The Saskatchewan
     Sunrise Problem




End of a month Sunset August 31st by JBAT
Sketch the graph of y = |2 - x|
Biography
Sketch the graph of                         Maria Gaetana Agnesi
                      The Witch of Agnesi




 ...
Sketch the graph of y = |ƒ(x)|
Given   sketch the graph of
Given ƒ(x) = 2sin(x) sketch the graph of
The Reciprocal Trigonometric Functions ...
Trigonometric Modeling
and Transformations

An Example
For a Saskatchewan town
the latest sunrise is on Dec
21 at 9:15 am....
Trigonometric Modeling and
Transformations

An Example
For a Saskatchewan town the
latest sunrise is on Dec 21 at
9:15 am....
a) Sketch the graph of the sinusoidal function described above.
b) Write 2 equations for the function; one using sine the other cosine.
c) Use one of the equations in (b) to predict the time of sunrise on April 6.
d) What is the average sunrise time througho...
d) What is the average sunrise time throughout the year?
e) On what days will the sunrise at 7:00am?
e) On what days will the sunrise at 7:00am?
The Reciprocal Trigonometric Functions ...
The Reciprocal Trigonometric Functions ...

HOMEWORK
Given   sketch the graph of   , that is
HOMEWORK
Given   sketch the graph of
HOMEWORK
Pre-Cal 40S Slides March 10, 2008
Pre-Cal 40S Slides March 10, 2008
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Pre-Cal 40S Slides March 10, 2008

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Review of reciprocal and absolute value function graphs. Applications of transformations of trigonometric functions.

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Pre-Cal 40S Slides March 10, 2008

  1. 1. The Saskatchewan Sunrise Problem End of a month Sunset August 31st by JBAT
  2. 2. Sketch the graph of y = |2 - x|
  3. 3. Biography Sketch the graph of Maria Gaetana Agnesi The Witch of Agnesi May 16, 1718 - January 9, 1799
  4. 4. Sketch the graph of y = |ƒ(x)|
  5. 5. Given sketch the graph of
  6. 6. Given ƒ(x) = 2sin(x) sketch the graph of
  7. 7. The Reciprocal Trigonometric Functions ...
  8. 8. Trigonometric Modeling and Transformations An Example For a Saskatchewan town the latest sunrise is on Dec 21 at 9:15 am. The earliest sunrise is on June 21 at 3:15 am. Sunrise times on other dates can be predicted using a sinusoidal equation. Note: There is no daylight savings time in Morning at Swiftcurrent Lake photo source: http://www.flickr.com/photos/58518845@N00/381683114 Saskatchewan. a) Sketch the graph of the sinusoidal function described above. b) Write 2 equations for the function; one using sine the other cosine. c) Use one of the equations in (b) to predict the time of sunrise on April 6. d) What is the average sunrise time throughout the year? e) On what days will the sunrise at 7:00am?
  9. 9. Trigonometric Modeling and Transformations An Example For a Saskatchewan town the latest sunrise is on Dec 21 at 9:15 am. The earliest sunrise is on June 21 at 3:15 am. Sunrise times on other dates can be predicted using a sinusoidal equation. Note: There is no daylight savings time in Saskatchewan. a) Sketch the graph of the sinusoidal function described above. b) Write 2 equations for the function; one using sine the other cosine. c) Use one of the equations in (b) to predict the time of sunrise on April 6. d) What is the average sunrise time throughout the year? e) On what days will the sunrise at 7:00am?
  10. 10. a) Sketch the graph of the sinusoidal function described above.
  11. 11. b) Write 2 equations for the function; one using sine the other cosine.
  12. 12. c) Use one of the equations in (b) to predict the time of sunrise on April 6. d) What is the average sunrise time throughout the year? e) On what days will the sunrise at 7:00am?
  13. 13. d) What is the average sunrise time throughout the year?
  14. 14. e) On what days will the sunrise at 7:00am?
  15. 15. e) On what days will the sunrise at 7:00am?
  16. 16. The Reciprocal Trigonometric Functions ...
  17. 17. The Reciprocal Trigonometric Functions ... HOMEWORK
  18. 18. Given sketch the graph of , that is HOMEWORK
  19. 19. Given sketch the graph of HOMEWORK

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