More trigonometric modeling.

1. The Mathematics In Jen's Foot
(a problem in trigonometric modeling)
the girl's got some class by
flickr user eyesplash Mikul

2. 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. Morning at Swiftcurrent Lake
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 sun rise at 7:00am?

3. 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. Morning at Swiftcurrent Lake
Note: There is no daylight
savings time in Saskatchewan.
a) Sketch the graph of the sinusoidal
function described above.

4. Trigonometric Modeling and Transformations
b) Write 2 equations for the function; one using sine the other cosine.
Morning at Swiftcurrent Lake
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 sun rise at 7:00am?

5. Trigonometric Modeling and Transformations
b) Write 2 equations for the function; one using sine the other cosine.
Morning at Swiftcurrent Lake
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 sun rise at 7:00am?

6. Trigonometric Modeling and Transformations
b) Write 2 equations for the function; one using sine the other cosine.
Morning at Swiftcurrent Lake
e) On what days will the sun rise at 7:00am?

10. 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.
Jen pedals at a rate of 20 cycles per minute.
a) What is the period, in seconds for this function?

11. b) At t = 0, Jen'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 Jen's right foot 20 cm, or higher,
above the ground?