Trigonometry in the hand (trigonometrie in the fingers)
Author: Daniel Mentrard

 \frac{ π }{6 } 

 \frac{ π }{4 } 

 \frac{ π }{3 } 

 \frac{ π }{2 } 

 \frac{ π }{6 } 

 \frac{ π }{4 } 

 \frac{ π }{3 } 

 \frac{ π }{2 } 

0

0

1

2

3

4

sin \frac{π }{2} \;  = \;    \frac{  \sqrt{ 4 }  }{ 2} \;   = \;  \frac{ 2 }{2 }  \; = \; 1

sin \frac{π }{3} \;  = \;    \frac{  \sqrt{ 3}  }{ 2} 

sin \frac{π }{4} \;  = \;    \frac{  \sqrt{ 2 }  }{ 2}

sin \frac{π }{6} \;  = \;    \frac{  \sqrt{ 1}  }{ 2}  \; = \;  \frac{ 1 }{2 } 

Pas de doigt en dessous

sin 0  \; =  \;  \frac{  \sqrt{ 0}  }{ 2}  \; =  \; 0

Sinus

Cosinus

1

2

3

4

cos \frac{π }{4} \;  = \;    \frac{  \sqrt{ 2}  }{ 2}

cos \frac{π }{3} \;  = \;    \frac{  \sqrt{ 1}  }{ 2} \; =  \;  \frac{ 1 }{ 2} 

Pas de doigt au dessus

cos \frac{ π }{2 } \;  = \;  \frac{  \sqrt{ 0 }  }{ 2}  \; =  \; 0

cos \frac{π }{6} \;  = \;    \frac{  \sqrt{3}  }{ 2}

cos 0 \;  = \;    \frac{  \sqrt{ 4}  }{ 2} \; = \;  \frac{ 2 }{2 }  \; = \; 1

Fonctionnement

Une méthode

Le \;  sinus  \; de  \; l'angle \;  est  \; égal \;  à \;  \frac{ \sqrt{ Nombre \;  de  \; doigts \;  en  \; dessous }   }{2 } 

Le \;  cosinus  \; de  \; l'angle \;  est  \; égal \;  à \;  \frac{ \sqrt{ nombre \;  de  \; doigts \;  au  \; dessus }   }{2 }

Sine  \; of  \; the \; angle \;  is \; equal \; at \;  \frac{ \sqrt{ Number \;  of  \; fingers \;  under }   }{2 } 

Cosine  \; of  \; the \; angle \;  is \; equal \; at \;  \frac{ \sqrt{ Number \;  of  \; fingers \;  above }   }{2 } 

Method

Operation

Sine

Cosine

No finger under

No finger above

French/Français

English/Anglais

Seno

Coseno

Seno \; del \; ángulo: \frac{\sqrt{No \; de \; dedos \; abajo}}{2}

Coseno \; del \; ángulo: \frac{\sqrt{No \; de \; dedos \; arriba}}{2}

A = Point(xAxis)
B = Point(xAxis)
a = Segment(B, A)
E = (-3.7298238970807454, -4.7328070301397505)
F = (5.911786810574536, -4.7328070301397505)
A'_1 = Rotate(A, 30*°, B)
α = Angle(A, B, A'_1)
c = Ray(B, A'_1)
A'_2 = Rotate(A, 45*°, B)
β = Angle(A, B, A'_2)
d = Ray(B, A'_2)
A'_3 = Rotate(A, 60*°, B)
γ = Angle(A, B, A'_3)
e = Ray(B, A'_3)
b = OrthogonalLine(B, a)
g = Segment(F, E)
h = OrthogonalLine(E, g)
C = Point(h)
f = Circle(B, a)
D, G = Intersect(f, b)
H = (12.844458476739133, -0.5018726940217355)
k = Circle(H, a)
u = Vector(B, H)
I = Translate(A'_1, u)
J = Translate(A'_2, u)
A'' = Translate(A'_3, u)
G' = Translate(G, u)
A' = Translate(A, u)
i = Segment(H, A')
F' = Translate(F, u)
E' = Translate(E, u)
C' = Translate(C, u)
Ángulo = 3 (slider from 0 to 4, step 1)
l = Segment(H, I)
n = Segment(H, J)
p = Segment(H, A'')
q = Segment(H, A')
r = Segment(H, G')
s = Segment(B, A'_1)
t = Segment(B, A'_2)
a_1 = Segment(B, A'_3)
c_1 = Segment(B, A)
j = Segment(B, G)
d_1 = CircleArc(B, A, G)
b_1 = Segment(H, G')
e_1 = CircleArc(H, A', G')
m = 1 (slider from 0 to 1, step 1)
K: H - (-1, 2)
Liste1: {1, 2, 3, 4}
texte21: "" + (Element[Liste1, Ángulo]) + " doigt(s) en dessous"
L: H - (-1, 1)
M = (8.796783010900624, 5.993798113431679)
N = (8.772545433260873, -5.979565240605585)
f_1 = Line(M, N)
liste2: {4, 3, 2, 1}
O = (7.269815619596277, 7.036013951940995)
P = (10.663076489161496, 7.036013951940995)
v = Vector(O, P)
texte30: "" + (Element[liste2, Ángulo + 1]) + " doigt(s) au dessus"
texte46: "" + (Element[liste2, Ángulo + 1]) + " finger(s) above"
texte48: "" + (Element[Liste1, Ángulo]) + " finger(s) under"