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# Applied 40S May 22, 2009

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Introduction to the sine function and modeling sinusoidal data.

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### Applied 40S May 22, 2009

1. 1. The quot;periodicquot; moments of our lives ... or Transformations of the sine function Sunshine Coast Panoramic by ﬂickr user El Fotopakismo
2. 2. Convert the following to radian. Write your answers using π and in decimal form to two decimal places. HOMEWORK 105° -11° 450°
3. 3. Convert the following to degrees. Write your answers rounded to the nearest degree. HOMEWORK 7π 3.52 -2 6
4. 4. What does periodic mean? Clock photo source
5. 5. What does periodic mean? Jupiter and Io photo source
6. 6. What does periodic mean? Low tide photo source
7. 7. What does periodic mean? Baby heartbeat photo source
8. 8. What does periodic mean? Heartbeat of Trees photo source
9. 9. The sine curve (graph) ...
10. 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. 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. 12. Properties and Transformations of the sine function ... Let's look at some graphs ... http://fooplot.com ƒ(x) = AsinB(x - C) + D
13. 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. 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. 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