Re:A new school curriculum
by whatshisface on Monday November 25, 2019 @10:29AM
(#21628911)
Bear in mind that memorizing trig identities was something you had to do for exams. If you want to get any use out of trig identities in "real life" you will need the kind of understanding that comes with being able to do the derivations yourself. In the time before computers there was a lot of value in being able to do the mechanistic kind of problem solving you're describing, but now that we have Mathematica, the only useful professional tasks that are left for humans to do involve the kind of knowledge it takes to do a derivation.
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Re:A new school curriculum
by mywittyname on Monday November 25, 2019 @11:09AM
(#21629414)
I had a professor that loved to make simple substitutions to values in questions, where the original question would be incredibly difficult, but if you spotted the substitution, the amount of work you had to do was dramatically reduced. Think something like integrate cos x + i sin x dx, if you spot that cos x + i sin x = e^(ix), and perform substitution, the problem becomes trivial.
Deriving information from facts is a vital skill. But recalling facts is also incredibly important as well. Having knowledge immediately available for use allows a person to apply that knowledge in real-time, which is important for problem solving and thinking on your feet.
Every college math class I took gave me a sheet with those kinds of identities on it. If I was doing the kind of work where I actually had to do calculus involving trig functions, you can bet I'd pull up a similar sheet while I was working. Sure having it memorized would be a bit faster, but that's true for far more things than I can actually memorize.