Which actually answers the first part of our question. So we get pi radians are equal to 180 degrees. And we have still the units which are degrees. Now can we simplify this a little bit? Well sure, Both two pi and 360 are divisible by two so lets divide things by two, and if we do that, what do we get? Or what are pi radians equal to? Well on the left side here we're just left with pi radians, and on the righthand side here, 360 divided by two is 180. You could literally write degrees instead of that little symbol. Sometimes it doesn't look like a unit but it is a unit. That is equal to 360 degrees Now, can we simplify this? That's a bore to write this little, superscript circle That's literally the units of the question. Now that exact same angle if we were to measure it in degrees, How many degrees is that? Well if you were doing degrees, it would be one full revolution. How many radians is that? Well we know that it is 2 pi radians. And the first question I'll ask you: If you do one revolution, You have an angle that went all the way around once. We're asked to convert pi radians and negative pi/3 radians to degrees. You will get a chance to work with plenty of decimals, though, because if a number of degrees does not form a nice fraction with 180, then we convert all the way to a decimal and just have to deal with the decimal places. A right angle is 90 degrees and that is pi/2. 30 degrees is pi/6 and Sal just showed us that 60 degrees is pi/3. Half of an equilateral triangle forms a 30-60-90 degree triangle. The diagonal of a square forms a 45 degree angle which is pi/4. In more advanced math, your first results are just stepping stones for all the other steps you need to do, so messy is not good.Īnother reason is that some angles show up in problems over and over, so they become old friends even when they are something like 4/3 pi. They get very messy when you do the next step, and the next step with your results. The size of the angle is exact when you use the fraction, but when you convert to decimals, most of your results are NOT exact-they are approximations. Rather than giving you radians, it gave you degrees squared :) Sal shows us how to line up the units so they cancel in this video and his video on converting degrees to radians, which is just the inverse of radians degrees-also in the units videos on Khan Academy.) That is an upside down conversion that you would get if you multiplied 240 times 180 and then divided by pi. (I think you used the wrong conversion process to get your 13750.99. (I know, a lot of people don't like fractions, but they are our friends!) It is easier to work with 4/3 pi than the decimal equivalent which is 4.188790. We usually use the fractions with pi when talking about radians because it is actually easier to work with the fractions.
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