Trigonometry
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Trigonometry

Reciprocal trigonometrical functions definitions and graphs | definition | example | |--|--| | $...

更新于 2024-01-06
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Reciprocal trigonometrical functions

definitions and graphs

definitionexample
cosecθ=1sinθcosecθ=\frac{1}{sinθ}cosec120°=23cosec120°=\frac{2}{\sqrt{3}} , cosec45°=2cosec45°=\sqrt{2}
secθ=1cosθsecθ=\frac{1}{cosθ}secπ4=2sec\frac{π}{4}=\sqrt{2}
cotθ=1tanθ(=cosθsinθ)cotθ=\frac{1}{tanθ}(=\frac{cosθ}{sinθ})cot330°=3cot330°=-\sqrt{3}, cot4π3=13cot\frac{4π}{3}=\frac{1}{\sqrt{3}}

exercise

3secx4=03secx-4=0 => x=41.4°x=41.4° or x=360°41.4°=318.6°x=360° - 41.4° = 318.6°

alternative trigonometrical forms of Pythagoras’ theorem:

tan2θ+1=sec2θtan^2θ + 1 = sec^2θ 1+cot2θ=cosec2θ1+cot^2θ = cosec^2θ

compound-angle formulae

sin(θ+φ)=sinθcosφ+cosθsinφsin(θ + φ) = sinθcosφ + cosθsinφ