Arc Length of a Circle: Learn the Proof!

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Homework Help Overview

The discussion revolves around understanding the formula for arc length in a circle, specifically focusing on the relationship between the angle in radians and the radius. Participants express a desire to grasp the proof behind the formula and clarify its application when angles are given in degrees.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the formula for arc length, noting its dependence on the angle measured in radians. Questions arise regarding the necessity of converting degrees to radians and the implications of using different units.

Discussion Status

The conversation includes attempts to clarify the correct formula for arc length when angles are expressed in degrees. Some participants acknowledge errors in their understanding, while others provide alternative formulas, indicating a productive exploration of the topic.

Contextual Notes

There is an ongoing discussion about the correct conversion between degrees and radians, with some confusion noted regarding the formulas presented. Participants are also considering the implications of using incorrect conversions in their calculations.

Miike012
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Homework Statement



Today we went over finding the arc length s of a circle with a given radian and radius...
Thus s = radian*radius...

Thats easy to remember but I think it will be more memorable for the long run if I knew the proof and understood it... can some one please post a website where I can read the proof... or if some one could explain that would be nice to .
Thank you.

Homework Equations





The Attempt at a Solution

 
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The arc length of the entire circle (its circumference) of radius r is 2 \pi r. IOW, the arc length associated with an angle of 2 \pi is 2 \pi r. Since the arc length is proportional to the angle between the two rays that subtend the arc, the arc length associated with an angle \theta is \theta r.

So s = radius * (angle measure in radians).
 
But this formula only works if I am presented with radians correct? So if I am given deg. I will have to convert into rad right?
 
Miike012 said:
But this formula only works if I am presented with radians correct? So if I am given deg. I will have to convert into rad right?

That's correct. Alternately, you could use this formula:

s=\frac{180}{\pi} \theta r

Where \theta is measured in degrees.
 
Say 64 is the deg. w/ radius of 1
Then your saying I can multiply 180/pi*64*1
= 3666... that seems to big to be an arc length of radius 1
 
That's because the formula is wrong. It should be
s=\frac{\pi}{180} \theta r
 
Thank you.
 
eumyang said:
That's because the formula is wrong. It should be
s=\frac{\pi}{180} \theta r

Oh, my bad... I got the conversion wrong, I guess.

Sorry, Miike!
 
Char. Limit said:
Oh, my bad... I got the conversion wrong, I guess.

Sorry, Miike!
Its cool no big deal
 

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