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The longest chapter in trig. We'll start off slow, developing understanding by using SohCahToa to derive only the first quadrant of the unit circle at first. Then we'll work through reference angles, sign tricks, negative angles, co-terminal angles and undefined functions until you can calculate the six trig functions for any angle. We'll finish up with some tricks for memorizing the Unit Circle Chart.
Csc, Sec & Cot Example Problems
If you're already a ChoShaCao master, perhaps you'll find this video a touch boring. But if you're in the 99% of trig students who find solving triangles and denominator-rationalizing confusing, by all means stick around, and you too can be bored by these "find the six trigonometric functions" questions!
Using a calculator on Secant, Co-Secant, Co-Tangent
These aren't buttons on your calculator, but they obviously should be. This video shows you how to fix what TI broke, turning your calculator into a powerful tool in your pursuit of better trig grades. (HINT: Main trick here is not to get burned by that little "-1" above the sine and cosine buttons, which don't mean reciprocal!)
Trickier Csc, Sec & Cot problems
* Burn examples
* How not to get burned
* Common errors
Introducing Secant, Co-Secant & Co-Tangent
ChoShaCao is one way to go, but let's face it, nobody except for one Brentwood student I know has ever done it. Instead, we'll always use the reciprocals method to find these puppies, since that will work in special and non-special triangles. We'll also get tons of practice rationalizing denominators, since that's usually the hardest thing about finding sec, csc & cot.
These new trig functions are just the reciprocal (flip) of sine, cosine and tangent, but they can be confusing, so we'll emphasize always writing them in the correct order each time, and we'll do lots of examples. I'll also show you how to do these on your calculator, which doesn't have buttons for these.
Super-Tricky Special Triangle Examples
If you've got a slightly mean teacher, or just a tricky one, they're going to try and burn you once or thrice with examples like the ones in this video. I'm talking putting a five under a square root, putting root-two's on a 30-60-90, and giving you massive messes of rationalizing denominators. If you're in honors, this one is also for you.
SohCahToa on Special Triangles
In this video, we apply the stuff we learned in the SohCahToa chapter and apply it to the special triangles we just learned. This is the main skill you'll use the special triangles for once you're into the unit circle: finding the sine & cosine of special angles using the special triangles.
Ratios: Solving Special Triangles The Easy Way
You could just get in the habit of always using SohCahToa to find the missing sides of a triangle, but it's not the fastest way. In this video, I'll explain how to use ratios (multiplying by root 2, for example) to fill in the missing sides of 30-60-90 and 45-45-90 triangles.
Intro to Special Triangles
The toughest thing for many students is to tell the 30-60-90 and 45-45-90 triangles apart based on their side lengths. So, in this video I introduce you to both the fractions and non-fractions versions of these "special" triangles, and I show you tricks to keep the two straight. (TIP: 90% of the time, if there's a "3" under the square root it's a 30-60, and if there's a "2" under any root it's a 45-45.)
Solving Triangles
"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!
Tricky SohCahToa Examples (Sine, Cosine & Tangent)
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.