okay so in 5.1 we're going to talk about angles so first to introduce some basic terminology we're going to talk about angles lines and Rays so this guy has a starting point but it goes on forever in the other direction so we're going to call it a ray and we would name it Ray a with the following symbol the arrow goes in One Direction whereas this guy it goes on forever in both directions so it is a line and we would name it in a similar fashion but line AB so when we talk about an angle measure we're going to have a positive or A negative negative angle measure so it depends on the initial side where we start we can see here's where we start we move in a counterclockwise direction to get to our terminal side so counterclockwise will always be positive now we can see here we have the same initial and terminal sides but we're going the opposite direction we're going clock yse so that tells us we're going to have a negative angle measure now over here here's our terminal side and we're moving in this direction that is counterclockwise so it'll be positive and we can see that it's more than a full rotation so it would be more than 360° so let's talk about standard position an angle Theta is set to be in standard position if one it's vertex X is the origin of a rectangular coordinate system so when we have our rectangular coordinate system here's our origin and two its initial side coincides with a positive xaxis so we can see this is the positive side of the xaxis and there is our Center so let's take a look at these two angles so here we have the correct Center as we do here is at the origin and our initial side is the positive portion of the xais so they're both central angles now when we take a look at this guy we go in a counterclockwise Direction so we can say Theta is positive whereas for this particular angle we go in a clockwise Direction so Theta is negative okay so a central angle is a positive angle so it has to have a positive angle measure meaning going in a uh counterclockwise Direction whose vertex is at the center of the circle okay so it's positive vertex is at the center so um we typically have two types when you see this guy the initial side is where it's supposed to be and the terminal side is in quadrant 2 remember with our coordinate plane we have quadrant one quadrant 2 quadrant 3 Quadrant 4 so we would say that this particular angle lies in quadrant 2 now when we take a look at the next guy here's our initial side this is where it's supposed to be our terminal side is uh another axis so because the terminal sides on an axis we can't say it lies in the quadrant we would say it is a quadrantal angle okay so let's make sure we're comfortable with some common uh angle measures so we know that one rotation is 360° now 180° is half of 360 so that is half a rotation 90° is half of that so half of a half is a quarter rotation and 45 is half of that so that's going to be an eth now before we move on we need to fix a typo down at the bottom that should be four rotations so two rotations would be 36 360 which is 720° three rotations we're going to add in another 360 which is 180° and four rotations again add another one in that's 1 , 440° so to talk about two common angles we have a right angle makes a 90° angle and a straight angle forms a straight line right 180° so this be 180° 90°