My older son is working through Art of Problem Solving’s Precalculus book this year. I love this book and am happy to help him work through it. For now the topic is trig functions. Here are three nice conversations we’ve had in the last week:

**(1) Exploring some parametric plots:**

We had been looking at graphs of sin(x) and cos(x), but what if I made the x-coordinate a function cos(t) and the y-coordinate function of sin(t)? What would that look like?

**(2) A clever homework problem that gave him some trouble**

The question to asked him to find the product:

**(3) Talking about the sum and difference formulas**

This morning he was working through the geometric proofs in the book that give you the sum and difference formulas for cos(a + b) and sin(a + b). After that I showed him how the formulas come from the formula: