>> Trigonometry comes to us from the ancient Greek, and the word "trigonometry" actually comes from three Greek words. Tri, gonya [phonetic], and metron [phonetic]. Tri, meaning three, gonya referring to sides, and metron meaning measure or measurement. So three-side measurement or the measurement of triangles. Let's begin our study with a little vocabulary here. Let's talk about angle first of all. Now, an angle in trigonometry is the opening between a couple of rays, and that's kind of a different kind of definition than you would find in geometry. Geometry, in geometry, we define an angle as a set of points, as the points of composing these two rays that have this common inpoint, and the opening is actually referred to as the measure of the angle, but here in trigonometry we, we talk about the angle as the opening between the two rays. OK. The rays are just like half lines, and they have a common inpoint here. That common inpoint is called the vertex of the angle, and in this generation of, in generating this opening between the two rays, we can think of an initial side and a terminal side. The initial side being a ray which is fixed, and a terminal side being one which, which kind of moves and rotates to a particular point and then stops, and then we have this terminal side idea. Well, as we study trigonometry, and we look at angles, we're going to refer to angles mostly in standard position. Standard position is a position of an angle where the initial side lies along the X axis, the positive X axis, and the vertex is located at the origin of the coordinate plane. And that's just a real handy way for us to get into the study of, of angles, and so this terminal side can be generated up like this and way around over this way and so forth. And actually the terminal side can be generated in the other direction as well. And we say that there's a positiveness and negativeness associated with generating this terminal side in this direction or this direction. When we generate the terminal side by moving in this direction, however far, it's a positive-measured angle, and if we generate that terminal side in this direction, it's a negative angle. And, and when we talk about positive and negative angles in this way, then we can have a couple of angles that have exactly the same terminal side, and angles that have the same terminal sides are said to be co-terminal. Now, there are a lot of ways of generating co-terminal angles. If I have an angle like this, and notice that I'm in standard form here, that I'm thinking about the initial side here, and if this is the terminal side, then this angle is the same as another angle that would be generated in the same direction but clear around the circuit, you see, back to that same terminal side. So the two angles are co-terminal. There's another way to get to this same terminal side, and it would be to start here, and generate the angle in the negative direction and just back to that same position. So co-terminal angles. And we know that our coordinate plane is subdivided into four quadrants due to the X and Y axes. So we have quadrant 1 here, quadrant 2, quadrant 3, quadrant 4, and it turns out that we can label angles according to the quadrants that they fall in, and if an angle falls into or the terminal side happens to appear in our first quadrant, then the angle is said to be acute. Now generally we're, we're thinking of angles generated in the, a more normal way. That is the angle, this angle as being generated just kind of like that. You see the, the small opening right here for that angle, but at any rate, it's an acute angle if the terminal side falls within the first quadrant. And if the terminal side falls within the second quadrant, then we have an obtuse angle.