I am teaching PreCalc this year. We are knee deep in our trig unit and I am planning to teach Trig Angle Addition formulas on Monday. I seriously dread this day because I don't see any motivation for it. I mean we have a calculator to figure out what sin 75˚ or cos 165˚ is...who cares about the exact value???
So, I checked around the internet to see if I could find some motivation and I seriously still haven't found too many reasons why we are still actually teaching this topic, BUT I did find some motivation for me! I found several different (but similar) proofs of the formulas:
sin(x+y) = sin x cos y + cos x sin y
cos(x + y) = cos x cos y - sin y sin x
Can I tell you a secret? I never had any idea where these formulas came from. As a math teacher, I'm embarrassed to say that, but it is true!
So, I decided to give this proof a try during class last Monday. It went about as I expected - some students appreciated the proof...some students' eyes started to glaze over. But, I felt like I had done my duty and showed them some of the the beauty of mathematics. Formulas that we use come from unlikely places - someone had to think of them...they didn't just appear out of thin air.
Here are links to a few products that I have that encourage students to see the "proof" in mathematics. What proofs do you show your class?