However, I don't like having to do a week or two of abstract, context-free trig before really getting to students to see why it matters. So, to try something a bit different, I put together an intro task where they look at some more real data - in this case, a fellow teacher's monthly gas bill. You can find that task here. I give them this graph and a few questions:

*How many years of data is represented on the graph? How do you know?**Circle the point associated with the most expensive bill.*- How much did he pay?
- Which month of the year do you think that was? Why?
- Put a box around a point associated with an “average” bill.
- How much did he pay?
- Which month of the year do you think that was? Why?
- On the graph, sketch a curve that fits the data.
- Let’s convert that graph into a different form. Create a table for months 6 - 29.
- How would you describe the pattern of the gas bills?
- Predict what Mr. Bruns’ gas bill will be in the 40th month. Show or explain your reasoning.
- Predict what Mr. Bruns’ gas bill will be in the 100th month. Show or explain your reasoning.

*Hmm, it would be awfully nice if we had a function that could do some of the work for us...*

From here, I'm thinking that we would go on to develop a "cost" function, connect it to a circle, and then get to a point where there is a motivation to develop the unit circle, sine, and cosine:

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