Trigonometry | 花野猫的数字花园

Reciprocal trigonometrical functions

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

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

$sin(θ + φ) = sinθcosφ + cosθsinφ$

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°

x=360° - 41.4° = 318.6°

alternative trigonometrical forms of Pythagoras’ theorem:

tan^2θ + 1 = sec^2θ

1+cot^2θ = cosec^2θ