1. Modeling with sine or cosine functions

2. Project Overview What do you know about the sine graph? What do you know about the equation of the sine function? Real life examples.

7. Other Models Rainfall Snowfall Day light Dew point

8. Other models:

10. Other applications http://www.mathdemos.org/mathdemos/sinusoidapp/sinusoidapp. html#Platform: http://www.mathdemos.org/mathdemos/sinusoidapp/sinusoidapp. html#Platform:

11. Average Max. Temperature (F) Average Min. Temperature (F) Average Total Precipitation (in.) Average Total SnowFall (in.) Jan45.1345.413.2 Feb50.6363.911.1 Mar55.338.43.670.4 Apr60.841.92.490 May67.547.52.20 Jun73.252.91.540 Jul8056.80.550 Aug79.956.90.890 Sep75521.540 Oct63.645.23.050 Nov52.539.55.540.4 Dec4635.45.891.4 Annual62.544.736.696.6 Portland Oregon Monthly Climate Summary Average temperatures, precipitation, and snowfall data for Portland, Oregon, by month and annually. The following temperature and precipitation data was recorded at the Portland Oregon Weather Service Forecast Office:

12. PDX high Temps

13. PDX Average max Temps

14. PDX Average Max Temps

15. PDX average min Temps

16. PDX Average Max Temps

19. The harbor of Gorey, Jersey falls dry at low tide.Gorey, Jersey

20. OFFICIAL TIME LAPSE The world's highest tides - Hopewell Rocks, New Brunswick

21. Youngs Bay, Astoria Oregon http://www.hookandbullet.com/googlemap. aspx?lat=46.1748275756836&lon=- 123.8659744262695

22. Youngs Bay Astoria (Jan 1, 2015) Low Tide 3:26 am2.8 ft High Tide 9:59 am9.6 ft

27. ACCORDING TO YOUR MODEL: WHAT TIME DO YOU EXPECT THE LOW TIDE TO BE? WHAT TIME DO YOU EXPECT THE HIGH TIDE TO BE?

28. State a sine or cosine function to model the low and high tides in Youngs Bay. Show a complete solution that includes all your calculations. Plot the given points. Graph the function on the same grid… include a 24-hour cycle. Using the context of the problem state what each component of the equation represent.

29. Repeat the process: Youngs Bay Astoria (Jan 5, 2015) Low Tide 7:09 am3 ft High Tide 1:39 am8.4 ft

30. Fishing Tides in Astoria (Youngs Bay), Oregon

32. Winter Solstice: marks the shortest day of the year in the northern hemisphere and longest day in the southern hemisphere. But the earliest sunset – or earliest sunrise if you’re south of the equator – happens before the solstice. The north polar region of Earth is in 24-hour darkness, while the south polar region is in 24-hour daylight

33. summer Solstice : marks the longest day of the year in the northern hemisphere and shortest day in the southern hemisphere. But the earliest sunset. The north polar region of Earth is in 24- hour daylight, while the south polar region is in 24-hour darkness.

34. Vernal and Autumn Equinox the time at which the sun crosses the plane of the equator towards the relevant hemisphere, making day and night of equal length. It occurs about March 21 in the N hemisphere (Sept 23 in the S hemisphere)

35. Here are some facts for PDX: EventDateThe amount of daylight The last summer solstice in P- Town June 21, 201415:41:14 Last Autumn Equinox Sept 22, 201412:10:09 Last Winter Solstice Dec 21, 20148:42::06

36. Make a list your questions: Consider the data and the questions you might have. We will answer the questions as a class. Then as a group you will work on the questions listed on the next slide.

37. Determine: The amount of day light expected for Friday Jan 9, 2015. The amount of day light expected at the next Vernal Equinox: March 20, 2015. The amount of day light expected at your next birthday.

38. Homework: sec 8.3 Sec 8.3 Page #16, 17, 19 and 24