What is the angle in both radians and degrees determined by an arc of length 2pi meters on a circle of radius 8 meters?

The angle in both radians and degrees determined by an arc of length 2pi meters on a circle of radius 8 meters is π/4 rad and 45degrees respectively.

The length of an arc is expressed using the formula below as shown:

r is the radius of the arc = 8 m

theta is the angle subtended by the arc

L is the length of the arc = 2π meters

Substitute the given parameters into the formula as shown:

Convert 45 degrees to radians

Using the conversion rate 180 degrees = π rad

180 degrees = π rad

45 degrees = x

x= 45π/180

x = π/4 rad

Hence the angle in both radians and degrees determined by an arc of length 2pi meters on a circle of radius 8 meters is π/4 rad and 45degrees respectively.

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