Radians and Degrees (NancyPi)

MIT grad shows how to convert from radians to degrees, convert from degrees to radians, and explains what radians and degrees mean. To skip ahead: 1) For converting from DEGREES TO RADIANS, skip to time 4:50. 2) For converting from RADIANS TO DEGREES, skip to time 8:11. 3) For CONVERTING A DECIMAL number of radians into degrees, skip to time 10:50. Nancy formerly of MathBFF explains the steps.

Radians and degrees are just two different ways of expressing an angle, and they have different units. Angle measures written in degrees have a little superscript circle symbol after the number. Angle measures written in radians do not have the degree circle symbol and may or may not have the units "radians" or the abbreviation "rad." listed after the number.

1) TO CONVERT FROM DEGREES TO RADIANS: Multiply the number of degrees by the conversion factor PI OVER 180. For instance, to convert from 200 degrees into radians, you would multiply 200 degrees by the fraction quantity pi radians over 180 degrees. Since you are starting with degrees, and your conversion factor has degrees in the denominator, the degrees units will go away, or effectively cancel, and you will be left with the radian units you want. 200 times pi, divided by 180, simplifies to the quantity 10 pi over 9, which is now in radians. You can leave the symbol pi in your final answer.

2) TO CONVERT FROM RADIANS TO DEGREES: Multiply the number of radians by the conversion factor 180 OVER PI. For instance, to convert from 2 pi over 9 radians into degrees, you would multiply 2 pi over 9 by the fraction quantity 180 degrees over pi radians. Since you are starting with degrees, and your conversion factor has radians in the denominator, the radians units go away, or cancel out, and you will be left with the degree units you want. Since you are also starting with a pi in your angle measure, and the conversion factor has a pi in the denominator, the pi symbols will cancel out and you're left with just 2 times 180 over 9. 2 times 180 is 360, and 360 divided by 9 simplifies to 40, so your final answer is 40 degrees.

What is a radian? Technically, the definition is that if you had a circle with a radius r, an arc length distance of r around the circle would create an inside, central angle that is one radian.

How many degrees are in a circle? There are 360 degrees total in one full circle. Starting from zero degrees at the right-most point on the circle and moving counter-clockwise, one quarter of the way through a circle is 90 degrees, one half of the circle is 180 degrees, three-quarters of the way is 270 degrees, and one full circle is 360 degrees and brings you all the way back to your starting 0 degree point.

How many radians are in a circle? There are 2 pi radians total in one full circle. Starting from zero radians at the right-most point on the circle moving counter-clockwise, one quarter of the way through a circle is pi over 2 radians, one half of the circle is pi radians, three-quarters of the way is 3 pi over 2 radians, and one full circle is 2 pi radians and brings you back to your starting 0 radian point.

Notice that 360 degrees is equivalent to, or the same as, 2 pi. Since 360 degrees equals 2 pi, you could divide both sides of this equation by 2 and find that 180 degrees equals pi. You will use this equivalence, the fact that 180 degrees equals pi, to convert from degrees to radians, or from radians to degrees.

[ion]

I've been banging my head on my desk trying to figure out why i keep getting the wrong answer, but... AS SOON AS NANCY SAID "DIVIDE BY PI", I FLIPPED OUT. I FLIPPED OUT!!!! THANK YOU SO MUCH!!

[amiinhassen]

Yeah Nancy is back. We miss you, but I am in calculus 3 now, but I still like watching you. Big✊

[blitzblutz]

I wish that I had these videos when I was in high school! Nancy is the greatest math teacher!

[agathernakiweewa]

Thank you so much Nancy. You are saving the situation at hand. May God bless you.

[petrusenkali]

Nancypi you the best teacher. reporting from Namibia

[damienkimball]

You need to set up a school. Your explanations are so clear and understandable
Thank you

[ravikantpujari]

I had just started and had fear for this radians and angel suddenly I tuned to this channel and now I am confident. Tnx Nancy.

[Spractral]

Thanks my friend; you've helped explain these concepts in a much more clearly articulated manner than I've found in my texts so far.

[s_patzz]

I absolutely love this! I haven't done any serious maths for years outside of a bit of finance but your chilled approach is very cool and easy to follow. No doubt you will do some videos where i pull the ripcord early having no idea what's going on but so far, so good... Thank you so much!

[kkgill]

My teacher just showed this in class on Friday and people were complaining bcuz a pretty girl wuz doing "nerdy videos". If they think pretty girls can't b smart I think they're the ones with the problem. What im saying is I like ur videos; keep doing what ur doing. I like the message u r conveying. P.S U r very beautiful.

[maryjudielangus]

I really like Nancy, because she teaches us techniques and I can always trust her because shes smart.

[coreygraham]

Thank you Nancy for all of your amazing help. You explain things so amazingly and it is really helpful for me when I get stuck in my math and I just look up your videos. Look forward to your content as I start to work my way through calculus.

[goodwindmaritimeservices]

Nancy. Love your videos. Great review for me as I have not done any of this in 20 years. Thank you for the great explanation.

[Tanker]

Followed your channel for a while now. Gone back to school. Now that we don't have Dad anymore, it's the first time I've needed your help - thank you!

[elperron]

Nancy you just became my new best friend this semester 🤗

[samamohamed]

Actually I’m an egyption student …… i had a proplem with how to convert from degrees to radian but when i saw this video I really understand ♥️♥️thank you♥️♥️🌹

[ChrisWrightOM]

P.S. The writing backwards thing: it's not that difficult. Once, after visiting a car showroom and having the salesman write upside-down so we could read what he was writing immediately across the desk, I taught myself to do this (for limited characters) and sometimes use it with students. However, my guess is that she's right-handed, writes on the screen in normal orientation, then flips the video. The text then looks right from our perspective, and she appears left-handed.

[hsbpurgatorials]

I wish I had an awesome math teacher like you in my a bunch ma'am❤👏😀

[tshreddz]

Bro I love your videos so freaking simple and straight to the point thank you and God Bless 🙏🏿

[JoeSmith-reyu]

Nice explanation 👌. That's how it should be for every single matter. In fact for me, is more important the explanation rather than the operation itself. Just to make sure if u r doing right. explanation is the most important thing and u did it perfectly. More pls.