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Consider two circles, centered at the origin, of radii 1 and 2, respectively. In each circle, begin on thepositive x-axis and rotate counterclockwise by an angle of 210.(a) What is the length of the arc associated with this angle in the circle of radius 1? In the circle of radius 2?Also, what are the radian measure of this angle for each circle.

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An arc length represents a portion of the entire circumference of a circle with 360˚.

The circumference of a circle is defined by the formula: `C = 2pir`

A circle with a radius of 1 has a circumference of:

`C = 2pi*1 = 2pi`

Therefore the arc length would be:  

`210/360* 2pi = (7pi)/6` or  3.67 units

A circle with a radius of 2 has a circumference of:

`C=2pi*2 = 4pi`

Therefore the arc length would be:

`210/360* 4pi = (7pi)/3` or 7.33 units

The radian measures are given respectively as:

`(7pi)/6` and `(7pi)/3` as previously found when calculating units.

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