AdaAda

Home / Library / Digital SAT Math: Algebra, Advanced Math & Geometry / Synthetic flashcard

How are arc length $s$ and sector area $A_{\text{sector}}$ calculated for a central angle of $\theta$ radians and radius $r$?

Study flashcard from the deck Digital SAT Math: Algebra, Advanced Math & Geometry.

Answer

Arc length $s = r\theta$; Sector area $A_{\text{sector}} = \frac{1}{2} r^2 \theta$.

Explanation

If the central angle is in degrees: $s = 2\pi r \left(\frac{\theta}{360^\circ}\right)$ and $A_{\text{sector}} = \pi r^2 \left(\frac{\theta}{360^\circ}\right)$.

Synthetic content · Curated by Ada