What do the planets have to do with trigonometry?

Trigonometric Modeling and Transformations

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.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?

Morning at Swiftcurrent Lakephoto source: http://www.flickr.com/photos/58518845@N00/381683114

Trigonometric Modeling and Transformations

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.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?