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# Radian angles & quadrants

## Video transcript

what I want to do in this video is get some practice or become familiar with what different angle measures in radians actually represent and to get our familiarity we're going to start with a ray that starts at the origin and moves along and and and moves and points along the positive x-axis so this start with this magenta ray and we're going to we're going to rotate it around the origin counterclockwise by different angle measures and think about what quadrant do we fall into if we start with this and we were to rotate by counterclockwise by three PI over five radians and then if we start with this and we were to rotate counterclockwise by two PI over seven radians or if we were to start with this and then rotate counterclockwise by three radians so I encourage you to pause the video and think about starting with this if we're to rotate counterclockwise by each of these what what quadrant are we going to end up in so assume you have had you've you pause the video and you tried it out on your own so let's try this first one 3 PI over 5 so 3 PI over 5 so we're going to start rotating so if we get if we go straight up if we if we rotate it essentially if you want to think in degrees if you rotate a counter clockwise 90 degrees that is going to get us to PI over 2 so that would have been PI a rotation a counterclockwise rotation of PI over 2 radians now it's 3 PI over 5 greater or less than that well 3 PI over 5 3 PI over 5 is greater than or I guess in other word could say it is 3 PI over 6 is less than 3 PI over 5 you make the denominator smaller you're making the fraction larger so 3 PI over 6 is the same thing as PI over 2 so let me write it this way so 3 PI over 2 is less than 3 PI over 5 so it's definitely passed to this we're going to go past this now does that get us all the way over here if we were to go essentially be pointed in the opposite direction instead of being pointed to the right making a full you should say 180-degree counterclockwise rotation that would be PI radians that would be PI radians but this thing is less than PI pi would be 5 5 over 5 so this is less than PI radians so we are going to sit we are going to sit someplace someplace and I'm just estimating it if we are going to sit someplace like that and so we are going to sit in the second quadrant now let's think about two PI over seven so two PI over seven do we even get past PI over two well PI over two here would be three point five PI over seven so we don't even get to PI over two we're going to end up we're going to end up someplace someplace over here this thing is let it's greater than zero so we're going to definitely start moving counterclockwise but we're not even get to where this thing is less than PI over two so this is going to throw us in the first quadrant now what about three radians so one way to think about it is three is a little bit less than PI right three is less than PI but it's greater than PI over two how do we know that well PI is pi is approximately 3.14159 and it just keeps going on and on forever so three is definitely closer to that than it is to half of that so it's going to be between PI over 2 and PI so it's going to be if we start with this magenta this magenta red we rotate counterclockwise by 3 radians we are going to get picture it's probably going to be it's going to look something it's going to be something like this but for the sake of this exercise we have gotten ourselves once again into the second quadrant