Trigonometry Values Pi/18

The exact values of $\cos(\pi/18)$ and $\sin(\pi/18)$ are given by infinite Nested Radicals.

$\displaystyle \sin\left({\pi\over 18}\right)$	$\textstyle =$	$\displaystyle {\textstyle{1\over 2}}\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{2-\ldots}}}}$
	$\textstyle \approx$	$\displaystyle 0.17365,$

where the sequence of signs +, +,

repeats with period 3, and

$\displaystyle \cos\left({\pi\over 18}\right)$	$\textstyle =$	$\displaystyle {\textstyle{1\over 6}}\sqrt{3}\left({\sqrt{8-\sqrt{8-\sqrt{8+\sqrt{8-\ldots}}}}+1}\right)$
	$\textstyle \approx$	$\displaystyle 0.98481,$

where the sequence of signs

, + repeats with period 3.