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În cadrul supematematicii, funcțiile trigonometrice circulare pot fi generalizate prin funcţiile trigonometrice excentrice:

Sinusul excentric Edit

sex_{1, 2} (\theta, S) = \sin \{ \theta \mp \arcsin [s \cdot \sin (\theta - \varepsilon)] \}= \!
= -s \cos \theta \sin (\theta - \varepsilon) \pm \sqrt {1-s^2 \sin^2 (\theta- \varepsilon)} \!

sau:

sex_{1, 2} (x, S) = \sin \{ x \mp \arcsin [s \cdot \sin (x-z)] \} = \!
= -s \cdot \cos x \cdot \sin(x-z) \pm \sqrt{1-s^2 \cdot \sin^2 (x-z)} \!

Cosinusul excentric Edit

cex_{1, 2}(\theta, S) = \cos \{ \theta \mp \arcsin [s \cdot \sin (\theta - \varepsilon)] \}= \!
= s \cdot \sin \theta \cdot \sin (\theta- \varepsilon) \pm \sqrt {1-s^2 \cdot \sin^2(\theta- \varepsilon)} \!

sau

cex_{1, 2} (x, S) = \cos \{ x \mp \arcsin [s \cdot \sin (x-z)] \} =  \!
= s \cdot \sin x \sin (x-z) \pm \sqrt {1-s^2 \cdot \sin^2 (x-z)}. \!
Graficele functiilor excentrice.png

Graficele funcţiilor trigonometrice excentrice:
-stânga: cex_1 \theta \! (roşu) şi cex_2 \theta \! (albastru) sus şi c2ex_{12} \theta \! (jos)
-dreapta: sex_1 \theta \! (roşu) şi sex_2 \theta \! (albastru) sus şi s2ex_{12} \theta \! (jos)
pentru S (s \in [0, 1], \; \varepsilon =0) \!

Resurse Edit

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