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CCSS.Math:

we're asked to convert pi radians and negative PI over 3 radians to degrees so the first question I'll ask you if you do 1 revolution if you have an angle that went all the way around once how many radians is that well we know that that is 2 pi 2 pi radians now that exact same angle if we were to measure it in degrees how many degrees is that well you've heard of people doing a 360 doing one full revolution that is equal to 360 degrees now can we simplify this it's important to write this little little superscript circle that's literally the unit's under question sometimes it doesn't look like you know but it is a unit you could literally write degrees instead of that little symbol and the unit's right here of course are the word radians now can we simplify this a little bit well sure both 2 pi and 360 or divisible by 2 so let's divide things by 2 and if we do that what do we get for what PI radians are equal to well on the left-hand side here we're just left with PI radians PI radians and on the right-hand side here 360 divided by 2 is 180 and we have still the units which are degrees so we get PI radians are equal to 180 degrees which actually answer the first part of our question we wanted to convert pi radians well we just figured out pi radians are equal to 100 180 degrees PI radians are equal to 180 degrees and if you want to think about it we know PI radians are halfway around a circle halfway around a circle like that well and that's the same thing as 180 degrees so now let's think about the second part of it we want to convert negative PI over 3 radians I'm just in a new color negative PI over 3 so negative PI over 3 radians how can we convert that to degrees what do we get based on this information right over here well to figure this out we need to know how many how many degrees there are a Radian if we need to multiply this times degrees and I'm going to write the word out because if I just wrote a little circle here it would really it'd be hard to visualize that as as unit degrees per degrees per Radian so how many degrees are there per Radian well we know that for every 180 degrees for every 180 degrees we have pi radians we have pi radians or you could say that there are 180 over PI degrees per Radian and this is going to work out we have however many radians we have times the number of degrees per Radian so of course the units are going to work out radians cancel out the pie also cancels out the pie also cancels out and 180 so you're left with negative 180 divided by 3 leaving us with what is that negative 60 negative 60 and we don't want to forget the units we could write them out that's the only unit says left degrees which we could write out we could write out the word degrees or we could just put that little symbol there