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

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Trigonometry - Basic Introduction: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-g8VCHoSk5_o.html How To Graph Trig Functions: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-fQPOBOFb2sY.html Evaluating Inverse Trig Functions: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-so9Tjk6Ga2U.html

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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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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.

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

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@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

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

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

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

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

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

where did that formula s=ro come from

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Plz help,,, an arc of a circle of a radius 7.5 to 7.5cm long ,find the angle which the arc substends at the center of the circle

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

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

What's the formula to find R? Is it S/θ or Sθ?

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