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Daniel [21]
3 years ago
15

An arc subtends a central angle measuring 2pi/3

Mathematics
1 answer:
RoseWind [281]3 years ago
8 0

Answer:

1/3

Step-by-step explanation:

We know that angle subtended by whole circumference is 2\pi.

If r is the radius then Length of whole circumference is 2\pi r

2\pi radian has 2\pi r  length

dividing  both side by 2\pi we have

2\pi /2\pi  = 2\pi r/2\pi  \ circumference

1 radian has r length  

1 radian = r length      equation a

=> since we have to find value of circumference for 2\pi /3 we

multiply both side of equation a with 2\pi /3.

2\pi /3 \radian = r* 2\pi /3 \circumference

therefore, length of required arc is 2\pi r/3

________________________________________________

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 = =>(2\pi r/3) / 2\pi r\\=> 1/3

Thus, the given arc is 1/3 of circumference of circle.

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Step-by-step explanation:

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I'll include a plotted graph with our equation just so you can verify it is indeed the same.

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