# Working through some introductory trig ideas with my son

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:

$\tan(\pi/12)*\tan(2\pi/12)*\tan(3\pi/12)*\tan(4\pi/12)*\tan(5\pi/12)$

(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:

$e^{i \theta} = \cos{\theta} + i\sin{\theta}$

I’ve never taught a precalculus class before, so I’m explaining most of these ideas for the first time.  Hopefully the book will give him a good foundation and my fumbling around will show him one or two fun ideas.   I think this will be a fun year.