Trigonometry Angles--Pi/10
[画像:cos(pi/(10))] = 1/4sqrt(10+2sqrt(5))
(1)
[画像:cos((3pi)/(10))] = 1/4sqrt(10-2sqrt(5))
(2)
[画像:cot(pi/(10))] = sqrt(5+2sqrt(5))
(3)
[画像:cot((3pi)/(10))] = sqrt(5-2sqrt(5))
(4)
[画像:csc(pi/(10))] = 1+sqrt(5)
(5)
[画像:csc((3pi)/(10))] = sqrt(5)-1
(6)
[画像:sec(pi/(10))] = 1/5sqrt(50-10sqrt(5))
(7)
[画像:sec((3pi)/(10))] = 1/5sqrt(50+10sqrt(5))
(8)
[画像:sin(pi/(10))] = 1/4(sqrt(5)-1)
(9)
[画像:sin((3pi)/(10))] = 1/4(1+sqrt(5))
(10)
[画像:tan(pi/(10))] = 1/5sqrt(25-10sqrt(5))
(11)
[画像:tan((3pi)/(10))] = 1/5sqrt(25+10sqrt(5)).
(12)
To derive these formulas, use the half-angle formulas
= [画像:sqrt(1/2[1-cos(pi/5)])]
![画像:sqrt(1/2[1-cos(pi/5)])](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/TrigonometryAnglesPi10/Inline42.svg){kind=link}
(14)
= sqrt(1/2[1-1/4(1+sqrt(5))])
(15)
= 1/4(sqrt(5)-1)
(16)
= [画像:sqrt(1/2[1+cos(pi/5)])]
![画像:sqrt(1/2[1+cos(pi/5)])](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/TrigonometryAnglesPi10/Inline54.svg){kind=link}
(18)
= sqrt(1/2[1+1/4(1+sqrt(5))])
(19)
= 1/4sqrt(10+2sqrt(5))
(20)
= 1/5sqrt(25-10sqrt(5)).
(22)
See also
Decagon, Decagram, Trigonometry Angles, Trigonometry, Trigonometry Angles--Pi/5Explore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Trigonometry Angles--Pi/10." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TrigonometryAnglesPi10.html