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Algebra: Trigonometri

Hvilke eksakte verdier gir sinus, cosinus og tangens?

VGS

Sinus, cosinus og tangens gir desimaltal mellom -1 og 1, men noen vinkler gir eksakte verdier:

$x$ (grader)$0^o$$30^o$$45^o$$60^o$$90^o$$180^o$
$x$ (radianer)$0$$\frac{\pi}{6}$$\frac{\pi}{4}$$\frac{\pi}{3}$$\frac{\pi}{2}$$\pi$
$\sin x$$\frac{\textcolor{blue}{\sqrt{0}}}{2} = 0$$\frac{\textcolor{blue}{\sqrt{1}}}{2} = \frac{1}{2}$$\frac{\textcolor{blue}{\sqrt{2}}}{2}$$\frac{\textcolor{blue}{\sqrt{3}}}{2}$$\frac{\textcolor{blue}{\sqrt{4}}}{2} = 1$0
$\cos x$$\frac{\textcolor{blue}{\sqrt{4}}}{2} = 1$$\frac{\textcolor{blue}{\sqrt{3}}}{2}$$\frac{\textcolor{blue}{\sqrt{2}}}{2}$$\frac{\textcolor{blue}{\sqrt{1}}}{2} = \frac{1}{2}$$\frac{\textcolor{blue}{\sqrt{0}}}{2} = 0$1
$\tan x$$0$$\frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$$1$$\sqrt{3}$$-$0

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