Circular measure: radians, arc length and sector area

Learning objectives

Convert between degrees and radians using π radians = 180°, and work with the exact radian values π/6, π/4, π/3 and π/2 without a calculator

Calculate arc length using s = rθ and sector area using A = ½r²θ, with θ measured in radians, and rearrange each formula to find a missing radius or angle

Calculate the area of a segment as the sector area minus the area of the triangle, ½r²θ − ½r² sin θ, and the perimeter of a segment as the arc plus the chord

Solve composite problems involving several sectors, triangles and segments, for example finding the shaded area between overlapping circles or inside a regular polygon

Set up and solve equations for an unknown radius or angle from a given arc length, perimeter or area, giving exact answers in terms of π where required