An angle of one radian subtends an arc equal in length to the radius. In general, theta= sr, so s=rtheta, with theta in radians. A full turn is 2pi radians: 180 =pi rad. Convert degrees by multiplying by 180. The Basics of Angles bridge in Trigonometric Functions and Graphs supplies the angle-unit prerequisite. In the sector shown, let theta= 3. Then s=6(3)=2pi cm. The sector perimeter includes both radii: P=12+2pi cm. The major arc uses 2pi-theta, not theta. Recall s=rtheta: it is not on the examination formula sheet.

An angle of one radian subtends an arc equal in length to the radius. In general, \(\theta=\dfrac sr\), so \(s=r\theta\), with \(\theta\) in radians.

A full turn is \(2\pi\) radians: \(180^\circ=\pi\text{ rad}\). Convert degrees by multiplying by \(\dfrac\pi{180}\). The Basics of Angles bridge in Trigonometric Functions and Graphs supplies the angle-unit prerequisite.

In the sector shown, let \(\theta=\dfrac\pi3\). Then \(s=6\left(\dfrac\pi3\right)=2\pi\text{ cm}\). The sector perimeter includes both radii: \(P=12+2\pi\text{ cm}\).

The major arc uses \(2\pi-\theta\), not \(\theta\). Recall \(s=r\theta\): it is not on the examination formula sheet.

Radians and arc length

Radians and arc length