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Explain the relationship(s) among angle measure in degrees, angle measure in radians, and arc length.
One degree measure of an angle is defined as 1/360 of a full revolution in magnitude. Half revolution is
180 degrees and a right angle is one fourth of a revolution and its measure is 90 degrees. One radian
measure is defined as the angle formed by an arc of a circle of arc length same as its radius. Since one
complete circle with radius r has a circumference of 2πr, one revolution forms an angle of 2π radians.
Hence if the angle measure is in radians, we can find the arc length by simply multiplying the radius by
the angle measure. Similarly to find the angle in radians, divide the arc length by the radius.
The relationship between the angle in radian measure and arc length is S = rΘ, where S is the arc length,
r is the radius and Θ is the angle in radians.
The relationship between an angle in radian measure and degree measure is
One compete revolution = 3600 = 2π radians.
Hence 1 radian = (360/2π)0 = (180/π)0
And 10 = (π/180) radians.
Find the exact value of each of the following. In each case, show your work and explain the steps you
take to find the value.