Arc Length of a Circle: Learn the Proof!

AI Thread Summary
The discussion focuses on understanding the formula for arc length in a circle, which is given by s = radius * angle measure in radians. Participants clarify that this formula requires angles to be in radians, and if degrees are provided, they must be converted to radians first. An incorrect formula for converting degrees to arc length is identified, with the correct conversion being s = (π/180) * θ * r. The conversation emphasizes the importance of grasping the proof behind the arc length formula for better retention and understanding. Overall, the thread highlights the relationship between angle measures and arc length in circles.
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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