I've tutored a lot of trig over the years, and by far the biggest problem I see teachers make is teaching the class in the wrong order - starting things off from the "mathy" direction of functions, the second-most-reviled subject in math (trig is first). While this approach makes a lot of sense to math teachers (a.k.a. math studs who know trig and functions like the back of their hands), it makes zero sense to kids seeing this bizarre "trig junk" for the first time!
When I teach trig to a student who is struggling, we start over, coming at trig from the direction that actually makes sense to a first-timer: triangles. Once you get comfortable with SohCahToa, the Unit Circle suddenly starts making a lot more sense. I start off nice and slow, so if you're already a SohCahToa stud, I won't be offended if you skip down to where I get into the harder examples, or just move on to Special Triangles.
Intro to SohCahToa (Sine, Cosine & Tangent)
This video introduces the famed acronym for the sinusoidal functions, tells you how to use it, and most importantly helps you remember how to spell it. From here on out in trig, if you don't write "SohCahToa" at the top of all your homework, tests & quizzes, you're doing something wrong. (If you're not writing it at the top of your homework because you're not doing your homework, come closer to the screen so I can smack you!)
"Solving" a triangle is where they give you a side and an angle of a right triangle, and you have to use SohCahToa (sine, cosine & tangent) to get the remaining sides and angle. Why not use Pythagorean, you ask? Because in trig problems they only give you one side. Teachers are tricky, I'm telling you!
When does SohCahToa get tricky, you ask? It's just a simple acronym, you say? You'll drop that cocky attitude when you see a root three in a 45-45-90 triangle, a root-two in a 30-60-90, and a root-six... I don't even want to say where the root six pops up. The sinusoidal functions.
Angle of Elevation Problems
These are word problems which are designed to be confusing but are in fact just SohCahToa problems in disguise. They always involve someone looking at a distant object, noting the angle that they have to look up or down to see it, then using that angle to estimate either its height or its distance.
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...)