Question

若点（cosθ,sinθ）到直线χsinθ+ycosθ-1=0（0≤θ≤π／2）的距离是1／2,则θ的值为?

Answer 1

根据点到直线的距离公式：

| sinθcosθ + cosθsinθ - 1 | / 根号(sin^2θ+cos^2θ) = 1/2

| 2sinθcosθ - 1 | = 1/2

| sin2θ - 1 | = 1/2

∵0≤θ≤π／2,0≤2θ≤π

∴0≤sin2θ≤1

∴1-sin2θ=1/2

∴sin2θ=1/2

∴2θ = π/6,或5π/6

∴θ=π/12,或 5π/12