Trigonometry Angles--Pi/12

[画像:cos(pi/(12))] = 1/4(sqrt(6)+sqrt(2))

(1)

[画像:cos((5pi)/(12))] = 1/4(sqrt(6)-sqrt(2))

(2)

[画像:cot(pi/(12))] = 2+sqrt(3)

(3)

[画像:cot((5pi)/(12))] = 2-sqrt(3)

(4)

[画像:csc(pi/(12))] = sqrt(6)+sqrt(2)

(5)

[画像:csc((5pi)/(12))] = sqrt(6)-sqrt(2)

(6)

[画像:sec(pi/(12))] = sqrt(6)-sqrt(2)

(7)

[画像:sec((5pi)/(12))] = sqrt(6)+sqrt(2)

(8)

[画像:sin(pi/(12))] = 1/4(sqrt(6)-sqrt(2))

(9)

[画像:sin((5pi)/(12))] = 1/4(sqrt(6)+sqrt(2))

(10)

[画像:tan(pi/(12))] = 2-sqrt(3)

(11)

[画像:tan((5pi)/(12))] = 2+sqrt(3).

(12)

These can be derived using

[画像:sin(pi/(12))] = [画像:sin(pi/3-pi/4)]

(13)

= [画像:-sin(pi/4)cos(pi/3)+sin(pi/3)cos(pi/4)]

(14)

= -1/2sqrt(2)(1/2)+1/2sqrt(3)(1/2sqrt(2))

(15)

= 1/4(sqrt(6)-sqrt(2)).

(16)

Similarly,

[画像:cos(pi/(12))] = [画像:cos(pi/3-pi/4)]

(17)

= [画像:cos(pi/4)cos(pi/3)-sin(pi/3)sin(pi/4)]

(18)

= 1/2(1/2sqrt(2))+1/2sqrt(3)(-1/2sqrt(2))

(19)

= 1/4(sqrt(6)+sqrt(2)).

(20)

See also

Trigonometry Angles, Trigonometry, Trigonometry Angles--Pi/3, Trigonometry Angles--Pi/4, Trigonometry Angles--Pi/6

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Cite this as:

Weisstein, Eric W. "Trigonometry Angles--Pi/12." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TrigonometryAnglesPi12.html

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