\[\sin\frac{\pi}{10}=\frac{\sqrt{5}-1}{4}\] \[\sin\frac{\pi}{8}=\frac{\sqrt{2-\sqrt{2}}}{2}\] \[\sin\frac{\pi}{6}=\frac{1}{2}\] \[\sin\frac{\pi}{5}=\sqrt{\frac{5-\sqrt{5}}{8}}\] \[\sin\frac{\pi}{4}=\frac{\sqrt{2}}{2}\] \[\sin\frac{3\pi}{10}=\frac{\sqrt{5}+1}{4}\] \[\sin\frac{\pi}{3}=\frac{\sqrt{3}}{2}\] \[\sin\frac{3\pi}{8}=\frac{\sqrt{2+\sqrt{2}}}{2}\] \[\sin\frac{2\pi}{5}=\sqrt{\frac{5+\sqrt{5}}{8}}\]