for the following set of data. Write the values of the parameters in your equation to two decimal places. Homework

Source: Winnipeg weather statistics

Month J F M A M J J A S O N Dmm 19 15 23 36 60 84 72 75 51 30 21 19

Amount of Precipitation in Winnipeg (in mm)

Generate a sinusoidal equation and sketch the graph for the following set of data. Write the values of the parameters in your equation to two decimal places. Homework

Year 0 1 2 3 4 5 6 7 8Population 200 188 160 132 120 133 161 187 201

The data below show the population of a species of marmot in a given area over a 9-year period on June 1st of each year.