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...
_________________________
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...
_______________________________________
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

Пікірлер: 281

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor Жыл бұрын

    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

  • @aby5755
    @aby57554 жыл бұрын

    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 :)))

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    @whymemanwhyl0lp751

    4 жыл бұрын

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    @banditnic8938

    4 жыл бұрын

    Wow, I thought I'm the only one who does that. 😂

  • @zephyr1327

    @zephyr1327

    4 жыл бұрын

    trig is easy

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    @royal_throck2983

    4 жыл бұрын

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    @sweetteas2467

    4 жыл бұрын

    Same trig is annoying but if you want to pass you have to do it

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    @bpeasytech74644 жыл бұрын

    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

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    @SoupsStudios

    4 жыл бұрын

    BP EASY TECH so wholesome! Sorry about your teachers. I can relate.

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    @kksimulations5764

    3 жыл бұрын

    FACTS

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    @ravishingrabbits2980

    2 жыл бұрын

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    3 жыл бұрын

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    2 жыл бұрын

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    @yupitzmeeee

    2 жыл бұрын

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    @rayanbokhari4547

    Жыл бұрын

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    @beetooieru50573 жыл бұрын

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    @doggofv4 жыл бұрын

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    @zephyr1327

    4 жыл бұрын

    are you home schooled?

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    3 жыл бұрын

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    @sarahazman981

    3 жыл бұрын

    This is all of my online classes

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    @wolfie_catlover6807

    2 жыл бұрын

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    @flacketgaming73892 жыл бұрын

    Who is here a night before exams?

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    @juliboomusicstudio85194 жыл бұрын

    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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    @DK-jw4vf3 жыл бұрын

    This guy's going to get me through pre-calc

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    @TheOpraMan7 жыл бұрын

    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 :)

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    @lereverse1998

    4 жыл бұрын

    Ur in two countries at the same time

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    @madeusolivier8679

    4 жыл бұрын

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    4 жыл бұрын

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    @EHem-jo2hh

    3 жыл бұрын

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  • @vie-olence3930
    @vie-olence39306 жыл бұрын

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    @davidbanahene307

    5 жыл бұрын

    Tie E exactly

  • @mansoorahmadnasir9175
    @mansoorahmadnasir91752 жыл бұрын

    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

    @persondfppsdopsperd

    Ай бұрын

    WHO ASKED + MY CONTENT IS WAY BETTER + UTTP IS WAY BETTER THAN MATHS 😂😂

  • @persondfppsdopsperd

    @persondfppsdopsperd

    Ай бұрын

    WHO ASKED + MY CONTENT IS WAY BETTER + UTTP IS WAY BETTER THAN MATHS 😂😂

  • @momakplayz7985
    @momakplayz79854 жыл бұрын

    who else is watching this during quarantine?

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    @martha8315

    4 жыл бұрын

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  • @mEtAlMaNiAc787
    @mEtAlMaNiAc7874 жыл бұрын

    I'm more amazed by all the canceling lol and how you simplify it.

  • @studded8054
    @studded8054 Жыл бұрын

    Was here for Geometry, and now back for the SAT, Thank you so much.

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    @nickambrose505 жыл бұрын

    thanks i use your math videos to fall asleep

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    @choppu6049

    5 жыл бұрын

    *cool.*

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    @redmosquito2173

    5 жыл бұрын

    yes

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    @adrastos9464

    5 жыл бұрын

    exbrт Liberal

  • @LowPinq
    @LowPinq4 жыл бұрын

    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. 💯

  • @ReidCipriani
    @ReidCipriani3 жыл бұрын

    I sat through a 90min pre calc class confused as fuck. Watched this for 5 minutes and I get it

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    @kirilldjandjgava50514 жыл бұрын

    Your voice is so calming I literally fall asleep every time

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    @classicopop2158

    3 жыл бұрын

    That's not a good thing.... Right?

  • @rusandinuthara5060
    @rusandinuthara50604 жыл бұрын

    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

  • @mcvideovlogs9321
    @mcvideovlogs93214 жыл бұрын

    Thank you so much! If only my teacher could've explained it like this!

  • @georgesadler7830
    @georgesadler78302 жыл бұрын

    MR. Organic Chemistry Tutor, thank you for another awesome lecture on finding the Area and Arc Length of a Circle in Trigonometry.

  • @kushaansharma2433
    @kushaansharma24333 ай бұрын

    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

  • @bridgetboakye-danquah9704
    @bridgetboakye-danquah9704 Жыл бұрын

    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

  • @lorenzogurrola6084
    @lorenzogurrola60842 жыл бұрын

    Dude you are a great teacher! This is really helping my ACT Math knowledge

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    @markgarella84512 жыл бұрын

    his vids literally teach better than every math teacher that I've met

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    @sanopann18969 ай бұрын

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  • @momakplayz7985
    @momakplayz79854 жыл бұрын

    thanks i watch your vids on quarantine they are awesome man!!!

  • @CreativeBites5807
    @CreativeBites5807 Жыл бұрын

    Honestly l think by now your really aware that your the best, you always make things so simple for us students

  • @3me_sx810
    @3me_sx8103 жыл бұрын

    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?

  • @sweetteas2467
    @sweetteas24674 жыл бұрын

    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

  • @cattrickie
    @cattrickie4 жыл бұрын

    thank you for these videos! they help us out so much

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    @xero6188 Жыл бұрын

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    @dilahspardi5 жыл бұрын

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    @antsy39472 жыл бұрын

    Thanks helped me a bunch learned something useful in the very first minute :)

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    @rajveerbhardwaj84702 жыл бұрын

    Here to study for my Pre-Cal quiz tomorrow thank you so much !

  • @MyMinecrafter97
    @MyMinecrafter977 жыл бұрын

    Just want to thank you, you helped me pass calculus :D

  • @luciddreams1168
    @luciddreams11689 ай бұрын

    When i am searching for help on youtube about any consept, if there is your video i know that i will understant and it will be really clear ❤ thank you my lovely teacher

  • @serajayy
    @serajayy2 жыл бұрын

    sometimes i dont pay attention claas and then i just come to yuor channel an i ace my assignmentss THANK YOUUU!

  • @absolute6422
    @absolute64223 жыл бұрын

    You are a saint my friend. I wish nothing but the best for you in all your endeavors. You’ve helped me and more people than I can count understand concepts they previously struggled with and all in all have made this world a better place. God bless

  • @persondfppsdopsperd

    @persondfppsdopsperd

    Ай бұрын

    WHO ASKED + MY CONTENT IS WAY BETTER + UTTP IS WAY BETTER THAN MATHS 😂😂

  • @persondfppsdopsperd

    @persondfppsdopsperd

    Ай бұрын

    WHO ASKED + MY CONTENT IS WAY BETTER + UTTP IS WAY BETTER THAN MATHS 😂😂

  • @danieltoyo9029
    @danieltoyo90294 жыл бұрын

    You really helped me a lot, thanks by the way.

  • @isaacdestura7495
    @isaacdestura74954 жыл бұрын

    I'm genuinely failing trig. Thanks for much for helping me get by

  • @bryansaulon6257
    @bryansaulon6257 Жыл бұрын

    i hope yah continue teaching us... i appreciate it much personally all your videos

  • @SiddhantSinha-ew4fo
    @SiddhantSinha-ew4fo5 ай бұрын

    Bro this video is actually so helpful, u are the best!!

  • @puthtikmony4071
    @puthtikmony40714 жыл бұрын

    Currently prepping this for my online test thanks so much, wish me luck 👍🏽👍🏽

  • @persondfppsdopsperd

    @persondfppsdopsperd

    Ай бұрын

    WHO ASKED + MY CONTENT IS WAY BETTER + UTTP IS WAY BETTER THAN MATHS 😂😂

  • @persondfppsdopsperd

    @persondfppsdopsperd

    Ай бұрын

    WHO ASKED + MY CONTENT IS WAY BETTER + UTTP IS WAY BETTER THAN MATHS 😂😂

  • @ickn2005
    @ickn20055 ай бұрын

    I can not thank you enough for this lesson.

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    @momakplayz79854 жыл бұрын

    dont delete your channel i need all your vids till college keep posting new vids i love em

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    @antoinecharlesdegaulle580

    3 жыл бұрын

    he puts them on patreon

  • @user-ry2ur6vj6h
    @user-ry2ur6vj6h3 жыл бұрын

    Thank you from Houston, Texas!!!

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    @aricari93783 жыл бұрын

    dude you are a savior thank you

  • @dahlia5233
    @dahlia52333 жыл бұрын

    I wish you were my teacher, completely a life savior 😚

  • @devvratkhokhar2
    @devvratkhokhar22 жыл бұрын

    thanks bro nice explanation love from india

  • @laela6289
    @laela62894 жыл бұрын

    Thank you, dude

  • @davidheard709
    @davidheard7094 жыл бұрын

    This is a step to break down the basics..... other times it can boggle the mind.

  • @sarasaleh4598
    @sarasaleh45983 жыл бұрын

    this helped me sm. thank you! subscribed too!!

  • @thegreatcollector4548
    @thegreatcollector45483 ай бұрын

    You are amazing dude

  • @salmael-amin159
    @salmael-amin159 Жыл бұрын

    Thankyou tutor you helped me alot

  • @PEENUTSWHALE
    @PEENUTSWHALE6 жыл бұрын

    Thank you

  • @hollystop
    @hollystop5 жыл бұрын

    This channel is a life saver!!

  • @persondfppsdopsperd

    @persondfppsdopsperd

    Ай бұрын

    WHO ASKED + MY CONTENT IS WAY BETTER + UTTP IS WAY BETTER THAN MATHS 😂😂

  • @persondfppsdopsperd

    @persondfppsdopsperd

    Ай бұрын

    WHO ASKED + MY CONTENT IS WAY BETTER + UTTP IS WAY BETTER THAN MATHS 😂😂

  • @lolavanner7552
    @lolavanner75522 жыл бұрын

    I wish this man could understand the sheer impact he has on my gpa

  • @IfiokMkpong
    @IfiokMkpong10 ай бұрын

    Thank you for the video

  • @saraifrancis4989
    @saraifrancis49894 жыл бұрын

    This sounds like Jonah Marais from Why Don’t We!!

  • @nursultanbai2502
    @nursultanbai2502 Жыл бұрын

    You should honestly be nominated for a noble prize

  • @user-wu2rm3bh4y
    @user-wu2rm3bh4y5 ай бұрын

    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.

  • @AshAirheart1995
    @AshAirheart19952 жыл бұрын

    U have everything!

  • @betul-ev2fu
    @betul-ev2fu3 жыл бұрын

    THANKS A LOT!!!

  • @loveygummi
    @loveygummi4 жыл бұрын

    thank you smart person.

  • @mathgmathg923
    @mathgmathg9236 жыл бұрын

    Can you make a video finding area and arc length of polar coordinates , thanks

  • @junhuii
    @junhuii4 ай бұрын

    OMG MY TEACHER CANNOT TEACH N THIS HELPED ME SO MUCHHCH

  • @poojadatar8781
    @poojadatar87818 ай бұрын

    hello sir, is there a video for area of irregular shape in a circle or area between two circles

  • @_rottingfish
    @_rottingfish6 ай бұрын

    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

  • @salieubarrie4023
    @salieubarrie40234 жыл бұрын

    God bless u bro

  • @NewProfessor789
    @NewProfessor7892 жыл бұрын

    Nice 👌😊

  • @mango7639
    @mango76392 жыл бұрын

    thank you math daddy

  • @pillowyflunky9931
    @pillowyflunky9931 Жыл бұрын

    thank you sir

  • @ekpenyongsimeon6942
    @ekpenyongsimeon69425 жыл бұрын

    That's awesome my tutor

  • @ashleyyyyay9133
    @ashleyyyyay913311 ай бұрын

    I want to cry so bad cause you helped me so muchhhh

  • @nick3718
    @nick37182 жыл бұрын

    currently sitting in homeroom panicking

  • @malemon5665
    @malemon56653 жыл бұрын

    indeed they are many ways to kill a cat. you just nailed it ,my teacher was just mumbling

  • @user-wu2rm3bh4y
    @user-wu2rm3bh4y5 ай бұрын

    In the formula Acs = (1 / 2) • θ • r^2 the θ denotes the number of radians (it does not have the unit "rad").

  • @user-or7ob7wy7g
    @user-or7ob7wy7g4 жыл бұрын

    @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

    @user-or7ob7wy7g

    4 жыл бұрын

    @@jelly_blue oh sorry I didn't see that, Thank you

  • @user-ng1qq4kd5p
    @user-ng1qq4kd5p8 ай бұрын

    Much better 🎉

  • @pranaaviyer2374
    @pranaaviyer23744 жыл бұрын

    Hello, just a question, why do you use radian form always instead of degree form?

  • @winterberry3412

    @winterberry3412

    4 жыл бұрын

    Idk how to explain it but the formula only works when the arc degree measure is in radians.

  • @matildawillcox1693
    @matildawillcox16934 жыл бұрын

    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

  • @ritawashere5787
    @ritawashere57874 жыл бұрын

    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

  • @avanith3579
    @avanith35794 жыл бұрын

    I wish you showed how to get the radius if given the area of a sector and theta.

  • @davidben5159
    @davidben51593 жыл бұрын

    If I had him my teacher I will be flying to Jupiter and back long ego.

  • @smangeleshandu3495
    @smangeleshandu34953 жыл бұрын

    Plz plz teach about calculating major segment and minor segment plz. I tried but I failed to calculate it

  • @pinofleitas4986
    @pinofleitas49863 жыл бұрын

    Thx tomorrow i have the 0606 mock

  • @iqintellegenceforellegento2068
    @iqintellegenceforellegento20685 жыл бұрын

    Actually brilliant

  • @troodonkanna
    @troodonkanna2 жыл бұрын

    Thanks.

  • @adminspiderman5378
    @adminspiderman53783 жыл бұрын

    Tysm.

  • @isarasenarathne1840
    @isarasenarathne18407 жыл бұрын

    thankz alot man

  • @TheOrganicChemistryTutor

    @TheOrganicChemistryTutor

    7 жыл бұрын

    You're welcome

  • @roberthales2579
    @roberthales25792 жыл бұрын

    FOR ARC LOU I STILL LOVE THEM

  • @thatpacho
    @thatpacho5 жыл бұрын

    thank

  • @LostJoestar
    @LostJoestar2 жыл бұрын

    SAT TOMORROW THANK YOU

  • @THEJAGM-mk5hb
    @THEJAGM-mk5hb Жыл бұрын

    In India we learn this in 10th grade [15yrs] and we do not call it trigonometry🤣😂 BUT TO BE HONEST GREAT WORK

  • @nicdrew101

    @nicdrew101

    3 ай бұрын

    ur not that guy pal I learned it at 9th grade

  • @garbanzoo_4515
    @garbanzoo_45153 жыл бұрын

    how do you find the value of the theta if given the area of the sector of the circle?

  • @k1tooy-yt
    @k1tooy-yt4 жыл бұрын

    Why does the area of the sector has a 1/2 in the equation?

  • @kylekerdsri2324
    @kylekerdsri23242 жыл бұрын

    I love you so much