Tarea 2

1) Cambiar las coordenadas cilindricas dadas, a coordenadas rectangulares.

a)
x = r Cos ----> 5 Cos = 5 (0) = 0

y = r Sen ----> 5 Sen = 5 (1) = 5

z = z ----------------------------> = 3

P (0, 5, 3)

b)
x = r Cos ----> 6 Cos = 6 ( ) = 3

y = r Sen ----> 5 Sen = 6 =

z = z ----------------------------> = -5

P (3, , -5)

2) Cambiar las coordenadas rectangulares a coordenadas esfèricas.

a)

=2

Arctan =


Arctg = 1
Arctg = 45º
=







Cos =

P ()

b)

= 2

ArcTg =



ArcTg =

=







= 0

P(2, , )

3) Convertir las coordenadas esfèricas dadas a coordenadas cilìndricas.

a) Esfericas-Cartesianas

x =

= 4 Sen Cos

=(4) ( ) ()

= 1.73

y =

= 4Sen Sen

= (4) () ()

= 3

z =

= 4 Cos

= (4) ()

= 2
P (1.79, 3, 2)

Cartesianas-Cilindricas

r =

=

=

= 3.46

Arctg =

=

= 1.73

=

=

z = z

= 2

P(3.46, , 2)

b) Esfericas-Cartesianas

x =

= 2 Sen Cos

= (2) () ()

= 0.70

y =

= 2 Sen Sen

= (2) () ()

= 0.70

z =

= 2 Cos

= (2) ()

= -1.73

P(0.70, 0.70, -1.73)

r =

=

=

= 0.99

Arctg =

=

= 1

= 1

=

z = z

= -1.73

P(0.99, , -1.73)

4) Describir la grafica de la ecuacion en 3 dimensiones.

a)

=



z

P

b)

C(0, 0, 2)