One radian subtends an arc equal in length to the radius. 180 =pi radians; multiply degrees by pi180 to convert to radians. For theta in radians, s=rtheta and A_sector= 12r2theta. Sector perimeter is rtheta+2r, not just arc length. For a minor segment with 0 <= theta <= pi, subtract the triangle: A_segment= 12r2(theta-sintheta). Select the intended minor or major region before calculating. Example For r=6, theta= 2pi3: s=4pi, sector area 12pi, and segment area 12pi-9 3.

One radian subtends an arc equal in length to the radius. \(180^\circ=\pi\) radians; multiply degrees by \(\dfrac{\pi}{180}\) to convert to radians.

For \(\theta\) in radians, \(s=r\theta\) and \(A_{\text{sector}}=\dfrac12r^2\theta\). Sector perimeter is \(r\theta+2r\), not just arc length.

For a minor segment with \(0\le\theta\le\pi\), subtract the triangle: \(A_{\text{segment}}=\dfrac12r^2(\theta-\sin\theta)\). Select the intended minor or major region before calculating.

For \(r=6\), \(\theta=\dfrac{2\pi}{3}\): \(s=4\pi\), sector area \(12\pi\), and segment area \(12\pi-9\sqrt3\).

Arc Length and Area of Sector

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Radians, Arcs and Sectors

Radians, Arcs and Sectors