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Originally Posted by phrontist
Trig Identities - Ah, but which should I really commit to memory? Which will really be useful in calculus? Which will be helpful in calculus?
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I've been a TA for first year Calculus for four years now. When in comes to Trig, there's very little that you actually have to memorize. Here's the musts.
- Your friendly triangles -- (1,1, root 2) & (1, root 3, 2)
- Your basic trigonometric ratios -- SOH-CAH-TOA, and the reciprocals
- From these first two, you know calculate the values of any basic angles
- (Sin x)^2 + (Cos x)^2 =1
With a working knowledge of elementary geometry, you can derive everything else you'll ever need. But if you don't want to be doing that during a test, here's the next level of stuff you'll want to committ to memory.
- The double angle formulae for Sin and Cos
- With the double angle formulae, you can now get radical expressions for things as complicated as Sin 1
I'm a firm believer that when it comes to math, you really don't need to memorize. I tend to derive pretty much everything on the fly. I've found that this style of learning and doing, allows for a much more fluent application of the knowledge. Math means so much more, when you know where all you formulas are coming from.
There are hundreds of trig identities you could memorize, but you'll save yourself a lot of time if you just learn how to derive them.