I don’t think I’m alone in harboring ill-feelings toward trig functions, particularly as they apply to integration. Don’t get me wrong, I understand the importance of trig. But I find Calculus at its most enervating when trig is involved. The basic concepts at play in this section are straightforward
Just working with trig functions demands memorization, at a minimum, of the derivatives and integrals of the core trig functions. But at this point, those alone won’t get you through. You should also have random access to reciprocal identities and pythagorean identities. Although that, too, won’t really be enough – you need half-angle identities and inverse trig identities. Yet there also seems to be an ever growing list of “standard antiderivatives” that are at play.
Somehow I should remember that sec3(x) = ½ sec(x)tan(x) + ½ ln|sec(x) + tan(x)| + C. Yes, that’s right. I know I should. So, I’ll stop whinging. I get that much of what I’m learning here is to recognize patterns. As such, I should in fact memorize all these formulas, identities, etc. And I’ve bought myself a stack of flash cards, because I don’t already have enough to do in my 14 hour workdays.
I suspect that even after I’ve memorized all these, I’ll still find myself frustrated. But that’s as it should be, right? I know I’m learning when I’m frustrated. And I don’t expect the frustration to subside moving forward. So bring on the frustration.