TABELE WARTOŚCI FUNKCJI TRYGONOMETRYCZNYCH
Tabela wartości funkcji trygonometrycznych dla najczęściej spotykanych kątów
| \(\alpha\) | \(30^o\) | \(45^o\) | \(60^o\) |
|---|---|---|---|
| \(\alpha\) | \(\displaystyle\frac{\pi}6\) | \(\displaystyle\frac{\pi}4\) | \(\displaystyle\frac{\pi}3\) |
| \(\displaystyle\sin \alpha\) | \(\displaystyle\frac12\) | \(\displaystyle\frac{\sqrt2}2\) | \(\displaystyle\frac{\sqrt3}2\) |
| \(\displaystyle\cos \alpha\) | \(\displaystyle\frac{\sqrt3}2\) | \(\displaystyle\frac{\sqrt2}2\) | \(\displaystyle\frac{1}2\) |
| \(\displaystyle \text{tg}\,\alpha\) | \(\displaystyle\frac{\sqrt3}3\) | \(\displaystyle 1\) | \(\displaystyle\sqrt3\) |
| \(\displaystyle \text{ctg}\,\alpha\) | \(\displaystyle\sqrt3\) | \(\displaystyle 1\) | \(\displaystyle\frac{\sqrt3}3\) |
| \(\alpha\) | \(0^o\) | \(90^o\) | \(180^o\) | \(270^o\) | \(360^o\) |
|---|---|---|---|---|---|
| \(\alpha\) | \(0\) | \(\displaystyle\frac{\pi}2\) | \(\displaystyle \pi\) | \(\displaystyle\frac{3\pi}2\) | \(\displaystyle 2\pi\) |
| \(\displaystyle\sin \alpha\) | \(0\) | \(1\) | \(0\) | \(-1\) | \(0\) |
| \(\displaystyle\cos \alpha\) | \(1\) | \(0\) | \(-1\) | \(0\) | \(1\) |
| \(\displaystyle \text{tg}\,\alpha\) | \(0\) | nie istnieje |
\(0\) | nie istnieje |
\(0\) |
| \(\displaystyle \text{ctg}\,\alpha\) | nie istnieje |
\(0\) | nie istnieje |
\(0\) | nie istnieje |
| \(\alpha\) | \(15^o\) | \(18^o\) | \(22\frac12^o\) | \(75^o\) |
|---|---|---|---|---|
| \(\alpha\) | \(\displaystyle\frac{\pi}{12}\) | \(\displaystyle\frac{\pi}{10}\) | \(\displaystyle\frac{\pi}{8}\) | \(\displaystyle\frac{5\pi}{12}\) |
| \(\displaystyle\sin \alpha\) | \(\displaystyle\frac{\sqrt6-\sqrt2}{4}\) | \(\displaystyle\frac{1-\sqrt5}{4}\) | \(\displaystyle\frac{\sqrt{2-\sqrt2}}{4}\) | \(\displaystyle\frac{\sqrt6+\sqrt2}{4}\) |
| \(\displaystyle\cos \alpha\) | \(\displaystyle\frac{\sqrt6+\sqrt2}{4}\) | \(\displaystyle\frac{\sqrt{10+2\sqrt{5}}}{4}\) | \(\displaystyle\frac{\sqrt{2+\sqrt2}}{4}\) | \(\displaystyle\frac{\sqrt6-\sqrt2}{4}\) |
| \(\displaystyle \text{tg}\,\alpha\) | \(\displaystyle2-\sqrt3\) | \(\displaystyle\frac{\sqrt{25-10\sqrt{5}}}{5}\) | \(\displaystyle\sqrt2-1\) | \(\displaystyle2+\sqrt3\) |
| \(\displaystyle \text{ctg}\,\alpha\) | \(\displaystyle2+\sqrt3\) | \(\displaystyle\sqrt{5+2\sqrt{5}}\) | \(\displaystyle\sqrt2+1\) | \(\displaystyle2-\sqrt3\) |
Wartość funkcji dla danego kąta odczytujemy na przecięciu się danej funkcji i kąta.
Przykłady
\(\displaystyle\sin 45^o = \frac{\sqrt2}2\)
\(\displaystyle\cos 60^o = \frac{1}2\)
\(\displaystyle tg \frac{\pi}2 = nie\,\,istnieje\)
\(\displaystyle ctg \frac{\pi}6 = \sqrt3\)