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@ -6,4 +6,37 @@ tags:
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# Cotangens
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$\cotg \alpha$
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Přilehlá strana ku protilehlé straně v pravoúhlém trojúhelníku.
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Převrácená hodnota [$\tg \alpha$](./Tangens.md) ($\frac{1}{\tg \alpha}$).
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Převrácená hodnota [$\tg \alpha$](./Tangens.md) ($\frac{1}{\tg \alpha}$).
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Zakázané osy: $k\pi; k\in\mathbb{Z}$
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$D_{\cotg}=\mathbb{R}\backslash\{k\pi;k\in\mathbb{Z}\}$
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$H_{\cotg}=\mathbb{R}$
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prostá není
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monotonie: klesající $(k\pi;\pi+k\pi) k\in\mathbb{Z}$
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parita: lichá
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omezená není
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extrémy nemá
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perioda: $\pi$
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průsečík:
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- osa Y - neexistuje
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- osa X - $[\frac\pi2+k\pi,k\in\mathbb{Z};0]$
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---
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Předpis funkce $y=\tg x$
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vyjádřete jako transformaci $\cotg x$
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$y=-\cotg(x+\frac\pi2)$
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---
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Popište transformaci ve funkci
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$y=3\tg(\frac{x}4+\frac\pi2)-2$
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“roztáhne” se podél Y 3x.
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posunutí o 2 $\downarrow$
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“splácnutí” podél X 4x.
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posunutí doleva o půl periody
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@ -33,6 +33,12 @@ $\tan(x+k\pi)=\tan x$
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ve 3. kv. je $\frac--=+$
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---
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$x=\frac{\pi}4=45\degree$
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