Kunnskapsgnist
Hvilke eksakte verdier gir sinus, cosinus og tangens?Sinus, cosinus og tangens gir desimaltal mellom -1 og 1, men noen vinkler gir eksakte verdier:
| $x$ (grader) | $0^{\circ}$ | $30^{\circ}$ | $45^{\circ}$ | $60^{\circ}$ | $90^{\circ}$ | $180^{\circ}$ |
|---|---|---|---|---|---|---|
| $x$ (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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