So throughout most of physics, we're gonna be talking about sines, cosines and tangents. It's gonna 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 uh sine cosines and tangents basically just relate all those three things together. So always just remember SOCA to, that's probably something you've heard before basically just helps you understand which things are getting, getting divided. So for sign, it's gonna be opposite over hypotenuse. That's the so parts. So in this case, the sign of this angle over here is gonna be the opposite side divided by the hypotenuse, it's three or five. So the cosine is gonna be the adjacent side over Hyotan, that's the part of SOTO. And so in this case, the theta or the, the cosine of this is gonna be the adjacent side over the hypotenuse that's 4/5. And then the tangent is actually gonna be the opposite over the adjacent side, that's the to parts. And so in this case, the tangent of this angle is gonna be the uh sorry, the opposite side divided by the adjacent side. So this is gonna be 3/4 all right. So um that's just how to use soto uh some of the other equations that you might have to know are just how to get the opposite side, which is gonna be the hypotenuse time sign or cosine. Um And some other helpful formulas are gonna be, you know, things like the Pythagorean theorem or just this uh sort of like basic identity of signs and cosines where sine squared and cosine squared is just one. And then also just this one over here where tangent is signed over cosine, all these things are going to be very, very helpful for you to understand as you get into physics. All right. 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 zero. It's gonna be really helpful to sort of memorize them because we'll be using them a lot in physics. So we're gonna go over them really quickly here. So remember that the unit circle is really just a circle with a radius of one. 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 hypothesis of those triangles will always have a value of one. And so, for example, this uh triangle over here has an angle of 30 this one has 45 this one has 60 the opposite and the adjacent sides will always have different values. Uh Basically, depending on what those angles are. And I've got a table here that kind of summarizes this. So really quickly here, uh for 90 degrees, you've got 10 and the tangent actually just doesn't exist. But basically, what you're also gonna see here is that as you go down on this, on this graph here for or this table for sign values, it's actually like sort of going up on the cosine value thing. These are things are almost like their exact sort of mirror opposites of each other. Um So really, these are the only ones that you actually have to memorize because the tangent remember is always just equal to sign 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 to what the tangent value is, right? So I'm not gonna go through them, you can just look at them. Um just sort of make sure that you understand and memorize these things. Um The only other thing that I have to point out is that these things will actually have positive and negative values depending on which quadrant of the graph that you're in. Um So for example, everything is positive here, whereas the only thing that's positive over here is sign tangents and then cosign for the different quadrants of the unit circle. All right. That's just a hopefully a pretty, pretty quick review.
