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Nested Trig Functions (Composite Functions)

Like Russian dolls, these problems have one trig function inside another, such as sin^-1(cos60). This is a type of problem that every trig teacher loves, so I've given them their own video. They're not too bad if you break it down and work from the inside out. I'll also show you a trick to spot whether they'll just cancel each other out, like in Arcsin[sin(60)].

Inverse Trig on the Calculator

Trig teachers usually don't explain how to do trig on a calculator because... I'm not sure why, maybe they're just mean, since they usually also give you a few problems that you MUST use a calculator on. Don't worry, though, I've got your back with this handy-dandy tutorial on doing inverse trig on your TI-83, TI-84, etc.

Inverse Sec Csc Cot

These are very similar to the inverse sine, cosine and tangent problems, except worse because these always involve the extra step of flipping and rationalizing first. No fun! There is also a common mistake that I've seen a lot of students make, so I'll show you how to avoid that one.

Inverse Trig Examples!

In this video I'll just take the inverse trig function stuff we touched on in the last video and work a ton of example problems, still just for sin^-1, cos^-1 & tan^-1. Good thing too since this is one of the more confusing things about trig, and you'll have to be good at this if you're going to solve trig equations in upcoming chapters.

How to find Co-Terminal Angles with Radians

If you're a fraction hater, this one isn't going to be too pretty, since we're going to be adding 2 pi to lots of crazy fractions. But hey, practice a little here, and you'll do fine on the test!

How to Convert Radians to Degrees

Not only is this a useful skill if you're more comfortable with degrees than radians, it's also a type of problem that every trig teacher puts on quizzes and tests. In this video I show you how to convert radians to degrees, and degrees to radians, and as usual I work a bunch of examples.

Tips For Memorizing Radian Unit Circle

In this video I get into all the stuff from the unit circle chapter, except this time with radians. Negative angles. Improper fractions. And of course, awesome tricks to help you do problems like sin(5pi/6) in your head. I'll show you how simple patterns can be used to write out the unit circle, anytime you need it.

Trig Functions of Radians

In this video we'll learn how to find the sine and cosine of all those nasty radian angles on the unit circle, and we'll practice finding the trig functions of them in a bunch of examples. We'll also learn the best trick ever for quickly converting radian angles to degrees -- in your head -- using just the denominator!

What The Heck Are Radians?

In this video we'll explain where radians come from. Why is pi equal to 180 degrees? If you have an honors teacher who is a real stickler, this video is for you. If you just want to know how to "do" radian problems and find their trig functions, my other radians videos are for you!

* Pi equals 180 degrees

* Negative radian angles

Another Trick To Memorize Unit Circle: "Bowtie Angles"

(click for FREE printable BOWTIE ANGLES™ CHART)

The Unit Circle Chart (and tips for memorizing it)

(click for printable Unit Circle CHART)

Co-Terminal Angles (a.k.a. angles bigger than 360)

In this video, we find out how to find sine, cosine, and all the other trig functions of co-terminal angles. The short version is "just take away 360 again and again until it's on the unit circle." (With radians it's the same, we'll just use 2pi instead.)

Test Video Post

Is there a video showing to the right? How about margins?

Sine and Cosine of Negative Angles

This is another topic that I get tons of questions about because teachers seem to give too little attention to it, so I'm giving negative angles their own video. It's easy to say "go around clockwise instead of counterclockwise," but harder in practice, so I work a bunch of examples. For simplicity this video is degrees only, but the concepts are the same for radians.

More Special Angles - 0, 90, 180, 270

The four "compass points" of the unit circle chart (N, S, E, W) are the angles that have coordinates of 0 and 1 or -1, and they're special because you can't draw a reference angle triangle for them: you've just got to use the unit circle. Sine and cosine aren't too bad for these, but for tangent and the reciprocal functions you've got to choose between zero and undefined, so that's fun. Can't divide by zero!

Putting It Together: Trig functions of obtuse angles

It's finally time to combine the lessons of the last few videos and find the sine and cosine of angles from the second, third and fourth quadrants! Not exciting, I know, but necessary since it's gonna be on a million tests. From sin135 to cot330 to sec240, by the end of this lesson, you too will be able to derive the unit circle chart using (cosX, sinX)!

How to Calculate Reference Angles

Many students I've tutored have trouble with reference angles, but I think it's mostly because teachers barely teach it, thus making it confusing. In this video I'll teach you a couple of easy-to-remember formulas for calculating reference angles, a skill that will serve you well throughout trig.

"All Students Take Calculus" - the other three quadrants

In this video, we'll take a look at the acronym/pneumonic device that will save your grade whenever you're trying to figure out whether a trig function on the unit circle chart is positive or negative, which is the easiest way to lose points on a quiz or test! A is for All, S is for sine, T is for tangent, and C is for cosine.

First Quadrant of Unit Circle

Rather than tackle the unit circle chart all at once, in this video we'll "ease into the pool" by looking at the first quadrant first. I'll show you how to get the first quadrant unit circle values from your special triangles, a key skill that will make the other four quadrants a lot easier to understand and memorize.