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Trigonometry Angles--Pi/18


The exact values of cos(pi/18) and sin(pi/18) can be given by infinite nested radicals

 sin(pi/(18))=1/2sqrt(2-sqrt(2+sqrt(2+sqrt(2-...)))),

where the sequence of signs +, +, - repeats with period 3, and

 cos(pi/(18))=1/6sqrt(3)(sqrt(8-sqrt(8-sqrt(8+sqrt(8-...))))+1),

where the sequence of signs -, -, + repeats with period 3.


See also

Trigonometry Angles, TrigonometryTrigonometry Angles--Pi/9

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Cite this as:

Weisstein, Eric W. "Trigonometry Angles--Pi/18." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TrigonometryAnglesPi18.html

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