Answer:
1/3
Step-by-step explanation:
We know that angle subtended by whole circumference is [tex]2\pi[/tex].
If r is the radius then Length of whole circumference is [tex]2\pi r[/tex]
[tex]2\pi[/tex] radian has [tex]2\pi r[/tex] length
dividing both side by [tex]2\pi[/tex] we have
[tex]2\pi /2\pi = 2\pi r/2\pi \ circumference[/tex]
1 radian has r length
1 radian = r length equation a
=> since we have to find value of circumference for [tex]2\pi /3[/tex] we
multiply both side of equation a with [tex]2\pi /3[/tex].
[tex]2\pi /3 \radian = r* 2\pi /3 \circumference[/tex]
therefore, length of required arc is [tex]2\pi r/3[/tex]
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we have to find how much is this as fraction of total circumference of circle
fraction of circumference = value of arc length / total length of circumference
fraction of circumference = [tex]=>(2\pi r/3) / 2\pi r\\=> 1/3[/tex]
Thus, the given arc is 1/3 of circumference of circle.
