Arc Length of a Circle: Given \(\theta\) measured in radians in a circle with radius \(r\), the arc length, \(s\), is given by the formula:

\[s=r\theta\]

Sector Area of a Circle: Given a central angle \(theta\) measured in radians subtending a sector of a circle with radius \(r\), the area of the sector is given by the formula:

\[A = \dfrac{{1}}{{2}}\theta r^2\]