learning radians can be pretty easy it's a little bit like cutting a pizza so watch me slice this up hey welcome back this is Tammy and I do math for coffee okay we have to start by talking about the circumference of the circle first so starting with the whole circle the formula for circumference is 2 times pi times the radius well in the unit circle the radius is 1. so the circumference is going to be 2 pi going all the way around this circle one time that equals 2 pi and that's radians That's the basis of radians the basis of degrees was 360 degrees is a full circle but in radians we know a full circle is 2 pi so let's do a little more with that the unit circle we know it has a radius of one there are an infinite number of points on the circle but the unit circle has 16 points that are super interesting and the very first one is at zero but zero is also two Pi once you go all the way around once now I'd like you to split that Circle in half and if you split 2 pi in half you get Pi now I'd like you to split the top in half and if you take pi and divide it in half you get pi over 2 1 half pi count to yourself one pi over 2 2 pi over 2 3 pi over 2 that is the fourth Point all right let's find the rest of the points we're going to start with this 30 degree angle and I want you to think about this you know that this is 180 degrees and so this whole top part has how many 30 degree angles in it it has six of them so that means Pi is split into six parts well that means each one of these little sectors is pi over 6. so let's look at the angles the very first one is 1 pi over six the second one is two pi over six but that's not in lowest terms and so we're going to put that in lowest terms and this one is going to be pi over 3. the third point we already know what that point is one two three pi over sixes if you reduce that it's pi over 2. that should look familiar the next one this is 4 pi over 6 1 2 3 4 we have four sections so it's 4 pi over 6 also not in lowest terms so we're going to write it down as 2 pi over 3. the next one 5 pi over 6 that is in lowest terms so we'll just leave it there the next one is six pi over 6. this reduces to Pi then the next one must be 7 pi over 6. this guy down here is 8 pi over 6 also not in lowest terms so when we do that it becomes 4 pi over 3 but it started out as 8 pi over 6. I hope you are seeing the easy way to remember this you just set it up in the sixes and you count so the next one would be 9 pi over 6 and that reduces to 3 pi over 2. we already met that point before so okay but now it still works like you can just count up by the sixes and you're going to end up with three pi over 2. so the next one should be ten pi over 6 which reduces to 5 pi over three and there it is if you're following the pattern you know what the next guy is going to be 11 pi over 6 already in Lost terms we don't have to do anything more with that and if we close this circle we end up at 12 pi over 6 which reduces to 2 pi which is what we expected right this last set of points is going to be based on what happens when you divide this circle up into 45 degree angles and 180 is the same thing as Pi radians each sector is going to be pi over 4 in size so the first radian will be pi over 4. the second one is going to be 2 pi over 4 which needs to be reduced to pi over 2. again we know that one already three pi over four again we're counting up 1 pi over 4 2 pi over 4 3 pi over four this one's fine it doesn't need to be reduced then 4 pi over 4 and that's going to reduce to Pi moving down South we have 5 pi over four this one is going to be 6 pi over 4 which reduces to 3 pi over two again there's repetition here but depending on how you count up you're going to land on that point again that has to be 7 pi over four that doesn't reduce closing the circle we end up with eight pi over 4 which reduces to 2 pi which is no big surprise right all right let's put it all together foreign now for the next thing we need to learn is how to find the coordinates for each one of those points watch that video next [Applause] [Music]