Rote regurgitation is only useful for teaching the basics, not advanced stuff. I propose testing this, asking students not to cheat, and catching cheaters later, in case they screwed themselves by skipping the basics.
Why do math students need to know the sine doubling rule? Not so they can calculate with it (they could look that up) but so they can reduce certain expressions to sin(2x). That's why calculus teaches this stuff.
> Why do math students need to know the sine doubling rule? Not so they can calculate with it (they could look that up) but so they can reduce certain expressions to sin(2x). That's why calculus teaches this stuff.
Why make math students memorize random trigonometric identities that they'll use once and then immediately forget when you could teach them a more general fact that they can derive the identities from?
sin(2x) = Im(cos 2x + i sin 2x)
= Im(e^2ix)
= Im(e^ix * e^ix)
= Im((cos x + i sin x)^2)
= Im(cos^2 x + 2i cos x sin x + sin^2 x)
= Im(cos^2 x - sin^2 x + 2i cos x sin x)
= 2 cos x sin x
Why do math students need to know the sine doubling rule? Not so they can calculate with it (they could look that up) but so they can reduce certain expressions to sin(2x). That's why calculus teaches this stuff.