So throughout most of physics, we're going to be talking about sines, cosines, and tangents. It's going to be really helpful for you to refresh on your trigonometry. So remember that sines, cosines, and tangents all basically relate angles and sides of a right triangle. If I have a right triangle like this and we've got the angle that's on my left side over here, I've got the adjacent, opposite, and hypotenuse sides of a right triangle. And side sine, cosines, and tangents basically just relate all those three things together. Always just remember SOHCAHTOA. That's probably something you've heard before. It basically just helps you understand which things are getting divided. So for sine, it's going to be opposite over hypotenuse. That's the 'so' part. So in this case, the sine of this angle over here is going to be the opposite side divided by the hypotenuse. It's 35. So the cosine is going to be the adjacent side over our hypotenuse. That's the 'kah' part of SOH CAH TOA. And so in this case, the cosine of this is going to be the adjacent side over the hypotenuse, that's 45. And then the tangent is actually going to be the opposite over the adjacent side. That's the 'TOA' parts. And so in this case, the tangent of this angle is going to be the, sorry, the opposite side divided by the adjacent side. So this is going to be 34. Alright? So, that's how to use SOHCAHTOA. Some of the other equations that you might have to know are just how to get the opposite side, which is going to be the hypotenuse times sine or cosine. And some other helpful formulas are going to be, you know, things like the Pythagorean theorem or just this, sort of, like, basic identity of sines and cosines where sine squared and cosine squared is just 1. And then also just this one over here where tangent is sine over cosine. All these things are going to be very, very helpful for you to understand as you get into physics. Alright.

So now that we've got a basic understanding of sine, cosines, and tangents, those three things will all have special values for very common angles that pop up in physics, like 30, 60, 90, 45, and 0. It's going to be really helpful to sort of memorize them because we'll be using them a lot in physics. So we're going to go over them really quickly here. So remember that the unit circle is really just a circle with a radius of 1, and the basic idea here is that you can basically just sort of create a bunch of right triangles by sweeping out angles of different values, and so you can just create a bunch of triangles everywhere. And the hypotenuses of those triangles will always have a value of 1. And so, for example, this triangle over here has an angle of 30. This one has 45. This one has 60, and the opposite and the adjacent sides will always have different values, depending on what those angles are. I've got a table here that kinda summarizes this. So really quickly here, for 90 degrees, you've got and the tangent actually just doesn't exist. But, basically, what you're also going to see here is that as you go down on this table for sine values, it's actually, like, sort of going up on the cosine values, and these are things that are almost like their exact mirror opposites of each other. So really, these are the only ones that you actually have to memorize because the tangent, remember, is always just equal to sine divided by cosine. So if you ever forget the tangent values, all you have to do is just if you remember these values over here, you can just divide them, and you could always get what the tangent value is. Right? So I'm not going to go through them. You can just look at them, just sort of make sure that you understand and memorize these things. The only other thing I have to point out is that these things will act