Exact values of the trig functions

Geometry

ValueSineCosineTangentProof
$ 3 \degree $ or $ \frac{1}{60} \pi \space \mathrm{rad} $$ \tfrac14 \sqrt{8 - \sqrt3 - \sqrt{15} - \sqrt{10 - 2\sqrt5}} $$ \tfrac14 \sqrt{8 + \sqrt3 + \sqrt{15} + \sqrt{10 - 2\sqrt5}} $$ \sqrt{\frac{8 - \sqrt3 - \sqrt{15} - \sqrt{10 - 2\sqrt5}}{8 + \sqrt3 + \sqrt{15} + \sqrt{10 - 2\sqrt5}}} $Read here
$ 15 \degree $ or $ \frac{1}{12} \pi \space \mathrm{rad} $$ \frac{1}{4} \sqrt{8 - 4\sqrt3} $$ \frac{1}{4} \sqrt{8 + 4\sqrt3} $$ \sqrt{7 - 4\sqrt3} $Read here
$ 18 \degree $ or $ \frac{1}{10} \pi \space \mathrm{rad} $$ \frac{1}{4} \sqrt{6 - 2\sqrt5} $$ \frac{1}{4} \sqrt{10 + 2\sqrt5} $$ \frac{1}{5} \sqrt{25 - 10\sqrt5} $Read here
$ 30 \degree $ or $ \frac{1}{6} \pi \space \mathrm{rad} $$ \frac{1}{2} $$ \frac{1}{2} \sqrt{3} $$ \frac{1}{3} \sqrt{3} $Read here
$ 36 \degree $ or $ \frac{1}{5} \pi \space \mathrm{rad} $$ \frac{1}{4} \sqrt{10 - 2\sqrt5} $$ \frac{1}{4} \sqrt{6 + 2\sqrt5} $$ \sqrt{5 - 2\sqrt5} $Read here
$ 45 \degree $ or $ \frac{1}{4} \pi \space \mathrm{rad} $$ \frac{1}{2} \sqrt{2} $$ \frac{1}{2} \sqrt{2} $$ 1 $Read here
$ 54 \degree $ or $ \frac{3}{10} \pi \space \mathrm{rad} $$ \frac{1}{4} \sqrt{6 + 2\sqrt5} $$ \frac{1}{4} \sqrt{10 - 2\sqrt5} $$ \frac{1}{5} \sqrt{25 + 10\sqrt5} $Read here
$ 60 \degree $ or $ \frac{1}{3} \pi \space \mathrm{rad} $$ \frac{1}{2} \sqrt{3} $$ \frac{1}{2} $$ \sqrt{3} $Read here