论文部分内容阅读
一、定理:已知二面角的平面角为φ,在二面角的棱上任取一点A分别在两个半平面内作射线,两射线所成的角为θ,两射线与棱为公共边所成的角分别为θ_1和θ_2,则有: cosθ=cosθ_1 cosθ_2+sinθ_1 sinθ_2 coφ 当印φ=90°时,公式为cosθ=cosθ_1 cosθ_2 证明:(设φ,θ_1,θ_2均为锐角) 如图,∠BAC=θ,∠BAQ=θ_1,∠CAQ=θ_2,在PQ上任取一点D,在平面α和β内分别作BD⊥PQ交AB于B,作DC⊥PQ,交AC于C,连BC,则∠BDC=φ,并设AD=a,
I. Theorem: Given that the plane angle of the dihedral angle is φ, any point A on the dihedral angle takes a ray in two half-planes, respectively, and the angle formed by the two rays is θ, and the two radii and the edge are public The angles formed by the edges are θ_1 and θ_2, respectively: cosθ = cosθ_1 cosθ_2 + sinθ_1 sinθ_2 coφ When the print φ = 90 °, the formula is cosθ = cosθ_1 cosθ_2 Proof: (suppose φ, θ_1, θ_2 are acute angles) BAC = θ, ∠BAQ = θ_1, ∠CAQ = θ_2, take a point D on the PQ, in the plane of α and β respectively for BD ⊥ PQ AC AB in B, for DC ⊥ PQ AC AC in C, Even BC, then ∠ BDC = φ, and set AD = a,