anonymous
  • anonymous
(will give medal to the person who helps) Circle O has a radius of 5 centimeters and central angle AOB with a measure of 60° Describe in complete sentences how to find the length, in terms of a radian measure, of . arc AB (picture will be below)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
|dw:1440122370445:dw|
mathstudent55
  • mathstudent55
\(s = r\theta\)
anonymous
  • anonymous
well I would like a explanation to ..

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anonymous
  • anonymous
|dw:1440133220991:dw| 180 degree= pi radians \[60~ degree=\frac{ \pi }{ 180 } \times 60=\frac{ \pi }{ 3 } radians\] \[l= r \theta =5 \times \frac{ \pi }{ 3 }=?\]
anonymous
  • anonymous
wouldnt the fraction be pi ? pi is 3.14 right? and the fraction it pi over 3 ? @surjithayer
anonymous
  • anonymous
it would make it a whole number right?
mathstudent55
  • mathstudent55
The definition of a radian: A central angle of 1 radian tends an arc of length 1 radian in a unit circle.
mathstudent55
  • mathstudent55
|dw:1440123188616:dw|
mathstudent55
  • mathstudent55
The above is true for a unit circle.
anonymous
  • anonymous
you're confusing me :( idk where you got s from.... ~~ @surjithayer Was I correct about what I said ?? I got 15.7 for the answer.
mathstudent55
  • mathstudent55
|dw:1440123441936:dw|
anonymous
  • anonymous
in my lesson it didn't say anything about that symbol, and i thought the arc is the same as the center angle.
mathstudent55
  • mathstudent55
Here is the general case for any radius. A full circle has circumference \(2\pi r\). The circumference of a full circle can be thought of as the arc length of an arc whose central angle is \(2 \pi\) radians. For a full circle, s, the circumference is: \(s = 2 \pi r\) For any central angle, \(\theta\), the arc length is a fraction of the full circle's central angle, \(2 \pi\). \(s = \dfrac{\theta}{2 \pi }\ \cdot 2 \pi r\) \(s = \dfrac{\theta}{\cancel{2 \pi}}\ \cdot \cancel{2 \pi} r\) \(s = r \theta\) This is how you get the formula \(s = r \theta\) If you have a circle of radius r, and a central angle of \(\theta \) radians, then the arc length is simply \(s = r \theta\)
anonymous
  • anonymous
yes thats the equation right ??
anonymous
  • anonymous
and the other person plugged in the numbers correctly ?
mathstudent55
  • mathstudent55
You have a central angle of 60 degrees and a radius of 5 cm. You can use the formula \(s = r \theta\), but you must convert 60 degrees to radians first. \(60^\circ \times \dfrac{\pi ~radians}{180^\circ} = \dfrac{\pi}{3} ~radians\) Now that we have the angle of 60 degrees converted to radians, we use the formula \(s = r \theta\) \(s = 5 ~cm \times \dfrac{\pi}{3} \) \(s = \dfrac{5 \pi}{3} cm\) That is the exact arc length. If you want an approximate answer, just use 3.14 for \(\pi\). \(s = \dfrac{5 \times 3.14}{3} ~cm\)
anonymous
  • anonymous
so it would be pi basicly ? if you times 5 by pi oits 15.7 then you divide it by 5 its pi again.
anonymous
  • anonymous
@mathstudent55
mathstudent55
  • mathstudent55
pi is not exactly 3. It's a little more than 3. When you multiply 5 by pi and divide by 3, you get a number a little larger than 5. 5 * 3.14 / 3 = 5.23
anonymous
  • anonymous
well alright, thanks for explaining it to me. ~~~ ! It helped alot

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