Radian Measure and Arc of a Circle
There is a formula that relates the arc length of a circle of radius, r, to the central angle, $$ \theta$$ in radians.
The picture below illustrates the relationship between the radius, and the central angle in radians. The formula is $$ S = r \theta $$ where s represents the arc length, $$ S = r \theta$$ represents the central angle in radians and r is the length of the radius.
The interative demonstration below illustrates the relationship between the central angle of a circle, measured in radians, and the length of the intercepted arc. Just click and drag the points.
Use the $$ S = r \theta $$ formula.
S = 3(Π/3) = Π.
Use the formula for S = r Θ and calculate the intercepted arc: 6Π.
Use the formula for S = r Θ and calculate the intercepted arc: 4Π.
Use the formula for S = r Θ and calculate the solution.
