Radians, arc length and sector area (copy)

1 radian, π radians, π/2 radians, π/4 radians, 2π radians

57.29°, 180°, 90°, 45°, 360°

converting from degrees to radians

θ/180 x π

converting from radians to degrees

θ/π x 180

arc length in degrees

θ/360 × 2πr

= πrθ/180

arc length in radians

θ/2π x 2πr

= rθ

sector area in degrees

θ/360 x πr²

sector area in radians

θ/360 x πr²

= θr²/ 2 (or ½θr²)

segment area

made up of a triangle and a sector

A triangle = ½absinθ = ½r²sinθ

A sector = ½θr²

∴ A segment = ½θr² - ½r²sinθ

= ½r² (θ - sinθ)