einheitskreisn

Einheitskreis

sin(α)

cos(α)

cos

sin

Spur

Animation

Graph

tan(α)

tan

gl1: x = -1
O: (0, 0)
MP: (-1, 0)
α = 0 rad (slider from 0° to 360°, step 1°)
O' = Rotate(O, α, MP)
h = OrthogonalLine(O', xAxis)
A = Intersect(h, xAxis)
A' = Rotate(A, 90°, MP)
EK = Circle((-1, 0), 1)
β = Angle(O, MP, O')
f = Segment(MP, O)
g = Segment(MP, O')
i = Segment(A, O')
j = Segment(A, MP)
P: (α, 0)
Text1: "" + (LaTeX[α]) + ""
a: (° * °°)
k = Line(O', xAxis)
l = OrthogonalLine(P, k)
B = Intersect(k, l)
m = Segment(O', B)
n = Segment(B, P)
C = Midpoint(n)
MP' = Rotate(MP, 90°, MP)
j' = Segment(A', MP')
p = OrthogonalLine(A', gl1)
c = CircleArc(MP, A, A')
D = Intersect(l, p)
q = Segment(A', D)
r = Segment(P, D)
E = Midpoint(r)
Text2: "" + (LaTeX[y(B)]) + ""
Text4: "" + (LaTeX[y(D)]) + ""
mitcos = false
mitsin = false
mitspur = false
s = Segment(A, O')
t = Segment(A, MP)
mitani = false
Ortslinie1 = Locus(B, α)
Ortslinie2 = Locus(D, α)
OP: (-1, 1)
LP: (-2, 0)
UP: (-1, -1)
b = Segment(OP, UP)
d = Segment(LP, MP)
mitgraph = false
j_1 = Line(MP, O')
F = Intersect(j_1, yAxis)
e = Segment(O, F)
f_1 = Line(F, xAxis)
g_1 = OrthogonalLine(P, f_1)
G = Intersect(f_1, g_1)
h_1 = Segment(P, G)
Text6: "" + (LaTeX[y(G)]) + ""
Ortslinie3 = Locus(G, α)
i_1 = Segment(MP, F)
k_1 = Segment(F, G)
mittan = false
H = Midpoint(P, G)
PP: H
tantextungenau: "tan(" + (LaTeX[α]) + ")\approx" + (LaTeX[y(G)]) + ""
costextungenau: "cos(" + (LaTeX[α]) + ")\approx" + (LaTeX[y(D)]) + ""
sintextungenau: "sin(" + (LaTeX[α]) + ")\approx" + (LaTeX[y(B)]) + ""
sintextgenau: "sin(" + (LaTeX[α]) + ")=" + (LaTeX[y(B)]) + ""
costextgenau: "cos(" + α + ")=" + (y(D)) + ""
tantextgenau: "tan(" + α + ")=" + (y(G)) + ""
γ = Angle(O', A, MP)
δ = Angle(MP, A, O')