My memories of high school trigonometry involve lots of graphing on the calculator. I didn't want to take this approach. My kids already seem to rely to much on the calculator to do their thinking for them. And, I feel like one of the areas I failed these kids in Algebra 2 was transforming functions. When they see a trig function, I want them to really see and think about what is going on with the graph, not just type an equation in their calculator and sketch the result.
So, long story short, my kids didn't really freak out when I asked them to graph trig functions by hand. In fact, they think it's a completely normal thing to do. Yay :) Eventually, I had to spill the beans and admit to them that I doubt their college professors will ever ask them to graph a translated tangent graph by hand. "But why not? It's so easy!"
One thing I've done this year is ask my students to create mini-posters that summarize how to graph various trig functions by hand. Some of my kids did a much better job at this than others, but I think they all learned from this process. Instead of giving them each an equation to graph, I had them make their own equation. (However - they can't use the equations from their notes or their neighbor's equations!) Because my kids are smart/lazy/, they started thinking about what a,b,c,d values would make their functions easy to graph. A lot of them realized that if they changed the b value on their sine or cosine graph to pi, they could mark their x axis in terms of integers instead of in terms of pi. And, the best thing would be when my kids accidentally made mistakes with their graphing. Normally, mistakes wouldn't make me that happy. But, so many of my students would figure out how to change their equation to account for the "mistake" instead of re-graphing the entire function. Then, it wasn't a mistake anymore. :)
I snapped some pictures of the posters made by my students. Some of these have errors. So, please don't take them for gospel!
Notes to myself for next time I teach trig:
* Take better notes over how to identify/label the period/amplitude of a graph
* Have students do everything but the final graph in pencil. Graph the final graph (after translations) in color.
* Give the mini-poster project as an assignment BEFORE the quiz instead of after it. Lots of awesome learning happened in the process. :)