Trigonometry Angles--Pi/32

[画像:cos(pi/(32))] = [画像:1/2sqrt(2+sqrt(2+sqrt(2+sqrt(2))))]

(1)

[画像:cos((3pi)/(32))] = [画像:1/2sqrt(2+sqrt(2+sqrt(2-sqrt(2))))]

(2)

[画像:cos((5pi)/(32))] = [画像:1/2sqrt(2+sqrt(2-sqrt(2-sqrt(2))))]

(3)

[画像:cos((7pi)/(32))] = [画像:1/2sqrt(2+sqrt(2-sqrt(2+sqrt(2))))]

(4)

[画像:cos((9pi)/(32))] = [画像:1/2sqrt(2-sqrt(2-sqrt(2+sqrt(2))))]

(5)

[画像:cos((11pi)/(32))] = [画像:1/2sqrt(2-sqrt(2-sqrt(2-sqrt(2))))]

(6)

[画像:cos((13pi)/(32))] = [画像:1/2sqrt(2-sqrt(2+sqrt(2-sqrt(2))))]

(7)

[画像:cos((15pi)/(32))] = [画像:1/2sqrt(2-sqrt(2+sqrt(2+sqrt(2))))]

(8)

[画像:sin(pi/(32))] = [画像:1/2sqrt(2-sqrt(2+sqrt(2+sqrt(2))))]

(9)

[画像:sin((3pi)/(32))] = [画像:1/2sqrt(2-sqrt(2+sqrt(2-sqrt(2))))]

(10)

[画像:sin((5pi)/(32))] = [画像:1/2sqrt(2-sqrt(2-sqrt(2-sqrt(2))))]

(11)

[画像:sin((7pi)/(32))] = [画像:1/2sqrt(2-sqrt(2-sqrt(2+sqrt(2))))]

(12)

[画像:sin((9pi)/(32))] = [画像:1/2sqrt(2+sqrt(2-sqrt(2+sqrt(2))))]

(13)

[画像:sin((11pi)/(32))] = [画像:1/2sqrt(2+sqrt(2-sqrt(2-sqrt(2))))]

(14)

[画像:sin((13pi)/(32))] = [画像:1/2sqrt(2+sqrt(2+sqrt(2-sqrt(2))))]

(15)

[画像:sin((15pi)/(32))] = [画像: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 Resource. https://mathworld.wolfram.com/TrigonometryAnglesPi32.html

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