Applications of transformations and trig functions - class 1.

1. 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?

3. Trigonometric Modeling and Transformations
An Example
For a Saskatchewan town the latest sunrise is on Dec 21 at 9:15am. The earliest
sunrise is on June 21 at 3:15am 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.

5. Trigonometric Modeling and Transformations
An Example
For a Saskatchewan town the latest sunrise is on Dec 21 at 9:15am. The earliest
sunrise is on June 21 at 3:15am Sunrise times on other dates can be predicted
using a sinusoidal equation.
Note: There is no daylight savings time in Saskatchewan.
b) Write 2 equations for the function; one using sine the other cosine.

6. Trigonometric Modeling and Transformations
An Example
For a Saskatchewan town the latest sunrise is on Dec 21 at 9:15am. The earliest
sunrise is on June 21 at 3:15am Sunrise times on other dates can be predicted
using a sinusoidal equation.
Note: There is no daylight savings time in Saskatchewan.
c) Use one of the equations in (b) to predict the time of sunrise on April 6.

8. Trigonometric Modeling and Transformations
An Example
For a Saskatchewan town the latest sunrise is on Dec 21 at 9:15am. The earliest
sunrise is on June 21 at 3:15am Sunrise times on other dates can be predicted
using a sinusoidal equation.
Note: There is no daylight savings time in Saskatchewan.
d) What is the average sunrise time throughout the year?

9. Trigonometric Modeling and Transformations
An Example
For a Saskatchewan town the latest sunrise is on Dec 21 at 9:15am. The earliest
sunrise is on June 21 at 3:15am Sunrise times on other dates can be predicted
using a sinusoidal equation.
Note: There is no daylight savings time in Saskatchewan.
e) On what days will the sunrise at 7:00am?

13. How many days of the year will the sun rise earlier than 7 am?

14. Now you try ...
The pedals on a bicycle have a maximum height of 30 cm
above the ground and a minimum distance of 8 cm above the
ground. Jeng pedals at a rate of 20 cycles per minute.
a) What is the period, in seconds for this function?
b) At t = 0, Jeng's right foot is closest to the ground.
i) Write 2 equations that represent the height of her right foot above the
ground; 1 sine; 1 cosine.
ii) For how long per cycle is Jeng's right foot 20 cm, or higher, above the
ground?

15. The pedals on a bicycle have a maximum height of 30 cm above the
ground and a minimum distance of 8 cm above the ground. Jeng pedals at
a rate of 20 cycles per minute.
b) At t = 0, Jeng's right foot is closest to the ground.
i) Write 2 equations that represent the height of her right foot above the
ground; 1 sine; 1 cosine.

16. The pedals on a bicycle have a maximum height of 30 cm above the
ground and a minimum distance of 8 cm above the ground. Jeng pedals at
a rate of 20 cycles per minute.
ii) For how long per cycle is Jeng's right foot 20 cm, or higher, above the
ground?
To be completed ...