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anonymous
 one year ago
(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)
anonymous
 one year ago
(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)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440122370445:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well I would like a explanation to ..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw: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
 one year ago
Best ResponseYou've already chosen the best response.0wouldnt the fraction be pi ? pi is 3.14 right? and the fraction it pi over 3 ? @surjithayer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it would make it a whole number right?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The definition of a radian: A central angle of 1 radian tends an arc of length 1 radian in a unit circle.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440123188616:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The above is true for a unit circle.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you'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
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440123441936:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0in my lesson it didn't say anything about that symbol, and i thought the arc is the same as the center angle.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Here 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
 one year ago
Best ResponseYou've already chosen the best response.0yes thats the equation right ??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and the other person plugged in the numbers correctly ?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You 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
 one year ago
Best ResponseYou've already chosen the best response.0so it would be pi basicly ? if you times 5 by pi oits 15.7 then you divide it by 5 its pi again.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1pi 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
 one year ago
Best ResponseYou've already chosen the best response.0well alright, thanks for explaining it to me. ~~~ ! It helped alot
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