Final answer:
The circumference of a circle is divided into approximately 6.28 radians, corresponding to a complete revolution or 2π radians. This is option (a) and is derived from the fact that 2π is roughly equal to 6.28.
Step-by-step explanation:
The circumference of a circle is divided into approximately 6.28 radians, which is option (a) 3.14 times 2, or about 6.28. This value comes from the relationship between the circumference of a circle and its radius (C = 2πr), where π (pi) approximates to 3.14159. Since the radius is r, and we are talking about a complete revolution, the circumference equals 2πr, which simplifies to 2π as the r (radius) cancels out, resulting in the angle of rotation in radians.
One radian is approximately 57.3° as shown in reference 6.1. This unit of measurement is called a radian because it is the ratio of the arc length to the radius, which are both in the same unit of measure, hence it is a dimensionless quantity. We can deduce that since 2π radians are equivalent to one full circle (or one revolution), and 2π is roughly 6.28, then the circumference of a circle is divided into approximately 6.28 radians.