Arc Length of a Circle Formula - Sector Area, Examples, Radians, In Terms of Pi, Trigonometry

[@TheOrganicChemistryTutor]

Trigonometry - Free Formula Sheet: bit.ly/47diggI Trigonometry Video Lessons: www.video-tutor.net/basic-trigonometry.html

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trig is easy

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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!😊

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

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[@CecilBonvill6980]

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[@mEtAlMaNiAc787]

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

[@georgesadler7830]

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

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[@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

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[@CecilBonvill6980]

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[@isaacdestura7495]

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

[@ReidCipriani]

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

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Thank you from Houston, Texas!!!

[@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?

[@cattrickie]

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

[@JoséAntonioBottino]

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

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[@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

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[@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

[@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.

[@Familycomp4]

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

[@aricari9378]

dude you are a savior thank you

[@poojadatar8781]

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

[@davidheard709]

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

[@The_FootballPulse]

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

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Thankyou tutor you helped me alot

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[@JoséAntonioBottino]

Many people wonder why radians do not appear when we have radians*meters (rad • m). 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 β = n°, we can pose a rule of three: 360° _______ 2 • 𝜋 • r n° _______ s Then s = (n° / 360°) • 2 • 𝜋 • r If β = 180° (which means that n = 180, the number of degrees), then s = (180° / 360°) • 2 • 𝜋 • r The units "degrees" cancel out and the result is s = (1 / 2) • 2 • 𝜋 • r s = 𝜋 • r that is, half of the circumference 2 • 𝜋 • r. If the arc subtends an angle measuring β = 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 β = 𝜋 rad (which means that θ = 𝜋, the number of radians), 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 s = 𝜋 • r that is, half of the circumference 2 • 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 = β / (1 rad) and θ is a dimensionless variable [rad/rad = 1]. 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 rad • m = m since, according to them, the radian is a dimensionless unit. This solves the problem of units for them and, as it has served them for a long time, they see no need to change it. But the truth is that the solution is simpler, what they have to take into account is the meaning of the variables that appear in the formulas, i.e. θ is just the number of radians without the unit rad. Mathematics and Physics textbooks state that s = θ • r and then θ = s / r It seems that this formula led to the error of believing that 1 rad = 1 m/m = 1 and that the radian is a dimensionless derived unit as it appears in the International System of Units (SI), when in reality θ = 1 m/m = 1 and knowing θ = 1, the angle measures β = 1 rad. 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 speed. My guess is that actually the angular speed ω is not measured in rad/s but in (rad/rad)/s = 1/s = s^(-1).

[@isavenewspapers8890]

9:30 The solution you gave to this problem seems overcomplicated. You can just directly express the measure of the right angle in radians and plug it into the first formula. I mean, you wrote that formula down yourself. I can only really think of one reason you didn't do this, which is that you're worried about radians being confusing; however, students are going to have to learn to deal with radians anyway, and this would've been good practice. Of course, there's a tried-and-true method to counteract the confusingness of radians: use τ. τ is the ratio of a circle's circumference to its radius, about 6.28 and equal to 2π. How many radians is 1/12 of a full turn? τ/12. What about 1/8 turn? τ/8. What about 1/6 turn? τ/6. Using this has helped drastically reduce confusion about radians for some students. In our case, the measure of a right angle is a quarter-turn, which is τ/4 radians. Now we use the formula: A = (1/2)(τ/4)10^2 = 100τ/8 = 25τ/2 cm^2 Or, if you prefer: = 25π cm^2 And we are done.

[@kylekerdsri2324]

I love you so much

[@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.

[@thegreatcollector4548]

You are amazing dude

[@nrv2478]

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

[@YegorLunaVolkov]

Can i ask why did you break down the 3 x 12? 6:30

[@IfiokMkpong]

Thank you for the video

[@mathgmathg923]

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

[@THEJAGM-mk5hb]

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

[@nicdrew101]

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

[@avanith3579]

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

[@laela6289]

Thank you, dude

[@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

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Thank you

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

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Life saver fr

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That's awesome my tutor

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After watching this video few moments later l went to write a test guess how much l got? 99/100❤ With this guy forward we are going

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Damm any way you can help me??

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With?

[@guntherthepenguin4237]

@@bigmanthendo1743 understanding linear and angular velocity I'm having a really hard time

[@bigmanthendo1743]

Is this guy not covering them?

[@michelazar6352]

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

[@betul-ev2fu]

THANKS A LOT!!!

[@pinofleitas4986]

Thx tomorrow i have the 0606 mock

[@saraifrancis4989]

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

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PLEASE can you just be my math teacher for the rest of my school career 😭

[@alexaceguray9051]

Ok so am i the only one who still can't understand😭

[@singhshailesh5416]

I think yes

[@adriannagulto]

[@a7xfan778]

I'm relearning this just for the heck of it. Messed up at 14:30 bc I put 60 degrees as pi/6 instead of pi/3 😅

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but who asked?

[@eqzpredator1730]

Could you please tell Which software do you use.

[@smangeleshandu3495]

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