| $0$ | $0^{\circ}$ | $0$ | $1$ | $0$ | $\infty$ | $1$ | $\infty$ |
| $\dfrac{\pi}{24}$ | $7.5^\circ$ | $\dfrac{1}{2}\sqrt{2 - \sqrt{2 + \sqrt{3}}}$ | $\dfrac{1}{2}\sqrt{2 + \sqrt{2 + \sqrt{3}}}$ | $\sqrt{6} - \sqrt{3} + \sqrt{2} - 2$ | $\sqrt{6} + \sqrt{3} + \sqrt{2} + 2$ | $-$ | $-$ |
| $\dfrac{\pi}{12}$ | $15^\circ$ | $\dfrac{\sqrt{2}}{4} (\sqrt{3} - 1)$ | $\dfrac{\sqrt{2}}{4} (\sqrt{3} + 1)$ | $2 - \sqrt{3}$ | $2 + \sqrt{3}$ | $\sqrt{2}(\sqrt{3} - 1)$ | $\sqrt{2}(\sqrt{3} + 1)$ |
| $\dfrac{\pi}{10}$ | $18^\circ$ | $\dfrac{\sqrt{5} - 1}{4}$ | $\dfrac{\sqrt{10 + 2 \sqrt{5}}}{4}$ | $\dfrac{\sqrt{25 - 10 \sqrt{5}}}{5}$ | $\dfrac{\sqrt{5 + 2 \sqrt{5}}}{5}$ | $\dfrac{\sqrt{50 - 10 \sqrt{5}}}{5}$ | $1 + \sqrt{5}$ |
| $\dfrac{\pi}{8}$ | $22.5^\circ$ | $\dfrac{\sqrt{2 - \sqrt{2}}}{2}$ | $\dfrac{\sqrt{2 + \sqrt{2}}}{2}$ | $\sqrt{2} - 1$ | $\sqrt{2} + 1$ | $\sqrt{4 - 2 \sqrt{2}}$ | $\sqrt{4 + 2 \sqrt{2}}$ |
| $\dfrac{\pi}{6}$ | $30^\circ$ | $\dfrac{1}{2}$ | $\dfrac{\sqrt{3}}{2}$ | $\dfrac{1}{\sqrt{3}}$ | $\sqrt{3}$ | $\dfrac{2}{\sqrt{3}}$ | $2$ |
| $\dfrac{\pi}{5}$ | $36^\circ$ | $\dfrac{\sqrt{10 - 2 \sqrt{5}}}{4}$ | $\dfrac{1 + \sqrt{5}}{4}$ | $\dfrac{\sqrt{5 - 2 \sqrt{5}}}{5}$ | $\dfrac{\sqrt{25 + 10 \sqrt{5}}}{5}$ | $\dfrac{\sqrt{5} - 1}{2}$ | $\dfrac{\sqrt{50 + 10 \sqrt{5}}}{5}$ |
| $\dfrac{\pi}{4}$ | $45^\circ$ | $\dfrac{\sqrt{2}}{2}$ | $\dfrac{\sqrt{2}}{2}$ | $1$ | $1$ | $\sqrt{2}$ | $\sqrt{2}$ |
| $\dfrac{3\pi}{10}$ | $54^\circ$ | $\dfrac{1 + \sqrt{5}}{4}$ | $\dfrac{\sqrt{10 - 2 \sqrt{5}}}{4}$ | $\dfrac{\sqrt{25 + 10 \sqrt{5}}}{5}$ | $\sqrt{5 - 2 \sqrt{5}}$ | $\dfrac{\sqrt{50 + 10 \sqrt{5}}}{5}$ | $\sqrt{5} - 1$ |
| $\dfrac{\pi}{3}$ | $60^\circ$ | $\dfrac{\sqrt{3}}{2}$ | $\dfrac{1}{2}$ | $\sqrt{3}$ | $\dfrac{1}{\sqrt{3}}$ | $2$ | $\dfrac{2}{\sqrt{3}}$ |
| $\dfrac{3\pi}{8}$ | $67.5^\circ$ | $\dfrac{\sqrt{2 + \sqrt{2}}}{2}$ | $\dfrac{\sqrt{2 - \sqrt{2}}}{2}$ | $\sqrt{2} + 1$ | $\sqrt{2} - 1$ | $4 + 2 \sqrt{2}$ | $4 - 2 \sqrt{2}$ |
| $\dfrac{2\pi}{5}$ | $72^\circ$ | $\dfrac{\sqrt{10 + 2 \sqrt{5}}}{4}$ | $\dfrac{\sqrt{5} - 1}{4}$ | $\sqrt{5 + 2 \sqrt{5}}$ | $\dfrac{\sqrt{25 - 10 \sqrt{5}}}{5}$ | $1 + \sqrt{5}$ | $\dfrac{\sqrt{50 - 10 \sqrt{5}}}{5}$ |
| $\dfrac{5\pi}{12}$ | $75^\circ$ | $\dfrac{\sqrt{2}}{4} (\sqrt{3} + 1)$ | $\dfrac{\sqrt{2}}{4} (\sqrt{3} - 1)$ | $2 + \sqrt{3}$ | $2 - \sqrt{3}$ | $\sqrt{2}(\sqrt{3} + 1)$ | $\sqrt{2}(\sqrt{3} - 1)$ |
| $\dfrac{\pi}{1}$ | $90^\circ$ | $1$ | $0$ | $\infty$ | $0$ | $\infty$ | $1$ |