This activity uses actual temperature data to initiate an exploration of the connections between coefficients and graphs of sine equations. It is an extension of a lesson taught by Andy McFarland and further developed by Robin Ward, at the time students at the University of Virginia.

Mathematics Topics: This activity involves sine equations and their coefficients (amplitude, period, vertical shift, horizontal shift), curve fitting, and regression.

Mathematical Thinking: Students interpret scatterplots, and derive coefficients for "best fit" sine equations, numerically and graphically.

Technology: Graphing calculators are used to draw scatterplots, draw graphs of various sine curves, and calculate regression equations.

Sample Screen Shots:
Below are screenshots showing: (1) average monthly temperature data for 3 cities, and (2) a series of scatterplots of the Washington DC data illustrating a method to curve fit the data.

Figure 1. Average Monthly Temperature for Washington, Verhoyansk, and Buenos Aires

Figure 2. An Incremental Approach to Curve-Fitting the Washington data