Arc Length of a Circle Formula - Sector Area, Examples, Radians, In Terms of Pi, Trigonometry
This geometry and trigonometry video tutorial explains how to calculate the arc length of a circle using a formula given the angle in radians the and the length of the radius. It also explains how to calculate the sector area in terms of pi or in radians. In addition, it also explains how to determine the area of a sector of a circle using an equation where the angle is given in degrees instead of radians. This video contains plenty of examples and practice problems.
Trigonometry - Basic Introduction:
• Trigonometry
Introduction to Angles:
• Introduction to Angles
Radians and Degrees:
• Radians and Degrees
What Exactly Is a Radian?
• Trigonometry - What Ex...
Coterminal Angles:
• Coterminal Angles In R...
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Decimal Degrees to DMS:
• Decimal Degrees to DMS...
Arc Length of a Circle and Sector Area:
• Arc Length of a Circle...
Linear Speed and Angular Velocity:
• Linear Speed and Angul...
Clock to Angle Problems:
• Clock Aptitude Reasoni...
The Unit Circle:
• The Unit Circle, Basic...
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Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Trigonometry - Basic Introduction: kzread.info/dash/bejne/mWyKpaqog86bj9I.html How To Graph Trig Functions: kzread.info/dash/bejne/mIWEsaSIdsWYo7w.html Evaluating Inverse Trig Functions: kzread.info/dash/bejne/paNttsykZqrHYrg.html
I had a whole mental breakdown and a half over trigonometry and I swear your videos gave me a peace of mind I never thought I'd have, thank you so much :)))
@whymemanwhyl0lp751
4 жыл бұрын
*It be like that tho*
@banditnic8938
4 жыл бұрын
Wow, I thought I'm the only one who does that. 😂
@zephyr1327
4 жыл бұрын
trig is easy
@royal_throck2983
4 жыл бұрын
@@zephyr1327 then why are you here
@sweetteas2467
4 жыл бұрын
Same trig is annoying but if you want to pass you have to do it
you literally teach better than all my teachers, I always come here if I can't understand a topic at school thank you for helping me every single time
@SoupsStudios
4 жыл бұрын
BP EASY TECH so wholesome! Sorry about your teachers. I can relate.
@kksimulations5764
3 жыл бұрын
FACTS
@ravishingrabbits2980
2 жыл бұрын
fax
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@sobrankewat6138
3 жыл бұрын
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@i4ykl979
2 жыл бұрын
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@yupitzmeeee
2 жыл бұрын
Lmao
@rayanbokhari4547
Жыл бұрын
haha
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My teacher did 1 problem as fast as he could and said ok do the homework then sat down and watched basketball... Bruh.
@zephyr1327
4 жыл бұрын
are you home schooled?
@mhfbn6898
3 жыл бұрын
Mr. Brazil crazy fr fr
@sarahazman981
3 жыл бұрын
This is all of my online classes
@wolfie_catlover6807
2 жыл бұрын
Don’t even get me started on my math teacher (why I’m here)
Who is here a night before exams?
Brah i literally stop the video to clap my hands😂that's how much this helped me..now back to finishing it😏
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Hey, I just wanted to thank you for all the effort you put into making the videos, I especially loved the Org. Chemistry ones, you break things down very nicely and make them plain and simple. I've been wondering, what was your major, where did you study? Maybe you'd like to do a Q&A sometime, I'm sure there'd be people who'd love to watch it! Cheers from Ukraine & Poland :)
@lereverse1998
4 жыл бұрын
Ur in two countries at the same time
@madeusolivier8679
4 жыл бұрын
@@lereverse1998 💀💀💀
@zjn3898
4 жыл бұрын
@@lereverse1998 he lives on the border
@EHem-jo2hh
3 жыл бұрын
Yeah and also what is his current job.
I actually understand this when this guy explains it
@davidbanahene307
5 жыл бұрын
Tie E exactly
For calculating in degrees, my teacher gave me this formula: S=rθπ/180° But I find yours much more easier to remember: S=(θ/360°) 2πR I guess it's just a method of dividing, but this formula cleared my concept, so thanks!😊
@persondfppsdopsperd
Ай бұрын
WHO ASKED + MY CONTENT IS WAY BETTER + UTTP IS WAY BETTER THAN MATHS 😂😂
@persondfppsdopsperd
Ай бұрын
WHO ASKED + MY CONTENT IS WAY BETTER + UTTP IS WAY BETTER THAN MATHS 😂😂
who else is watching this during quarantine?
@martha8315
4 жыл бұрын
GGgamerplayz Gaming ME 😔😔😔
I'm more amazed by all the canceling lol and how you simplify it.
Was here for Geometry, and now back for the SAT, Thank you so much.
thanks i use your math videos to fall asleep
@choppu6049
5 жыл бұрын
*cool.*
@redmosquito2173
5 жыл бұрын
yes
@adrastos9464
5 жыл бұрын
exbrт Liberal
Just found your channel and couldn’t be more happier because you literally just blessed me for a last second study session because I really was not prepared for a quiz that I was going to have till I found your channel so big thanks to you. 💯
I sat through a 90min pre calc class confused as fuck. Watched this for 5 minutes and I get it
Your voice is so calming I literally fall asleep every time
@classicopop2158
3 жыл бұрын
That's not a good thing.... Right?
Thanks SO much for this.. I had an emergency assessment to turn in and i wasn't paying attention in class when this was going on...YOU REALLY SAVED MA LIFE TODAY
Thank you so much! If only my teacher could've explained it like this!
MR. Organic Chemistry Tutor, thank you for another awesome lecture on finding the Area and Arc Length of a Circle in Trigonometry.
I flippin love this dude i never paid attention in my additional mathematics class for this topic, I jus switched on this vid and they explained everything in 16mins my teacher said in an hour and 20 mins
God bless your heart fr! i was really struggling with the basics of circles because my professor has this long, extra, and difficult way of getting the arc lengths, or radians or degrees and you just made it so simple for me! i really appreciate it
Dude you are a great teacher! This is really helping my ACT Math knowledge
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I’m having a mental breakdown. One of my problems says a circle has an arc lenght of 13 feet that is intercepted by a central angle of pie radians. What is the circumference of the circle?
I’m going to be honest a lot of math is not going to be useful to you in the long run but knowing this can help you get through school thank you
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Thanks helped me a bunch learned something useful in the very first minute :)
Here to study for my Pre-Cal quiz tomorrow thank you so much !
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@persondfppsdopsperd
Ай бұрын
WHO ASKED + MY CONTENT IS WAY BETTER + UTTP IS WAY BETTER THAN MATHS 😂😂
@persondfppsdopsperd
Ай бұрын
WHO ASKED + MY CONTENT IS WAY BETTER + UTTP IS WAY BETTER THAN MATHS 😂😂
You really helped me a lot, thanks by the way.
I'm genuinely failing trig. Thanks for much for helping me get by
i hope yah continue teaching us... i appreciate it much personally all your videos
Bro this video is actually so helpful, u are the best!!
Currently prepping this for my online test thanks so much, wish me luck 👍🏽👍🏽
@persondfppsdopsperd
Ай бұрын
WHO ASKED + MY CONTENT IS WAY BETTER + UTTP IS WAY BETTER THAN MATHS 😂😂
@persondfppsdopsperd
Ай бұрын
WHO ASKED + MY CONTENT IS WAY BETTER + UTTP IS WAY BETTER THAN MATHS 😂😂
I can not thank you enough for this lesson.
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@antoinecharlesdegaulle580
3 жыл бұрын
he puts them on patreon
Thank you from Houston, Texas!!!
dude you are a savior thank you
I wish you were my teacher, completely a life savior 😚
thanks bro nice explanation love from india
Thank you, dude
This is a step to break down the basics..... other times it can boggle the mind.
this helped me sm. thank you! subscribed too!!
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Thank you
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@persondfppsdopsperd
Ай бұрын
WHO ASKED + MY CONTENT IS WAY BETTER + UTTP IS WAY BETTER THAN MATHS 😂😂
@persondfppsdopsperd
Ай бұрын
WHO ASKED + MY CONTENT IS WAY BETTER + UTTP IS WAY BETTER THAN MATHS 😂😂
I wish this man could understand the sheer impact he has on my gpa
Thank you for the video
This sounds like Jonah Marais from Why Don’t We!!
You should honestly be nominated for a noble prize
Many people wonder why radians do not appear when we have radians * meters. Here is an attempt at an explanation: Let s denote the length of an arc of a circle whose radius measures r. If the arc subtends an angle measuring α = n°, we can pose a rule of three: 360° _______ 2 • 𝜋 • r n° _______ s Then s = (n° / 360°) • 2 • 𝜋 • r If α = 180° (which means that n = 180), then s = (180° / 360°) • 2 • 𝜋 • r The units "degrees" cancel out and the result is s = (1 / 2) • 2 • 𝜋 • r that is, half of the circumference 2 • 𝜋 • r s = 𝜋 • r If the arc subtends an angle measuring α = θ rad, we can pose a rule of three: 2 • 𝜋 rad _______ 2 • 𝜋 • r θ rad _______ s Then s = (θ rad / 2 • 𝜋 rad) • 2 • 𝜋 • r If α = 𝜋 rad (which means that θ = 𝜋), then s = (𝜋 rad / 2 • 𝜋 rad) • 2 • 𝜋 • r The units "radians" cancel out and the result is s = (1 / 2) • 2 • 𝜋 • r that is, half of the circumference 2 • 𝜋 • r s = 𝜋 • r If we take the formula with the angles measured in radians, we can simplify s = (θ rad / 2 • 𝜋 rad) • 2 • 𝜋 • r s = θ • r where θ denotes the number of radians (it does not have the unit "rad"). θ = α / (1 rad) and θ is a dimensionless variable. However, many consider θ to denote the measure of the angle and for the example believe that θ = 𝜋 rad and radians * meter results in meters. Mathematics and Physics textbooks state that s = θ • r and then θ = s / r It seems that this formula leads to the error of believing that 1 rad = 1 m / m and that the radian is a dimensionless derived unit as it appears in the International System of Units (SI). In the formula s = θ • r the variable θ is a dimensionless variable, it is a number without units, it is the number of radians. When confusing what θ represents in the formula, some mistakes are made in Physics in the units of certain quantities, such as angular velocity.
U have everything!
THANKS A LOT!!!
thank you smart person.
Can you make a video finding area and arc length of polar coordinates , thanks
OMG MY TEACHER CANNOT TEACH N THIS HELPED ME SO MUCHHCH
hello sir, is there a video for area of irregular shape in a circle or area between two circles
3:49 why is this method way easier to understand then the one my teacher taught us. Like I prefer this over measure of arc/360 • 2 (pi)r
God bless u bro
Nice 👌😊
thank you math daddy
thank you sir
That's awesome my tutor
I want to cry so bad cause you helped me so muchhhh
currently sitting in homeroom panicking
indeed they are many ways to kill a cat. you just nailed it ,my teacher was just mumbling
In the formula Acs = (1 / 2) • θ • r^2 the θ denotes the number of radians (it does not have the unit "rad").
@organic chemistry I think you got your formula wrong, you wrote (theta/360)*πr^2 but shouldn't it be (π/360)*theta*r^2 at 10:27
@user-or7ob7wy7g
4 жыл бұрын
@@jelly_blue oh sorry I didn't see that, Thank you
Much better 🎉
Hello, just a question, why do you use radian form always instead of degree form?
@winterberry3412
4 жыл бұрын
Idk how to explain it but the formula only works when the arc degree measure is in radians.
The conversion to degrees at 10:10 - how come you didn't multiply by 360/2π ? I'm confused because I can see how the twos then cancel to get the formula. Definitely being thick here
hi there, if I have the measurement from A to B and one more measurement from the center of a and b to the outer edge of circle "s" Am I able to at least get the length of the arc? And then therefore will I be able to figure out how large my circle will be? I do not have a radius. A+B= 10-10/16" D+ "F"= 2" Any help would be amazing. I'm building a large wheel for a project my grandson and I are making. A large hamster wheel, large enough for cat 😂 thank you in advance. Be well
I wish you showed how to get the radius if given the area of a sector and theta.
If I had him my teacher I will be flying to Jupiter and back long ego.
Plz plz teach about calculating major segment and minor segment plz. I tried but I failed to calculate it
Thx tomorrow i have the 0606 mock
Actually brilliant
Thanks.
Tysm.
thankz alot man
@TheOrganicChemistryTutor
7 жыл бұрын
You're welcome
FOR ARC LOU I STILL LOVE THEM
thank
SAT TOMORROW THANK YOU
In India we learn this in 10th grade [15yrs] and we do not call it trigonometry🤣😂 BUT TO BE HONEST GREAT WORK
@nicdrew101
3 ай бұрын
ur not that guy pal I learned it at 9th grade
how do you find the value of the theta if given the area of the sector of the circle?
Why does the area of the sector has a 1/2 in the equation?
I love you so much