Circular Measure
Circular measure deals with arcs, sectors, segments and chords using angles measured in radians. SPM tests the radian–degree conversion, the arc and sector formulas, and composite perimeters or areas where a triangle is subtracted from a sector.
Core rules
π radians = 180°, so degrees × π/180 gives radians. For a sector of radius r and angle θ radians: arc length s = rθ, area = ½r²θ, perimeter = 2r + rθ. The chord joining the arc's endpoints has length 2r sin(θ/2). The minor segment area is ½r²θ − ½r² sin θ, and the segment's perimeter uses the chord in place of the arc.
Worked example
A sector has r = 6 cm and θ = 1.2 rad. Arc = 6 × 1.2 = 7.2 cm. Area = ½ × 36 × 1.2 = 21.6 cm². Perimeter = 12 + 7.2 = 19.2 cm. The segment area is 21.6 − ½ × 36 × sin 1.2 ≈ 21.6 − 16.78 = 4.82 cm².
Traps
Leaving the calculator in degree mode; substituting degrees into s = rθ; giving sector area when the segment is requested; using the arc rather than the chord in a segment's perimeter.