| $$0$$ |
$$0^\circ$$ |
$$0$$ |
$$0$$ |
$$1$$ |
| $$\frac{\pi}{60}$$ |
$$3^\circ$$ |
$$\frac{\sqrt{2}\left(\sqrt{3}+1\right)\left(\sqrt{5}-1\right)-2\left(\sqrt{3}-1\right)\sqrt{5+\sqrt{5}}}{16}$$ |
$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{5}+1\right)\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{10-2\sqrt{5}}-2\right)}{8}$$ |
$$\frac{\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5+2\sqrt{5}}-2+\sqrt{3}\right)}{2}$$ |
| $$\frac{\pi}{30}$$ |
$$6^\circ$$ |
$$\frac{\sqrt{30-6\sqrt{5}}-\sqrt{5}-1}{8}$$ |
$$\frac{\sqrt{10-2\sqrt{5}}-\sqrt{15}+\sqrt{3}}{2}$$ |
$$-\sqrt{5-2\sqrt{5}}+\sqrt{3}$$ |
| $$\frac{\pi}{24}$$ |
$$7.5^\circ$$ |
$$\frac{\sqrt{8-2\sqrt{6}-2\sqrt{2}}}{4}$$ |
$$\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{2}-1\right)$$ |
$$\left(\sqrt{3}+1\right)\sqrt{4-\sqrt{6}-\sqrt{2}}$$ |
| $$\frac{\pi}{20}$$ |
$$9^\circ$$ |
$$\frac{-2\sqrt{5-\sqrt{5}}+\sqrt{10}+\sqrt{2}}{8}$$ |
$$-\sqrt{5+2\sqrt{5}}+\sqrt{5}+1$$ |
$$\frac{-2\sqrt{5+\sqrt{5}}+3\sqrt{2}+\sqrt{10}}{2}$$ |
| $$\frac{\pi}{15}$$ |
$$12^\circ$$ |
$$\frac{\sqrt{10+2\sqrt{5}}-\sqrt{15}+\sqrt{3}}{8}$$ |
$$\frac{\left(3-\sqrt{5}\right)\left(-\sqrt{10-2\sqrt{5}}+2\sqrt{3}\right)}{4}$$ |
$$\sqrt{15-6\sqrt{5}}-\sqrt{5}+2$$ |
| $$\frac{\pi}{12}$$ |
$$15^\circ$$ |
$$\frac{\sqrt{6}-\sqrt{2}}{4}$$ |
$$2-\sqrt{3}$$ |
$$\sqrt{6}-\sqrt{2}$$ |
| $$\frac{\pi}{10}$$ |
$$18^\circ$$ |
$$\frac{\sqrt{5}-1}{4}$$ |
$$\frac{\sqrt{25-10\sqrt{5}}}{5}$$ |
$$\frac{\sqrt{50-10\sqrt{5}}}{5}$$ |
| $$\frac{7\pi}{60}$$ |
$$21^\circ$$ |
$$\frac{-\sqrt{2}\left(\sqrt{3}-1\right)\left(\sqrt{5}+1\right)+2\left(\sqrt{3}+1\right)\sqrt{5-\sqrt{5}}}{16}$$ |
$$\frac{\left(\sqrt{3}+1\right)\left(\sqrt{5}-1\right)\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{10+2\sqrt{5}}-2\right)}{8}$$ |
$$\frac{\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)\left(-\sqrt{5-2\sqrt{5}}+2+\sqrt{3}\right)}{2}$$ |
| $$\frac{\pi}{8}$$ |
$$22.5^\circ$$ |
$$\frac{\sqrt{2-\sqrt{2}}}{2}$$ |
$$\sqrt{2}-1$$ |
$$\sqrt{4-2\sqrt{2}}$$ |
| $$\frac{2\pi}{15}$$ |
$$24^\circ$$ |
$$\frac{-\sqrt{10-2\sqrt{5}}+\sqrt{15}+\sqrt{3}}{8}$$ |
$$\frac{\left(3+\sqrt{5}\right)\left(\sqrt{10+2\sqrt{5}}-2\sqrt{3}\right)}{4}$$ |
$$\sqrt{15+6\sqrt{5}}-\sqrt{5}-2$$ |
| $$\frac{3\pi}{20}$$ |
$$27^\circ$$ |
$$\frac{2\sqrt{5+\sqrt{5}}-\sqrt{10}+\sqrt{2}}{8}$$ |
$$-\sqrt{5+2\sqrt{5}}+\sqrt{5}-1$$ |
$$\frac{2\sqrt{5-\sqrt{5}}-3\sqrt{2}+\sqrt{10}}{2}$$ |
| $$\frac{\pi}{6}$$ |
$$30^\circ$$ |
$$\frac{1}{2}$$ |
$$\frac{\sqrt{3}}{3}$$ |
$$\frac{2\sqrt{3}}{3}$$ |
| $$\frac{11\pi}{60}$$ |
$$33^\circ$$ |
$$\frac{\sqrt{2}\left(\sqrt{3}+1\right)\left(\sqrt{5}-1\right)+2\left(\sqrt{3}-1\right)\sqrt{5+\sqrt{5}}}{16}$$ |
$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{5}+1\right)\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{10-2\sqrt{5}}+2\right)}{8}$$ |
$$\frac{\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5+2\sqrt{5}}+2-\sqrt{3}\right)}{2}$$ |
| $$\frac{\pi}{5}$$ |
$$36^\circ$$ |
$$\frac{\sqrt{10-2\sqrt{5}}}{4}$$ |
$$\sqrt{5-2\sqrt{5}}$$ |
$$\sqrt{5}-1$$ |
| $$\frac{5\pi}{24}$$ |
$$37.5^\circ$$ |
$$\frac{\sqrt{8-2\sqrt{6}+2\sqrt{2}}}{4}$$ |
$$\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{2}+1\right)$$ |
$$\left(\sqrt{3}-1\right)\sqrt{4-\sqrt{6}+\sqrt{2}}$$ |
| $$\frac{13\pi}{60}$$ |
$$39^\circ$$ |
$$\frac{\sqrt{2}\left(\sqrt{3}+1\right)\left(\sqrt{5}+1\right)-2\left(\sqrt{3}-1\right)\sqrt{5-\sqrt{5}}}{16}$$ |
$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{5}-1\right)\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{10+2\sqrt{5}}-2\right)}{8}$$ |
$$\frac{\sqrt{2}\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5-2\sqrt{5}}-2+\sqrt{3}\right)}{2}$$ |
| $$\frac{7\pi}{30}$$ |
$$42^\circ$$ |
$$\frac{\sqrt{30+6\sqrt{5}}-\sqrt{5}+1}{8}$$ |
$$\frac{-\sqrt{10+2\sqrt{5}}+\sqrt{15}+\sqrt{3}}{2}$$ |
$$\sqrt{5+2\sqrt{5}}-\sqrt{3}$$ |
| $$\frac{\pi}{4}$$ |
$$45^\circ$$ |
$$\frac{\sqrt{2}}{2}$$ |
$$1$$ |
$$\sqrt{2}$$ |
| $$\frac{4\pi}{15}$$ |
$$48^\circ$$ |
$$\frac{\sqrt{10+2\sqrt{5}}+\sqrt{15}-\sqrt{3}}{8}$$ |
$$\frac{\left(3-\sqrt{5}\right)\left(\sqrt{10-2\sqrt{5}}+2\sqrt{3}\right)}{4}$$ |
$$\sqrt{15-6\sqrt{5}}+\sqrt{5}-2$$ |
| $$\frac{17\pi}{60}$$ |
$$51^\circ$$ |
$$\frac{\sqrt{2}\left(\sqrt{3}-1\right)\left(\sqrt{5}+1\right)+2\left(\sqrt{3}+1\right)\sqrt{5-\sqrt{5}}}{16}$$ |
$$\frac{\left(\sqrt{3}+1\right)\left(\sqrt{5}-1\right)\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{10+2\sqrt{5}}+2\right)}{8}$$ |
$$\frac{\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5-2\sqrt{5}}+2+\sqrt{3}\right)}{2}$$ |
| $$\frac{7\pi}{24}$$ |
$$52.5^\circ$$ |
$$\frac{\sqrt{8+2\sqrt{6}-2\sqrt{2}}}{4}$$ |
$$\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{2}-1\right)$$ |
$$\left(\sqrt{3}-1\right)\sqrt{4+\sqrt{6}-\sqrt{2}}$$ |
| $$\frac{3\pi}{10}$$ |
$$54^\circ$$ |
$$\frac{\sqrt{5}+1}{4}$$ |
$$\frac{\sqrt{25+10\sqrt{5}}}{5}$$ |
$$\frac{\sqrt{50+10\sqrt{5}}}{5}$$ |
| $$\frac{19\pi}{60}$$ |
$$57^\circ$$ |
$$\frac{-\sqrt{2}\left(\sqrt{3}-1\right)\left(\sqrt{5}-1\right)+2\left(\sqrt{3}+1\right)\sqrt{5+\sqrt{5}}}{16}$$ |
$$\frac{\left(\sqrt{3}+1\right)\left(\sqrt{5}+1\right)\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{10-2\sqrt{5}}-2\right)}{8}$$ |
$$\frac{\sqrt{2}\left(\sqrt{5}+\sqrt{3}\right)\left(-\sqrt{5+2\sqrt{5}}+2+\sqrt{3}\right)}{2}$$ |
| $$\frac{\pi}{3}$$ |
$$60^\circ$$ |
$$\frac{\sqrt{3}}{2}$$ |
$$\sqrt{3}$$ |
$$2$$ |
| $$\frac{7\pi}{20}$$ |
$$63^\circ$$ |
$$\frac{2\sqrt{5+\sqrt{5}}+\sqrt{10}-\sqrt{2}}{8}$$ |
$$\sqrt{5+2\sqrt{5}}+\sqrt{5}-1$$ |
$$\frac{2\sqrt{5-\sqrt{5}}+3\sqrt{2}-\sqrt{10}}{2}$$ |
| $$\frac{11\pi}{30}$$ |
$$66^\circ$$ |
$$\frac{\sqrt{30-6\sqrt{5}}+\sqrt{5}+1}{8}$$ |
$$\frac{\sqrt{10-2\sqrt{5}}+\sqrt{15}-\sqrt{3}}{2}$$ |
$$\sqrt{5-2\sqrt{5}}+\sqrt{3}$$ |
| $$\frac{3\pi}{8}$$ |
$$67.5^\circ$$ |
$$\frac{\sqrt{2+\sqrt{2}}}{2}$$ |
$$\sqrt{2}+1$$ |
$$\sqrt{4+2\sqrt{2}}$$ |
| $$\frac{23\pi}{60}$$ |
$$69^\circ$$ |
$$\frac{\sqrt{2}\left(\sqrt{3}+1\right)\left(\sqrt{5}+1\right)+2\left(\sqrt{3}-1\right)\sqrt{5-\sqrt{5}}}{16}$$ |
$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{5}-1\right)\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{10+2\sqrt{5}}+2\right)}{8}$$ |
$$\frac{\sqrt{2}\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5-2\sqrt{5}}+2-\sqrt{3}\right)}{2}$$ |
| $$\frac{2\pi}{5}$$ |
$$72^\circ$$ |
$$\frac{\sqrt{10+2\sqrt{5}}}{4}$$ |
$$\sqrt{5+2\sqrt{5}}$$ |
$$\sqrt{5}+1$$ |
| $$\frac{5\pi}{12}$$ |
$$75^\circ$$ |
$$\frac{\sqrt{6}+\sqrt{2}}{4}$$ |
$$2+\sqrt{3}$$ |
$$\sqrt{6}+\sqrt{2}$$ |
| $$\frac{13\pi}{30}$$ |
$$78^\circ$$ |
$$\frac{\sqrt{30+6\sqrt{5}}+\sqrt{5}-1}{8}$$ |
$$\frac{\sqrt{10+2\sqrt{5}}+\sqrt{15}+\sqrt{3}}{2}$$ |
$$\sqrt{5+2\sqrt{5}}+\sqrt{3}$$ |
| $$\frac{9\pi}{20}$$ |
$$81^\circ$$ |
$$\frac{2\sqrt{5-\sqrt{5}}+\sqrt{10}+\sqrt{2}}{8}$$ |
$$\sqrt{5+2\sqrt{5}}+\sqrt{5}+1$$ |
$$\frac{2\sqrt{5+\sqrt{5}}+3\sqrt{2}+\sqrt{10}}{2}$$ |
| $$\frac{11\pi}{24}$$ |
$$82.5^\circ$$ |
$$\frac{\sqrt{8+2\sqrt{6}+2\sqrt{2}}}{4}$$ |
$$\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{2}+1\right)$$ |
$$\left(\sqrt{3}+1\right)\sqrt{4+\sqrt{6}+\sqrt{2}}$$ |
| $$\frac{7\pi}{15}$$ |
$$84^\circ$$ |
$$\frac{\sqrt{10-2\sqrt{5}}+\sqrt{15}+\sqrt{3}}{8}$$ |
$$\frac{\left(3+\sqrt{5}\right)\left(\sqrt{10+2\sqrt{5}}+2\sqrt{3}\right)}{4}$$ |
$$\sqrt{15+6\sqrt{5}}+\sqrt{5}+2$$ |
| $$\frac{29\pi}{60}$$ |
$$87^\circ$$ |
$$\frac{\sqrt{2}\left(\sqrt{3}-1\right)\left(\sqrt{5}-1\right)+2\left(\sqrt{3}+1\right)\sqrt{5+\sqrt{5}}}{16}$$ |
$$\frac{\left(\sqrt{3}+1\right)\left(\sqrt{5}+1\right)\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{10-2\sqrt{5}}+2\right)}{8}$$ |
$$\frac{\sqrt{2}\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5+2\sqrt{5}}+2+\sqrt{3}\right)}{2}$$ |
| $$\frac{\pi}{2}$$ |
$$90^\circ$$ |
$$1$$ |
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