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Trigonometry Angles--Pi/32


cos(pi/(32))=1/2sqrt(2+sqrt(2+sqrt(2+sqrt(2))))
(1)
cos((3pi)/(32))=1/2sqrt(2+sqrt(2+sqrt(2-sqrt(2))))
(2)
cos((5pi)/(32))=1/2sqrt(2+sqrt(2-sqrt(2-sqrt(2))))
(3)
cos((7pi)/(32))=1/2sqrt(2+sqrt(2-sqrt(2+sqrt(2))))
(4)
cos((9pi)/(32))=1/2sqrt(2-sqrt(2-sqrt(2+sqrt(2))))
(5)
cos((11pi)/(32))=1/2sqrt(2-sqrt(2-sqrt(2-sqrt(2))))
(6)
cos((13pi)/(32))=1/2sqrt(2-sqrt(2+sqrt(2-sqrt(2))))
(7)
cos((15pi)/(32))=1/2sqrt(2-sqrt(2+sqrt(2+sqrt(2))))
(8)
sin(pi/(32))=1/2sqrt(2-sqrt(2+sqrt(2+sqrt(2))))
(9)
sin((3pi)/(32))=1/2sqrt(2-sqrt(2+sqrt(2-sqrt(2))))
(10)
sin((5pi)/(32))=1/2sqrt(2-sqrt(2-sqrt(2-sqrt(2))))
(11)
sin((7pi)/(32))=1/2sqrt(2-sqrt(2-sqrt(2+sqrt(2))))
(12)
sin((9pi)/(32))=1/2sqrt(2+sqrt(2-sqrt(2+sqrt(2))))
(13)
sin((11pi)/(32))=1/2sqrt(2+sqrt(2-sqrt(2-sqrt(2))))
(14)
sin((13pi)/(32))=1/2sqrt(2+sqrt(2+sqrt(2-sqrt(2))))
(15)
sin((15pi)/(32))=1/2sqrt(2+sqrt(2+sqrt(2+sqrt(2)))).
(16)

The functions cot(npi/32), csc(npi/32), sec(npi/32), and tan(npi/32) are roots of 8th degree polynomials, but the explicit expressions in terms of radicals are rather complicated.


See also

Icosidodecagon, Trigonometry Angles, Trigonometry, Trigonometry Angles--Pi/16

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Cite this as:

Weisstein, Eric W. "Trigonometry Angles--Pi/32." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TrigonometryAnglesPi32.html

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