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## Homework Statement

S = theta * radius

I dont understand how they came up with this formula.... can some one show me the proof how they derived this formula or can someone send me a link and I will just read it. Thank you.

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- Thread starter Miike012
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- #1

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S = theta * radius

I dont understand how they came up with this formula.... can some one show me the proof how they derived this formula or can someone send me a link and I will just read it. Thank you.

- #2

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The measurement of an angle in 'radians' is defined as the length of the arc that it subtends divided by the radius.

- #3

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[tex]C = 2\pi r[/tex]

Now if you use the formula

[tex]S_{arc} = \theta_{rad} r[/tex]

and plug in a degree [tex]\theta_{rad}[/tex] with respect to radians you end up with some result

[tex]N\pi r[/tex]

where N is a rational number.

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Ok... but what is the mathamatical proof.

- #5

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Ok... but what is the mathamatical proof.

There is no mathematical proof! That's how the quantities have been

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That would be nice..

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- #9

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I see no derivation of the

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Ok... but what is the mathamatical proof.

You can't have a mathematical proof for such a question. It's all part of the definition of the radian. One radian is the angle necessary within a circle of radius 1 to produce an arc that is also equal to 1, more formally 1rad = 180/pi. Further, radians are measured in terms of the length of the arc divided by the radius of the arc.

To ask for a mathematical "proof" is like proving that 1+1=2 instead of =zero. Why is it that that little + symbol doesn't decrease 1 from 1? You simply can't prove it, because humans have defined the symbols +, -, etc. at our discretion. We have likewise defined the definition of units of measure such as the radian. With other systems of measure, you can't prove that there are 24 hours in a day mathematically. Us humans have simply chosen to divide the day into 24 sections, and we gave these sections the name "hour."

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- #12

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thanks for all your help everyone

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