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Trigonometry Angles--Pi/24

cos(pi/(24))=1/2sqrt(2+sqrt(2+sqrt(3)))
(1)
cos((5pi)/(24))=1/2sqrt(2+sqrt(2-sqrt(3)))
(2)
cos((7pi)/(24))=1/2sqrt(2-sqrt(2-sqrt(3)))
(3)
cos((11pi)/(24))=1/2sqrt(2-sqrt(2+sqrt(3)))
(4)
cot(pi/(24))=+2+sqrt(2)+sqrt(3)+sqrt(6)
(5)
cot((5pi)/(24))=+2-sqrt(2)-sqrt(3)+sqrt(6)
(6)
cot((7pi)/(24))=-2-sqrt(2)+sqrt(3)+sqrt(6)
(7)
cot((11pi)/(24))=-2+sqrt(2)-sqrt(3)+sqrt(6)
(8)
csc(pi/(24))=sqrt(16+10sqrt(2)+8sqrt(3)+6sqrt(6))
(9)
csc((5pi)/(24))=sqrt(16-10sqrt(2)-8sqrt(3)+6sqrt(6))
(10)
csc((7pi)/(24))=sqrt(16+10sqrt(2)-8sqrt(3)-6sqrt(6))
(11)
csc((11pi)/(24))=sqrt(16-10sqrt(2)+8sqrt(3)-6sqrt(6))
(12)
sec(pi/(24))=sqrt(16-10sqrt(2)+8sqrt(3)-6sqrt(6))
(13)
sec((5pi)/(24))=sqrt(16+10sqrt(2)-8sqrt(3)-6sqrt(6))
(14)
sec((7pi)/(24))=sqrt(16-10sqrt(2)-8sqrt(3)+6sqrt(6))
(15)
sec((11pi)/(24))=sqrt(16+10sqrt(2)+8sqrt(3)+6sqrt(6))
(16)
sin(pi/(24))=1/2sqrt(2-sqrt(2+sqrt(3)))
(17)
sin((5pi)/(24))=1/2sqrt(2-sqrt(2-sqrt(3)))
(18)
sin((7pi)/(24))=1/2sqrt(2+sqrt(2-sqrt(3)))
(19)
sin((11pi)/(24))=1/2sqrt(2+sqrt(2+sqrt(3)))
(20)
tan(pi/(24))=-2+sqrt(2)-sqrt(3)+sqrt(6)
(21)
tan((5pi)/(24))=-2-sqrt(2)+sqrt(3)+sqrt(6)
(22)
tan((7pi)/(24))=+2-sqrt(2)-sqrt(3)+sqrt(6)
(23)
tan((11pi)/(24))=+2+sqrt(2)+sqrt(3)+sqrt(6).
(24)

See also

Icositetragon, Trigonometry Angles, Trigonometry, Trigonometry Angles--Pi/12

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Cite this as:

Weisstein, Eric W. "Trigonometry Angles--Pi/24." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TrigonometryAnglesPi24.html

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