sin(α)

r=1

cos(α)

α

tan(α)

tan(ε)

sin(γ)

sin(α)

cos(α)

tan(α)

2. Lösung

2. Lösung

2. Lösung

Spiegeln

Spiegeln

Spiegeln

IV

III

I

II

α = 0.6981317007977318 rad (slider from 0 to 6.283185307179586, step 1°)
gl1: x^(2) + y^(2) = 1
A = Point({cos(α), sin(α)})
B = Point({x(A), 0})
O = Point({0, 0})
C = Point({((-x(A)), y(A))})
D = Point({x(A), (-y(A))})
E = Point({1, tan(α)})
F = Point({-1, (-tan(α + 180°))})
f = Segment(B, A)
g = Segment(O, A)
h = Segment(O, B)
β_{1} = Angle((1, 0), O, A)
a: sin(α)
Text1: "sin(" + α + ")=" + a + ""
b: cos(α)
Text2: "cos(" + α + ")=" + b + ""
c: tan(α)
d: (1.002^(20) * 10000)
e(x, y) = x ≥ 0 ∧ y ≥ 0
k(x, y) = x ≥ 0 ∧ y ≤ 0
l(x, y) = x ≤ 0 ∧ y ≥ 0
m(x, y) = x ≤ 0 ∧ y ≤ 0
G = Point({1, 0})
H = Point({-1, 0})
j = If(α ≤ 90° ∨ α ≥ 270°, Segment[G, E], Segment[H, F])
i = If(α ≤ 90° ∨ α ≥ 270°, Segment[O, E], Segment[O, F])
n = 1.19175 (slider from -5 to 5)
p = If(α ≤ 90° ∨ α ≥ 270°, Segment[O, F], Segment[O, E])
q = If(α ≤ 90° ∨ α ≥ 270°, Segment[H, F], Segment[G, E])
r = Segment(A, C)
s = Segment((-B), C)
t = Segment(O, C)
f_1 = Segment(B, D)
g_1 = Segment(O, D)
o = false
h_1 = Segment(B, A)
u = false
v = true
w = false
γ = Angle(G, O, C)
a_1 = true
β = Angle(G, O, D)
b_1 = true
ε = If(x(A) ≥ 0, Angle[G, O, F], Angle[G, O, E])
c_1: sin(γ)
Text4: "γ=" + γ + " ⇒ sin(" + γ + ")=" + c_1 + ""
d_1: cos(β)
e_1: tan(ε)
Text6: "ε=" + ε + " ⇒ tan(" + ε + ")=" + e_1 + ""
Text5: "β = " + β + " ⇒ cos(" + β + ")=" + d_1 + ""
i_1 = false
j_1 = Segment(O, G)
k_1 = false
l_1 = true
I = (-1.5195421847038617, -4.981261158037942)
J = (3.8122172041237468, -4.981261158037942)
K = (-0.9641505817009848, -4.904784955002183)
L = (4.367608807126629, -4.904784955002183)
Text3: "tan(" + (LaTeX[α]) + ")=\frac{sin(" + (LaTeX[α]) + ")}{cos(" + (LaTeX[α]) + ")}=" + (LaTeX[c]) + ""