Trigonometry Angles--Pi/16
[画像:cos(pi/(16))] = 1/2sqrt(2+sqrt(2+sqrt(2)))
(1)
[画像:cos((3pi)/(16))] = 1/2sqrt(2+sqrt(2-sqrt(2)))
(2)
[画像:cos((5pi)/(16))] = 1/2sqrt(2-sqrt(2-sqrt(2)))
(3)
[画像:cos((7pi)/(16))] = 1/2sqrt(2-sqrt(2+sqrt(2)))
(4)
[画像:cot(pi/(16))] = +1+sqrt(2)+sqrt(4+2sqrt(2))
(5)
[画像:cot((3pi)/(16))] = -1+sqrt(2)+sqrt(4-2sqrt(2))
(6)
[画像:cot((5pi)/(16))] = +1-sqrt(2)+sqrt(4-2sqrt(2))
(7)
[画像:cot((7pi)/(16))] = -1-sqrt(2)+sqrt(4+2sqrt(2))
(8)
[画像:csc(pi/(16))] = sqrt(8+4sqrt(2)+2sqrt(20+14sqrt(2)))
(9)
[画像:csc((3pi)/(16))] = sqrt(8-4sqrt(2)+2sqrt(20-14sqrt(2)))
(10)
[画像:csc((5pi)/(16))] = sqrt(8-4sqrt(2)-2sqrt(20-14sqrt(2)))
(11)
[画像:csc((7pi)/(16))] = sqrt(8+4sqrt(2)-2sqrt(20+14sqrt(2)))
(12)
[画像:sec(pi/(16))] = sqrt(8+4sqrt(2)-2sqrt(20+14sqrt(2)))
(13)
[画像:sec((3pi)/(16))] = sqrt(8-4sqrt(2)-2sqrt(20-14sqrt(2)))
(14)
[画像:sec((5pi)/(16))] = sqrt(8-4sqrt(2)+2sqrt(20-14sqrt(2)))
(15)
[画像:sec((7pi)/(16))] = sqrt(8+4sqrt(2)+2sqrt(20+14sqrt(2)))
(16)
[画像:sin(pi/(16))] = 1/2sqrt(2-sqrt(2+sqrt(2)))
(17)
[画像:sin((3pi)/(16))] = 1/2sqrt(2-sqrt(2-sqrt(2)))
(18)
[画像:sin((5pi)/(16))] = 1/2sqrt(2+sqrt(2-sqrt(2)))
(19)
[画像:sin((7pi)/(16))] = 1/2sqrt(2+sqrt(2+sqrt(2)))
(20)
[画像:tan(pi/(16))] = sqrt(4+2sqrt(2))-sqrt(2)-1
(21)
[画像:tan((3pi)/(16))] = sqrt(4-2sqrt(2))-sqrt(2)+1
(22)
[画像:tan((5pi)/(16))] = sqrt(4-2sqrt(2))+sqrt(2)-1
(23)
[画像:tan((7pi)/(16))] = sqrt(4+2sqrt(2))+sqrt(2)+1.
(24)
These can be derived from the half-angle formulas
= [画像:sqrt(1/2(1-cospi/8))]
(26)
= [画像:sqrt(1/2(1-1/2sqrt(2+sqrt(2))))]
(27)
= [画像:sqrt(1/2-1/4sqrt(2+sqrt(2)))]
(28)
= 1/2sqrt(2-sqrt(2+sqrt(2)))
(29)
= [画像:sqrt(1/2(1+cospi/8))]
(31)
= [画像:sqrt(1/2(1+1/2sqrt(2+sqrt(2))))]
(32)
= [画像:sqrt(1/2+1/4sqrt(2+sqrt(2)))]
(33)
= 1/2sqrt(2+sqrt(2+sqrt(2)))
(34)
= sqrt(4+2sqrt(2))-sqrt(2)-1.
(36)
See also
Hexadecagon, Trigonometry Angles, Trigonometry, Trigonometry Angles--Pi/8Explore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Trigonometry Angles--Pi/16." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TrigonometryAnglesPi16.html