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Trig Question

  • Thread starter Miike012
  • Start date
  • #1
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Homework Statement



Today we went over finding the arc lenght 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

 

Answers and Replies

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

So s = radius * (angle measure in radians).
 
  • #3
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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?
 
  • #4
Char. Limit
Gold Member
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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:

[tex]s=\frac{180}{\pi} \theta r[/tex]

Where [itex]\theta[/itex] is measured in degrees.
 
  • #5
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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 lenght of radius 1
 
  • #6
eumyang
Homework Helper
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That's because the formula is wrong. It should be
[tex]s=\frac{\pi}{180} \theta r[/tex]
 
  • #7
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Thank you.
 
  • #8
Char. Limit
Gold Member
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That's because the formula is wrong. It should be
[tex]s=\frac{\pi}{180} \theta r[/tex]
Oh, my bad... I got the conversion wrong, I guess.

Sorry, Miike!
 
  • #9
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Oh, my bad... I got the conversion wrong, I guess.

Sorry, Miike!
Its cool no big deal
 

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