Radians and Degrees (NancyPi)
ฝัง
- เผยแพร่เมื่อ 5 ก.ย. 2024
- 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: • Basic Trigonometry: Si...
Follow me on Instagram! / mathnancy
Follow me on Twitter: / nancypi
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: nancypi.com
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
Th1cc J3ff simp
@@raspberryb1664 sure dude. stop begging for attention lmao
Me too
Nancypi you the best teacher. reporting from Namibia
Yeah Nancy is back. We miss you, but I am in calculus 3 now, but I still like watching you. Big✊
big?
@Blackhawk x big.
I wish that I had these videos when I was in high school! Nancy is the greatest math teacher!
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!
km im ki ,
You need to set up a school. Your explanations are so clear and understandable
Thank you
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.
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.
I really like Nancy, because she teaches us techniques and I can always trust her because shes smart.
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.
Thank you Nancy, you make it very easy to understand the concepts.
Thank you so much Nancy. You are saving the situation at hand. May God bless you.
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!
I wish I had an awesome math teacher like you in my school........Thanks a bunch ma'am❤👏😀
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.
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! :)
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.
Nancy you just became my new best friend this semester 🤗
wow........you're amazing, well explained, i wish my lecturer was like you
Yes mee too i wish i also get but why she is not uploading new videos i need it
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.
Nancy is so fancy
More like 🔥💃hot
@@brystonbower666 simp
yeah but she was never integrated into your life
Hii
Will you friendship me
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.
Thank you Nancy.Easy to understand because the way you explained it.
Your voice makes me sleepy, your view makes me awake and your thoughts makes me amazed….so far so good! :)
So far I like everything about the way you teach...I am struggling as 36 year old displaced 18 years from math never having learned this with algebra 2 being my last course. Thank you for the calm approach
This was really helpful please upload more topics on pre-cal and calculus!!!
bro i can literally just watch your math videos for fun now cause youre so pretty
Bro I love your videos so freaking simple and straight to the point thank you and God Bless 🙏🏿
You are the best teacher in this world
You teach things that I can understand
Thank you very much
You are a life saver math 30-2 is kicking my ass
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♥️♥️🌹
Yes nancyPi thanks for teaching
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.
wow this girl explain very clear... which i didn't understand earlier.. thanks
You litterally just saved my life. Thankuu🙇♀️
Hi Nancy! I love your videos. As a college student with dyscalculia and ADHD, your videos are WAY easier for me to follow than my instructor's lecture. Would you consider doing a video on substitution for systems of three equations? (My textbook uses the term Gaussian Elimination) I'm sure I'll be done with my class by the time you could make a video, but it may be useful for other learners out there.
Hi! I’m curious about your comment, were you diagnosed with dyscalculia? Are you pursuing a math degree as well?
How are you doing this in college? This is high school math
Thanks! This helped me to study for my test
You awsome teacher, doing nice work for students ,I remembered my school time after this video.
Thank you Nancy!
Didn't know about radians. Thanks for the explanation.
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!
Very useful and well explained! Thank you! I am a big fan of you.
Filter all other videos out, Nancy knows best!
If Nancy was my Math teacher I never wouldve missed a day of school.
@10:35. (2/9) * 180 -> division before multiplication is optimal... (good video).
Imagine being able to explain calculus concepts coherently while writing it backwards
Does she really write it backwards?
I would assume she writes it normally but flips the video lol
@@himanichunduru1102 lunchbar
The video is mirrored lol
This video was super helpful, thank you Soo much and I really appreciate
You!!
Thanks for teaching my Algebra 2 class Nancy!!!
Thank you Nancy
you have been a great help to simplify the conversion formula
You are a great teacher
Thanks
Hattem
Hey Nancy I'm from India and I am too much satisfied by your videos thnq
She’s back!!
Thank you Nancy, you are a great teacher.
I did math classes and went to school but none of the teachers were able to insta-slap such a good circle drawing first try
Thank you so much Nancy the video has helped me all the way from Zambia
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.
Thank you for this!
We understand that you are motivated professor Leonard's youtube lectures and his body. Maybe you love him. But, you know, he has a beautiful FAMILY. Don't be jealous sister :-)
.. You are also a good at math .. Good luck!
thanks. I just pass my exam❤❤❤❤❤❤❤❤❤bless you
mine is today after couple of hours i hope i can pass too wish me luck
I love your videos, this may be a harder topic to cover, but if possible can you do a video on arclengths ?
Why did u stop posting videos gurllll?U have a huge fam and we are waiting to see ur videos❤❤❤❤
thank you! awesome way of explaining this
I felt like she was flirting with me like "Hey, you like converting stuff, I could teach ya"
down horrendous
@@bellion9143 sometimes its like that bro 😔
Nancy π rad.
We knew that.
Nancy is a great teacher!
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 wish I could have a private tutor session with you Nancy to listen to your sweet voice for hours, then I'll die a happy man.
Mando M don’t we all my guy, don’t we all...
simp
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.
She’s so pretty tho, I remember watching her when my algebra 1 teacher sucked in online class and I didn’t understand anything.
I enjoy learning math with you.
Your videos help me a lot. I do my studies especially math on your videos, and honestly I'm in better position to do my exam.
Can you please do one on derivatives?
I love her all video explaination
Hi Nancy, thanks for the pure awesomeness of your videos. :) Have you done anything on Polar Coordinates?
13:15 so cute when you looked at the calculator 😂
I like your way of writing 👏👏👏
I literally love you
Nice explanation.
this helped me on my homework thanks nancy
girl girl girl you are the best!!
You are a great teacher i can understand every word you said although iam from arab country i can understand everything from you
Thank you so much... your explanation is soooo cleaarrrrrr.
W video
dab
Nancy, you look radiant along all those 360 degrees !
hiiii nancy.
why a circled is divided into 360 parts? for instance why we don't divide it into 400 parts?
Thanks Nancy ....Fancy.
SHES A QUEEN
Thank you so much. This helps me a lot
Thanks, I like math and your videos.
Mazaa aa Gaya maam, aapko dekh kar sab samajh aa Gaya. Aise hi Baal khule rakh kar padhaana please
Mirror writing. I learned a little when I was soldier. Try it not easy.
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.
Damn I wish I had her as my math teacher in high school. I'm not stupid after all!
Informative. Useful. Calming. Inspiring. Life-changing. Enjoyable. Heart-warming. Other.
Nancy u are amazing
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
She is our queen
Well done. Keep shining. :)
Yeah Nancy Plz is Back?!!
very nice. thank you.
Can you please upload a video on how to calculate trigonometric functions of angles in 2nd,3rd and 4th quardrant or how to express them by 180-theta,180+theta,360-theta and 90+theta and 90-theta please
Good explanation thank you