Trig Proofs & Identities: 3 Tricks to Make Them Easier
The biggest problem with trig proofs (other than the word "proof" causing flashbacks to geometry) is that teachers tend to make them look way too easy in class, so students get discouraged when they can't just whip them off the top of their heads like Teacher. The reality is that trig proofs are tough, even for teachers, and the only reason the teacher can make it look so easy is they've been teaching the same problems year after year! That's why in the videos below I break trig proofs down for you, revealing the Big Three basic types of trig proof that almost every proof falls into, and showing you the step-by-step process for working each type out. I also "wing it" a bit, working example problems I've never done before, so that you can see that even Trig Masters don't always see exactly how to solve a proof when they first see it, and that often it comes down to "messing around with it" and trying a few things before you find the path that will get you to the solution. The key is to not give up if you hit a few dead ends!
Basic Trig Proofs Using "Reciprocal Properties"
"Reciprocal Properties" is just a fancy way math teachers use to describe these three equations you already know: csc=1/sin, sec=1/cos, tan=sin/cos, and cot=cos/sin. Not so bad, right? The easiest trig proofs are the ones where you have a string of things multiplied together, so that if you turn them all into sin's & cos's, they'll cancel out. In this video I work a bunch of them, and show you how to spot this type.
The Pythagorean Identity: sin2X + cos2X = 1
The trig identity that you should never forget: sin2X + cos2X = 1. In this video I show you where it comes from, how to use it in proofs, and how to spot proofs where it might come in handy.
Proofs Using The "Other Two" Pythagorean Identities: tan2X+1 = sec2X & 1+cot2X = csc2X
These two identities show up all the time in trig proofs, but they're really easy to get mixed up (wait, does tan go with sec or csc?). So, in this video I show you a great trick to memorize them so you can write them down at the top of your quiz or test (a practice I highly recommend). I also show you how to spot trig proof problems where they'll come in handy, and work a few examples.
Trig Proofs With Complex Fractions
Trig proofs get a lot harder when they don't have exponents in them, since you can't use the Pythagorean Identities on them. Instead, you've got to use the tricks I show you in this video to turn denominators like (1 + sinX) and into expressions like (1 - sin2) where we CAN use the Pythagorean Identities. (If you still remember Algebra 2, you'll recognize this "conjugate trick" as a way we rationalized complex fractions and roots.)
Tricky Proofs - Honors Only! (free)
This video features some brutal examples which show how the Big Three proof tools can get you through even the diciest proofs. It also shows that even folks who are pretty good at trig don't necessarily see how to solve a proof when we begin; you just have to keep messing around until it gets there! If you're in honors, these trig proof examples are for you!
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)