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Funkcija sinus

pravokutni trokut A B C a b c α β
$$ \begin{aligned} & \sin\alpha = \frac{a}{c} \\ \\ & \sin\beta = \frac{b}{c} \end{aligned} $$

Grafikon

Funkcija sinus α sin α [°] [rad] 0 90° 180° 270° 360° 0,5π π 1,5π 2π 1 -1

Kalkulator

Unesite 1 vrijednost

α = 
α2 = 
sin α = 

Greška: 

 sin α > 1

Greška: 

 sin α < −1
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Formule

Funkcija sinus

pravokutni trokut A B C a b c α β
$$ \sin\alpha = \frac{a}{c} $$
$$ \sin\beta = \frac{b}{c} $$
$$ \begin{aligned} &\sin(\alpha + \beta) = \\& = \sin\alpha\cos\beta + \cos\alpha\sin\beta \\ \\ &\sin(\alpha - \beta) = \\& = \sin\alpha\cos\beta - \cos\alpha\sin\beta \end{aligned} $$
$$ \begin{aligned} &\sin\alpha + \sin\beta = \\& = 2\cdot\sin\frac{\alpha + \beta}{2}\cdot\cos\frac{\alpha - \beta}{2} \\ \\ &\sin\alpha - \sin\beta = \\& = 2\cdot\cos\frac{\alpha + \beta}{2}\cdot\sin\frac{\alpha - \beta}{2} \end{aligned} $$
$$ \begin{aligned} & \sin 2\alpha = 2\cdot\sin\alpha\cos\alpha \\ \\ & \sin(-\alpha) = -\sin\alpha \\ \\ & \left|\sin\frac{\alpha}{2}\right| = \sqrt{\frac{1-\cos\alpha}{2}} \end{aligned} $$
$$ \begin{aligned} & \sin^2\alpha + \cos^2\alpha = 1 \\ \\ & \tan\alpha \cdot \cot\alpha = 1 \ \Rightarrow \\ & \cot\alpha = \frac{1}{\tan\alpha} \\ \\ & \tan\alpha = \frac{\sin\alpha}{\cos\alpha} \\ \\ & \cot\alpha = \frac{\cos\alpha}{\sin\alpha} \end{aligned} $$

Ocjena

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