Chapter 9

Circular Measure

Radians, arc length and sector area — with an interactive exercise.

Circular Measure uses radians to measure angles: $\pi$ radians $=180°$.

Formulae (θ in radians)

Arc length $= r\theta$ · Sector area $= \tfrac12 r^2\theta$

Example: arc length with $r=5$, $\theta=2$ is $5\times 2 = 10$.

Remember

  • $\pi$ rad $=180°$; $2\pi$ rad $=360°$.
  • Arc $=r\theta$ · Sector $=\tfrac12 r^2\theta$.

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