Introduction to the sine function and modeling sinusoidal data.

1. The quot;periodicquot;
moments of our lives ...
or
Transformations of
the sine function
Sunshine Coast Panoramic by flickr user El Fotopakismo

2. Convert the following to radian. Write your answers using π and in
decimal form to two decimal places. HOMEWORK
105° -11° 450°

3. Convert the following to degrees. Write your answers rounded to
the nearest degree. HOMEWORK
7π 3.52 -2
6

4. What does periodic mean?
Clock photo source

5. What does periodic mean?
Jupiter and Io photo source

6. What does periodic mean?
Low tide photo source

7. What does periodic mean?
Baby heartbeat photo source

8. What does periodic mean?
Heartbeat of Trees photo source

9. The sine curve (graph) ...

10. Let's look at the weather ...
Winnipeg Weather Data as of May 21, 2009 for the last year
Temperature
Month J F M A M J J A S O N D
Mean -17 -14 -6 4 12 17 20 18 12 6 -4 -14
Source: Winnipeg weather statistics

11. Your turn ...
Hours of Sunshine
Month J F M A M J J A S O N D
Mean 120 140 178 232 277 291 322 286 189 150 95 99
Source: Winnipeg weather statistics
swivel your data

12. Properties and Transformations of the sine function ...
Let's look at some graphs ...
http://fooplot.com
ƒ(x) = AsinB(x - C) + D

13. The Role of Parameter D
D is the sinusoidal axis, average value of the function, or the
vertical shift.
D > 0 the graph shifts up D units. D < 0 the graph shifts down D units.

14. 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
Amount of Precipitation in Winnipeg (in mm)
Month J F M A M J J A S O N D
mm 19 15 23 36 60 84 72 75 51 30 21 19
Source: Winnipeg weather statistics

15. 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
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.
Year 0 1 2 3 4 5 6 7 8
Population 200 188 160 132 120 133 161 187 201