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Trigonometry Angles--Pi/15

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👁 cos(pi/(15))
👁 =
👁 1/8(sqrt(30+6sqrt(5))+sqrt(5)-1)
(1)
👁 cos((2pi)/(15))
👁 =
👁 1/8(sqrt(30-6sqrt(5))+sqrt(5)+1)
(2)
👁 cos((4pi)/(15))
👁 =
👁 1/8(sqrt(30+6sqrt(5))-sqrt(5)+1)
(3)
👁 cos((7pi)/(15))
👁 =
👁 1/8(sqrt(30-6sqrt(5))-sqrt(5)-1)
(4)
👁 cot(pi/(15))
👁 =
👁 sqrt(7+2sqrt(5)+2sqrt(15+6sqrt(5)))
(5)
👁 cot((2pi)/(15))
👁 =
👁 sqrt(7-2sqrt(5)+2sqrt(15-6sqrt(5)))
(6)
👁 cot((4pi)/(15))
👁 =
👁 sqrt(7+2sqrt(5)-2sqrt(15+6sqrt(5)))
(7)
👁 cot((7pi)/(15))
👁 =
👁 sqrt(7-2sqrt(5)-2sqrt(15-6sqrt(5)))
(8)
👁 csc(pi/(15))
👁 =
👁 sqrt(8+2sqrt(5)+2sqrt(15+6sqrt(5)))
(9)
👁 csc((2pi)/(15))
👁 =
👁 sqrt(8-2sqrt(5)+2sqrt(15-6sqrt(5)))
(10)
👁 csc((4pi)/(15))
👁 =
👁 sqrt(8+2sqrt(5)-2sqrt(15+6sqrt(5)))
(11)
👁 csc((7pi)/(15))
👁 =
👁 sqrt(8-2sqrt(5)-2sqrt(15-6sqrt(5)))
(12)
👁 sec(pi/(15))
👁 =
👁 +2-sqrt(5)+sqrt(15-6sqrt(5))
(13)
👁 sec((2pi)/(15))
👁 =
👁 -2-sqrt(5)+sqrt(15+6sqrt(5))
(14)
👁 sec((4pi)/(15))
👁 =
👁 -2+sqrt(5)+sqrt(15-6sqrt(5))
(15)
👁 sec((7pi)/(15))
👁 =
👁 +2+sqrt(5)+sqrt(15+6sqrt(5))
(16)
👁 sin(pi/(15))
👁 =
👁 1/4sqrt(7-sqrt(5)-sqrt(30-6sqrt(5)))
(17)
👁 sin((2pi)/(15))
👁 =
👁 1/4sqrt(7+sqrt(5)-sqrt(30+6sqrt(5)))
(18)
👁 sin((4pi)/(15))
👁 =
👁 1/4sqrt(7-sqrt(5)+sqrt(30-6sqrt(5)))
(19)
👁 sin((7pi)/(15))
👁 =
👁 1/4sqrt(7+sqrt(5)+sqrt(30+6sqrt(5)))
(20)
👁 tan(pi/(15))
👁 =
👁 sqrt(23-10sqrt(5)-2sqrt(255-114sqrt(5)))
(21)
👁 tan((2pi)/(15))
👁 =
👁 sqrt(23+10sqrt(5)-2sqrt(255+114sqrt(5)))
(22)
👁 tan((4pi)/(15))
👁 =
👁 sqrt(23-10sqrt(5)+2sqrt(255-114sqrt(5)))
(23)
👁 tan((7pi)/(15))
👁 =
👁 sqrt(23+10sqrt(5)+2sqrt(255+114sqrt(5))).
(24)

These can be derived using the trigonometric addition formulas

and

See also

Pentadecagon, Trigonometry Angles, Trigonometry, Trigonometry Angles--Pi/6, Trigonometry Angles--Pi/10

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Cite this as:

Weisstein, Eric W. "Trigonometry Angles--Pi/15." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TrigonometryAnglesPi15.html

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