# Exact values of the trig functions

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