Trigonometry

AL 国际课程

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

definition	example
$cosecθ=\frac{1}{sinθ}$	$cosec120°=\frac{2}{\sqrt{3}}$ , $cosec45°=\sqrt{2}$
$secθ=\frac{1}{cosθ}$	$sec\frac{π}{4}=\sqrt{2}$
$cotθ=\frac{1}{tanθ}(=\frac{cosθ}{sinθ})$	$cot330°=-\sqrt{3}$ , $cot\frac{4π}{3}=\frac{1}{\sqrt{3}}$

exercise

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

alternative trigonometrical forms of Pythagoras’ theorem:

$tan^2θ + 1 = sec^2θ$ $1+cot^2θ = cosec^2θ$

compound-angle formulae

$sin(θ + φ) = sinθcosφ + cosθsinφ$