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Trójkąty sferyczne I. BBB (3 x twierdzenie cosinusów dla boków) c b c b a A c b a A c b A c b c b a sin sin cos cos cos cos cos cos cos cos sin sin cos sin sin cos cos cos ⋅ ⋅ − = ⋅ − = ⋅ ⋅ ⋅ ⋅ + ⋅ = II. KKK (3 x twierdzenie cosinusów dla kątów) C B C B A a C B A a C B a C B C B A sin sin cos cos cos cos cos cos cos cos sin sin cos sin sin cos cos cos ⋅ ⋅ + = ⋅ + = ⋅ ⋅ ⋅ ⋅ + ⋅ − = III. KBK ( AbC ) 1. b C A C A B cos sin sin cos cos cos ⋅ ⋅ + ⋅ − = 2. AbCa – tw. Cotangensów ctgA C C b b tga b ctgA C C b ctga ctgA C C b ctga b ctgA C ctga b C b ⋅ + ⋅ = ⋅ + ⋅ = ⋅ + ⋅ = ⋅ ⋅ − ⋅ = ⋅ sin cos cos sin sin sin cos cos sin cos cos sin sin sin cos cos 3. cAbC ctgC A b A b tgc b ctgC A b A ctgc ctgC A b A ctgc b ctgC A ctgc b b A ⋅ + ⋅ = ⋅ + ⋅ = ⋅ + ⋅ = ⋅ ⋅ − ⋅ = ⋅ sin cos cos sin sin sin cos cos sin cos cos sin sin sin cos cos IV. BKB (cBa) 1. tw cosinusów dla boków B c a c a b cos sin sin cos cos cos ⋅ ⋅ + ⋅ = 2. AcBa tw cotangensów B c ctga c B tgA B B c ctga c ctgA B c ctga c ctgA B ctgA B ctga c B c cos cos sin sin sin cos cos sin cos cos sin sin sin sin cos cos ⋅ − ⋅ = ⋅ − ⋅ = ⋅ − ⋅ = ⋅ ⋅ − ⋅ = ⋅ 3. cBaC tw cotangensów a B ctgc a B tgC B a B ctgc a ctgC a B ctgc a ctgC B ctgC B ctgc a a B cos cos sin sin sin cos cos sin cos cos sin sin sin sin cos cos ⋅ − ⋅ = ⋅ − ⋅ = ⋅ − ⋅ = ⋅ ⋅ − ⋅ = ⋅ V. KKB (ABa) 1. tw sinusów A B a b A b B a B b A a sin sin sin sin sin sin sin sin sin sin sin sin ⋅ = ⋅ = ⋅ = b b b b o − = = 180 2 1 sprawdzamy czy oba są poprawne 2. tw cosinusów na kątów i tw cosinusów na boków ( ) ( ) b a B A b a B A B A C b a B A B A b a B A C b a B A B A C b a B A C C b a B A b a B A B A C C b a b a B A B A C C b a b a c c B A B A C sin sin sin sin 1 cos cos sin sin cos cos cos cos cos sin
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