Find perpendicular distance from the origin of the line joining the points (cosθ, sinθ) and (cosφ, sinφ).

The equation of the line joining the points (cosθ, sinθ) and (cosφ, sinφ) is given by

y - sinθ = ^{(sinφ - sinθ)}/_{(cosφ - cosθ)}(x - cosθ)

y(cosφ - cosθ) - sinθ(cosφ - cosθ) = x(sinφ - sinθ) - cosθ(sinφ - sinθ)

y(cosφ - cosθ) - sinθ(cosφ - cosθ) - x(sinφ - sinθ) + cosθ(sinφ - sinθ) = 0

x(sinθ - sinφ) + y(cosφ - cosθ) + sin(φ - θ) = 0

Ax + By + C = 0, where A = sinθ - sinφ, B = cosφ - cosθ, C = sin(φ - θ)

d = ^{|Ax₁ + By₁ + C|}/_{√(A² + B²)}

d = ^{|(sinθ - sinφ)(0) + (cosφ - cosθ)(0) + sin(φ - θ)|}/_{√((sinθ - sinφ)² + (cosφ - cosθ)²)}

= ^{|sin(φ - θ)|}/_{√(sin²θ + sin²φ - 2 sinθ sinφ + cos²φ + cos²θ - 2 cosφ cosθ)}

= ^{|sin(φ - θ)|}/_{√((sin²θ + cos²θ) + (sin²φ + cos²φ) - 2(sinθ sinφ + cosθ cosφ))}

= ^{|sin(φ - θ)|}/_{√(2(1 - cos(φ - θ)))}

= ^{|sin(φ - θ)|}/_{2|sin(^{(φ - θ)}/2)|}

= |cos(^{(φ - θ)}/₂)|