Author: Rafael Losada Liste

Centro:

Radio:

Plano tangente en P

x =

y =

α =

β =

α

Ver solo un huso

Esfera

β

PUNTO P

VECTOR CP

LONGITUD

COLATITUD

Centrar esfera

r: 4
C: (1, 2, 0)
a = Sphere(C, r)
texto1 = LaTeX(a, true, false)
CasillaDeEntrada1 = Textfield(C)
CasillaDeEntrada2 = Textfield(r)
c = false
x1 = 2
y1 = 3
z1: z(C) + sqrt(r^(2) - (x1 - x(C))^(2) - (y1 - y(C))^(2))
z2: z(C) - sqrt(r^(2) - (x1 - x(C))^(2) - (y1 - y(C))^(2))
P1: (x1, y1, z1)
P2: (x1, y1, z2)
CasillaDeEntrada3 = Textfield(x1)
CasillaDeEntrada4 = Textfield(y1)
texto2: "P " + P1 + ""
op = 1
texto3: "P " + P2 + ""
P = If(op ≟ 1, P1, P2)
v = Vector(C, P)
texto5 = LaTeX(v, true, true)
α = 0.7853981633974483 rad
CasillaDeEntrada5 = Textfield(α)
β = 0.3613671239067079 rad
CasillaDeEntrada6 = Textfield(β)
b: (x(v) * (x - x(P))) + (y(v) * (y - y(P))) + (z(v) * (z - z(P))) = 0
texto6 = LaTeX(b, true, false)
e: sqrt(15) + 2
d2 = CurveCartesian(x(C) + (r * cos(t)), y(C) + (r * sin(t)), z(C), t, 0, (2 * π))
f: asin(sqrt(15) / 4)
β1: ((acos(z(v) / r) * 180) * ° / π)
α1 = If(x(v) ≟ 0, 90°, ((atan(y(v) / x(v)) * 180) * ° / π))
P': (x(P), y(P), z(C))
g = Segment(P, P')
h = Segment(P', C)
B: C + (r, 0, 0)
i = Ray(C, P')
E, A = Intersect(i, a)
j = Segment(P', E)
γ = Angle(B, C, E)
texto7: "Ecuaciones paramétricas:
x = " + (x(C)) + "+ " + r + " cos(α) sen(β)
y = " + (y(C)) + "+ " + r + " sen(α) sen(β)
z = " + (z(C)) + "+ " + r + " cos(β) "
l = true
m = true
d = CurveCartesian(x(C) + (r * sin(t)), y(C), z(C) + (r * cos(t)), t, 0, π)
n = Segment(C, B)
d1 = CurveCartesian(x(C) + ((r * sin(t)) * cos(α)), y(C) + ((r * sin(t)) * sin(α)), z(C) + (r * cos(t)), t, 0, π)
F: (x(C), y(C), z(C) + r)
δ = Angle(P, C, F)
k = Surface(x(C) + ((r * cos(u)) * sin(v)), y(C) + ((r * sin(u)) * sin(v)), z(C) + (r * cos(v)), u, 0, α, v, 0, π)
F': (x(C), y(C), z(C) - r)
p = Segment(F, F')
texto10 = If(op ≟ 1, texto2, texto3)