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

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Trigonometry - Basic Introduction: kzbin.info/www/bejne/nWm5dHuliNBoldE How To Graph Trig Functions: kzbin.info/www/bejne/nIKzgHWFe8dlqbs Evaluating Inverse Trig Functions: kzbin.info/www/bejne/qaCchZ2ha6yUaLc

[@aby5755]

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]

*It be like that tho*

[@banditnic8938]

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

[@zephyr1327]

trig is easy

[@royal_throck2983]

@@zephyr1327 then why are you here

[@sweetteas2467]

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

[@bpeasytech7464]

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]

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

[@kksimulations5764]

FACTS

[@ravishingrabbits2980]

fax

[@mithrandir_1998]

My math and chemistry exams are sponsored by you, you’re a lifesaver. God bless you.💙💙💙

[@sobrankewat6138]

Jj

[@i4ykl979]

@@sobrankewat6138 ju

[@yupitzmeeee]

Lmao

[@rayanbokhari4547]

haha

[@beetooieru5057]

those who watched and learn from this guy's videos should always hit the like button. He deserves to get paid more from youtube

[@flacketgaming7389]

Who is here a night before exams?

[@TheOpraMan]

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]

Ur in two countries at the same time

[@madeusolivier8679]

@@lereverse1998 💀💀💀

[@zjn3898]

@@lereverse1998 he lives on the border

[@EHem-jo2hh]

Yeah and also what is his current job.

[@juliboomusicstudio8519]

Brah i literally stop the video to clap my hands😂that's how much this helped me..now back to finishing it😏

[@mariorobledo2538]

The number of people this man has helped graduate is unreal

[@mansoorahmadnasir9175]

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]

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

[@persondfppsdopsperd]

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

[@doggofv]

My teacher did 1 problem as fast as he could and said ok do the homework then sat down and watched basketball... Bruh.

[@zephyr1327]

are you home schooled?

[@mhfbn6898]

Mr. Brazil crazy fr fr

[@sarahazman981]

This is all of my online classes

[@wolfie_catlover6807]

Don’t even get me started on my math teacher (why I’m here)

[@DK-jw4vf]

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

[@LowPinq]

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. 💯

[@mEtAlMaNiAc787]

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

[@rusandinuthara5060]

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

[@vie-olence3930]

I actually understand this when this guy explains it

[@davidbanahene307]

Tie E exactly

[@3me_sx810]

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?

[@studded8054]

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

[@mcvideovlogs9321]

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

[@bridgetboakye-danquah9704]

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

[@kushaansharma2433]

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

[@momakplayz7985]

who else is watching this during quarantine?

[@martha8315]

GGgamerplayz Gaming ME 😔😔😔

[@georgesadler7830]

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

[@nickambrose50]

thanks i use your math videos to fall asleep

[@choppu6049]

*cool.*

[@redmosquito2173]

yes

[@adrastos9464]

exbrт Liberal

[@lorenzogurrola6084]

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

[@CreativeBites5807]

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

[@sweetteas2467]

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

[@ReidCipriani]

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

[@ritawashere5787]

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

[@rajveerbhardwaj8470]

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

[@momakplayz7985]

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

[@kirilldjandjgava5051]

Your voice is so calming I literally fall asleep every time

[@classicopop2158]

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

[@luciddreams1168]

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

[@antsy3947]

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

[@cattrickie]

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

[@dilahspardi]

I really appreciate this guy . Love this man !

[@serajayy]

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

[@markgarella8451]

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

[@isaacdestura7495]

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

[@puthtikmony4071]

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

[@persondfppsdopsperd]

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

[@persondfppsdopsperd]

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

[@MyMinecrafter97]

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

[@xero6188]

Once I struggled to something on math I instantly go to your channel

[@sanopann1896]

the only way to help this guy back is to watch the ads that popping out on his video and I'm going to write this comment to all of his video for you to know you can help him back by just watching his ads

[@absolute6422]

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]

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

[@persondfppsdopsperd]

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

[@poojadatar8781]

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

[@danieltoyo9029]

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

[@bryansaulon6257]

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

[@user-wu2rm3bh4y]

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.

[@SiddhantSinha-ew4fo]

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

[@mathgmathg923]

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

[@garbanzoo_4515]

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

[@momakplayz7985]

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

[@antoinecharlesdegaulle580]

he puts them on patreon

[@eqzpredator1730]

Could you please tell Which software do you use.

[@PEENUTSWHALE]

Thank you

[@nrv2478]

The Organic Chemistry Teacher, how can I find the radius if I am only given the perimeter and theta?

[@dahlia5233]

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

[@user-ry2ur6vj6h]

Thank you from Houston, Texas!!!

[@rjaph842]

where did that formula s=ro come from

[@alexandrenarolles7994]

Hi There, to the 10:00mn position, why do we use 1/2 and what is the meaning of 1/2? thanks in advance

[@ThePasserby76]

I understood it using the formula of the area of a triangle.

[@sarasaleh4598]

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

[@laela6289]

Thank you, dude

[@avanith3579]

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

[@ickn2005]

I can not thank you enough for this lesson.

[@davidheard709]

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

[@pranaaviyer2374]

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

[@winterberry3412]

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

[@aricari9378]

dude you are a savior thank you

[@smangeleshandu3495]

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

[@RaulFelixINC]

The formula my book is giving me is A= 1/2 r^2 (theta). Arent they different?

[@devvratkhokhar2]

thanks bro nice explanation love from india

[@thegreatcollector4548]

You are amazing dude

[@hollystop]

This channel is a life saver!!

[@persondfppsdopsperd]

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

[@persondfppsdopsperd]

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

[@IfiokMkpong]

Thank you for the video

[@lolavanner7552]

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

[@salmael-amin159]

Thankyou tutor you helped me alot

[@nursultanbai2502]

You should honestly be nominated for a noble prize

[@betul-ev2fu]

THANKS A LOT!!!

[@salieubarrie4023]

God bless u bro

[@user-or7ob7wy7g]

@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]

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

[@houndcraft1590]

is there a video for segments

[@NewProfessor789]

Nice 👌😊

[@jazmyncalles7946]

Hello, I am a geometry math teacher who is now needing to create videos for my students while doing distance learning through remote teaching. I am wanting to create videos similar to this for them however I do not know what software to use. What do you use or recommend?

[@bleachsmoothie3996]

I don't think he would see a comment on a video this old, you might have more luck asking on a newer video.

[@jazmyncalles7946]

Bleach Smoothie thank you:)

[@_rottingfish]

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

[@user-wu2rm3bh4y]

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

[@loveygummi]

thank you smart person.

[@Ade_Browne]

Pls am about to write an exam I wanted to ask if you could do an album of videos that come out in exams

[@matildawillcox1693]

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

[@aresascension121]

Sometimes it's just better or more proper to get down to 1 radian then 2 1 radian = 1pi 2 radians = 2pi

[@pillowyflunky9931]

thank you sir

[@saraifrancis4989]

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

[@AshAirheart1995]

U have everything!

[@_kitoy]

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

[@JisooKristo]

when do i convert Ft to cm or vice versa?

[@ammaar339]

Luismiguel Moratalla when they specifically say they want the answer in either cm or ft

[@lmroofmaster6198]

How to solve arc height using only two givens arc length and arc width what is the formula?

[@radenewinkelman340]

I cannot find your Trigonometry course on Udemy

[@educationandemotion4204]

To get better solution must visit : #EducationNext

[@The_FootballPulse]

in 10:27 why is the pi not equal to 180 degress ?????????

[@michelazar6352]

at 10:36, why and how does theta become the angle in degrees?

[@aresascension121]

Theta is the central angle, and in the center it contains a corner(the square in the middle) similar/same to a right triangle having 90 degrees.

[@pinofleitas4986]

Thx tomorrow i have the 0606 mock

[@junhuii]

OMG MY TEACHER CANNOT TEACH N THIS HELPED ME SO MUCHHCH

[@adls04]

Why do you multiply radius and theta to get arc length

[@delcreme]

ArthurHaXz idk man

[@user-ng1qq4kd5p]

Much better 🎉

[@isarasenarathne1840]

thankz alot man

[@TheOrganicChemistryTutor]

You're welcome