Pre-Cal 40S March 11, 2009

The Mathematics In Jen's Foot(a problem in trigonometric modeling)

the girl's got some class by flickr user eyesplash Mikul

An ExampleFor 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.

a) Sketch the graph of the sinusoidal function described above.

Trigonometric Modeling and Transformations

Morning at Swiftcurrent Lake

Note: There is no daylight savings time in Saskatchewan.

e) On what days will the sun rise at 7:00am?d) What is the average sunrise time throughout the year?c) Use one of the equations in (b) to predict the time of sunrise on April 6.b) Write 2 equations for the function; one using sine the other cosine.

An ExampleFor 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.

a) Sketch the graph of the sinusoidal function described above.

Trigonometric Modeling and Transformations

Note: There is no daylight savings time in Saskatchewan.

Morning at Swiftcurrent Lake

Trigonometric Modeling and Transformations

e) On what days will the sun rise at 7:00am?d) What is the average sunrise time throughout the year?c) Use one of the equations in (b) to predict the time of sunrise on April 6.

b) Write 2 equations for the function; one using sine the other cosine.

Morning at Swiftcurrent Lake

Trigonometric Modeling and Transformations

e) On what days will the sun rise at 7:00am?d) What is the average sunrise time throughout the year?

c) Use one of the equations in (b) to predict the time of sunrise on April 6.

b) Write 2 equations for the function; one using sine the other cosine.

Morning at Swiftcurrent Lake

Trigonometric Modeling and Transformations

e) On what days will the sun rise at 7:00am?

b) Write 2 equations for the function; one using sine the other cosine.

Morning at Swiftcurrent Lake

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?

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?