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.

For help with basic TRIGONOMETRY (SIN, COS, TAN), jump to: https://youtu.be/bSM7RNSbWhM

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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.

For more of my math videos, check out: http://nancypi.com

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@NancyPi are you writing backwards??

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We knew that.

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I don’t understand stand if you write backwards or edit it

MrTheTonypp technique whatever same thing, and even if it’s mirrored she’s obviously gonna talk right…She’s just going to be flipped

@Vidhi Patel you are still wrong that would mean she wrote backwards before putting on mirror effect.

MrTheTonypp ok u really don’t understand this lol, let me explain. She is writing on a glass normally so that she can see it, NOT BACKWARDS. So obviously we can’t see it correctly.WHICH IS WHY she puts the mirror effect while editing it so that it basically FLIPS IT. So to summarize, in reality she is sitting on the right and writing so that she can see it correctly while it’s impossible for us to read, but after she “mirrors” the video, we can see it properly.

@Vidhi Patel I am willimg to bet if you ask her is she is writing backwards she will say yes

MrTheTonypp Deal.

And thank you

begin{matrix}

angle & sin & cos \

0 & sqrt{0}/2 & sqrt{4}/2 \

pi/6 & sqrt{1}/2 & sqrt{3}/2 \

pi/4 & sqrt{2}/2 & sqrt{2}/2 \

pi/3 & sqrt{3}/2 & sqrt{1}/2 \

pi/2 & sqrt{4}/2 & sqrt{0}/2

end{matrix}

I have a head scratcher for you: I want to purchase a try square and accuracy is typically described “.001″ per inch”. I’m interested in one described as “.06 degrees” square. What does that convert to in thousandths of an inch?

hi , what kind of voodoo is this

Lol

Filter all other videos out, Nancy knows best!

Hi Nancy, thanks for the pure awesomeness of your videos. 🙂 Have you done anything on Polar Coordinates?

Can you not use that pink marker? Can’r see numbers properly.

Well done. Keep shining. 🙂

😍😁

Salla bakwas hai

Tnx i like math and your videos

Nancy you just became my new best friend this semester 🤗

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!

Thank you!!!!

This was really helpful please upload more topics on pre-cal and calculus!!!

Love this video! Really helped me out in understanding the conversion better. 🙂 I was wondering whenever you had the time if you could possibly do a video on arc length? Including how to find both arc length and the central degree? Either way, thanks for all the help! 🙂

Thanks nancy

Very useful like ur teaching style

I’m in Calculus-1 please continue with trigs

Degrees are rational ( ex 180 ) , but radians are irrational ( because Pi is irrational ).

So how can 180 equal to Pi ??? Because a rational number can never be an irrational number

It’s true that we tend to use rational numbers with degrees and irrational numbers with radians, but any real number can work for both ways of expressing angles. Also, this is a unit conversion. 180 doesn’t equal pi, but 180 degrees does equal pi radians.

😮

Madam mukherjee nagar aake pdha do naa, aap sahi taiyari kra doge ssc ki….

306 degrees = 2pi? Looks like one pie to me. LOL

how you can write like this

Very nice presentation but somehow I cannot concentrate very well on the concepts as one might expect Nancy being so presentable and me being a male…… your so lovely Nancy…do you do private lessons…chuckle I am so naughty.

From Iraq yr so beautiful 💓

Beautiful

thank u my nigga

You are the cutest math instructor I have ever had. Thanks

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love you

Oh, it’s so hard to concentrate while viewing this video. Nancy is so… beautiful… I’m sorry, but it’s true.

Да, ты правда. 😉

Same here 🙂

Thank you for this!

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

Thank you

put a video about the fourier series

Good

is she writing backwards???!

Is she writing backwards?

She probably flips it because you can do that on a computer.

TnX learned a lot

❤️👍👍

How the heck does she write/draw backwards ????

Rare to find someone so beautiful and so smart….Awesome Lady !!

Matt Miller N8QZH I think she’s either left handed or the video is flipped

1000th like is mine ahaha

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.

To be honest, I have no idea what you’re saying, but I appreciate your hard work!

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.

Wow! Alanis Morsette knows a lot about math!

it’s do cool. she is writing in reverse direction.

wait a second is it the flipped image of the real one.

but she is beautiful. she is braking my attention.

lol flipped image, you’re right

Thx❤️

Hi Nancy, thank you for your videos. Suggestion: can you do a video on why you can’t interchange degrees and radians in trigonometric arguments.

Thanks!

Thanks for the help! Nancy you are to sweet

It’s like u writing on my phone screen

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Im saying this to you becoz i think it is better than billions like ,subscribe and comments !

Please respond

Do a video on how to measure angles pls

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Hi Nancy your classes are very interesting. I have almost 50 video the sum of my eyes and abbonnés is not even worth 2% dun of your video,! maybe they will see your sexy voice or your beautiful eyes in my chain, Maybe the numbers of my abbonates will increase what do you think ..? I am also a matematician and physisian.😍

If you made a class on Udemy I would purchase it, and I have already purchased Krista’s

You awsome teacher, doing nice work for students ,I remembered my school time after this video.

Let’s suppose a circle of 2cm radius and an arc of length 2cm then the angle form by arc is the ratio of arc length / radius

So 2cm/2cm = 1 (it is real no.

thank you! awesome way of explaining this

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.

and she’s writing backwards

It’s mirror mode

Is she a teacher IRL?

If you think this through yourself (which is what you should do to understand it) this is easy stuff, just an exercise in proportions. Fabulous teaching though, Nancy.

I see that the calculator has three modes for using trig. and inverse trig. functions, which are degrees (deg), radians (rad), and gradians (grad). I know that we don’t talk about gradians in math class. I know that there is a conversion between degrees and radians with gradians.

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

Thank you Nancy, you are a great teacher.

You are a great teacher i can understand every word you said although iam from arab country i can understand everything from you

Can you make more videos on calculus ( like integration)

I keep waiting for Nancy to write backwards.

helpful

Wow your good

Thank you so much… your explanation is soooo cleaarrrrrr.

Nice work

Iss topic pr Mene bhi ek video banai h ek bar jarur dekho friends.

#studyfirst

The spacing on this will probably be wrong and it not look like its supposed to but I learned it with this:

Degrees x (pi symbol)

180

(pi symbol) x radians

how can you write with your left hand and mirrored in the same time?

Hi Nancy Pi. I’m about 30 years late to watch these videos for school, but I am using them to brush up on math for programming. It would be beneficial for your viewers if you added worksheets in the narrative section (“SHOW MORE/SHOW LESS”) for practice to improve memory retention. Thank you for your work and videos.

my favorite

1.75 speed worked for me

I wish I had an awesome math teacher like you in my school……..Thanks a bunch ma’am❤👏😀

Nancy😍🤣😍

at 4:06 lol i thought it said 11/180 i had to rewatch it twice XD

LMAOOO

Is she Being held hostage?

Very good, excellent video.

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its radiance of nancy

Hay Nancy love your content…..question…..the last one wouldn’t 1.5 pi be 270 degrees…I was totally with you all the way up to therw5…please please please clarify for me peace out

Sometimes she smiles a smile that used to be described as a “come-hither” smile; at least that’s how it’s interpreted by hormone-addled male college students. Even at MIT.

She’s right-handed. She then writes on the screen in the normal way and flips the video. The text is rendered the right way round and she appears left-handed.

Your voice makes me sleepy, your view makes me awake and your thoughts makes me amazed….so far so good! 🙂

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!! AHHHHHHHHHHHHHHHHHHHHHHH

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@Raspberry B tf

@Raspberry B sure dude. stop begging for attention lmao

Varsha cringe

I enjoy learning math with you.

THANK YOU, I LOVE YOU SO MUCH.

your so pretty Nancy

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Check your math Jesus doesn’t agree

I wish someone looked at me the way she looks at 2pi/9.

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.

Yes nancyPi thanks for teaching

Your an MIT grad? You look so uconfident but good writing baackwards skills

Between paying attention and telling my heart not to fall in love… so beautiful

simp

You are the best!!! thank you so much!!

Instead of dividing by pi….At 13:25 just multiply 1.5 times 57.3=85.95 in other words…(1.5 times (1 radian in degree = about 57.3)) that will get your answer.

Can you write a little faster? 🥴🥴🥴🥴

hiiii nancy.

why a circled is divided into 360 parts? for instance why we don’t divide it into 400 parts?

Learned a lot!

Wow …..you are amazing

Lefties are way too powerful.😅

Love your lessons! But how do you wright on the glass? Magic?

I’d like to know each of the 46 wankers who disliked this video

amazing, have been looking for some time for proper explanation, didn’t know how to phrase a proper question. you have cleared for me so much. By the way you are very pretty.

Damn I wish I had her as my math teacher in high school. I’m not stupid after all!

Back in the day, in the University I attend(ed) to, they wondered “How can we attract (have ’em enroll into) more students to the exact science – physics, math, statistics – programs?” I have the answer: By having you as student/teacher/asst teacher, the ammount of students would raise exponentially (at least male students). I mean, even if they couldn’t care less about science at all, neither they understand a word in the topic of each class/lecture, classes would be packed; they would attend every single class just to see/talk to you. The only calculus they would care about, is the odds (probability) of dating you. Maybe girls (the few of them in the programs) would feel a little intimidated by not being the center of atention anymore.😆 With all due respect the comment is both true and at the same time a recognition/compliment/tribute to your beauty and intelligence.

future wife goals.

“And you still have the pie, don’t forget the pie”

wow……..you’re amazing, well explained, i wish my lecturer was like you

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.

Fine.

Very useful and well explained! Thank you! I am a big fan of you.

what’s a good trick if you don’t have a zero on the top and bottom of the fraction when trying to solve in simplest form?

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دكري تعرفين منو دكري😂😂

دكري هو سيد علي 😂

Hi Nancy

Hard to not fall in love with her!

Nice

thank you so much live saver 🙂