Converting From Degrees to Radians and Radians to Degrees

in this video you're going to learn how to convert from degrees to radians and radians to degrees and we're going to go through four examples together so the first thing that you want to know and to memorize is that Pi radians is equal to 180 degrees or you could say 180 degrees is equal to Pi radians they're equivalent and so we're going to use that fact to convert from one unit measure to another unit measure now say we're given an angle here in radians like pi over 20. what we do is we multiply by 180 degrees divided by pi and the reason we set it up this way is because 180 and Pi are really the same so anything divided by itself is one and then one times this fraction it doesn't change the value it just changes the units so it's going to change the way that it looks and the other reason we set it this way is because the pi in the denominator is going to cancel with the pi in the numerator here so that goes in there one time and when we multiply now we can say 1 times 180 is 180. 20 times 1 is 20. and 20 goes into 180 nine times so it's 9 degrees so what this means is pi over 20 radians is equivalent to 9 degrees now let's do problem in the other way now say they're giving us the angle in degrees but we want to convert it into radians so how do we do that what we're going to do is we're going to multiply by conversion factor but in this case we're going to write it as Pi over 180. now the reason we set this up this way instead of 180 over Pi is so that the degree units in the denominator will cancel with the degree units in the numerator and you can think of 110 as like 110 over one anything divided by 1 is itself you can do little bit more cross reducing here you could say 10 goes into 110 11 times and 10 goes into 180 18 times so now when you multiply the numerators together and denominators together you're getting 11 pi over 18. radians and you got it let's look at another example so here we're given radians now you might be saying Mario how do you know that this is in radians well you'll know if it's in degrees because you'll see that little degree unit symbol if it doesn't have that then you know that it's going to be in radians and so when you set this up you're going to set it up like 180 divided by pi this way the pi in the denominator cancels with the pi in the numerator and we're left with the units which we want which are the degrees so it's kind of like dimensional analysis or unit conversions now you can do some more reducing top and bottom or on the diagonals so here can see that 18 goes in here once 18 goes in here 10 times and then when multiply across 5 times 10 is 50 degrees and you got it okay last example see if you can try this one we're going from degrees 36 degrees to radians so what do we want to multiply by here well you're going to set this up as times 1 over 180 and the reason chose this instead of the reciprocal is that so the degree units in the denominator cancel with the degree units in the numerator and we're going to be left with pi radians now can do little bit more reducing here 36 goes in here once 30 goes 36 goes into 185 times then when multiply the numerators together get pi and 1 times 5 is 5. so this is going to be pi over 5 radians so great job if you're able to follow these examples now if you're wondering what exactly is radian and you want to understand that at deeper level follow me over to that video did right there talking about radians and how we actually think about radians I'll see you in that video