evaluate the iterated integral. - washington and lee...
TRANSCRIPT
Evaluate the iterated integral.
Evaluate the iterated integral.
where G is the solid in the first octant that is bounded by the parabolic cylinder and the planes , and .
Evaluate the triple integral.
where G is the solid in the first octant that is bounded by the parabolic cylinder and the planes , and .
Evaluate the triple integral.
The wedge in the first octant that is cut from the solid cylinder by the planes and .
Use a triple integral to find the volume of the solid.
The wedge in the first octant that is cut from the solid cylinder by the planes and .
Use a triple integral to find the volume of the solid.
Let G be the solid enclosed by the surfaces in the accompanying figure. Fill in the missing limits of integration
(a)
(b)
Let G be the solid enclosed by the surfaces in the accompanying figure. Fill in the missing limits of integration
(a)
(b)
Let G be the solid enclosed by the surfaces in the accompanying figure. Fill in the missing limits of integration
(a)
(b)
Set up (but do not evaluate) an iterated triple integral for the volume of the solid enclosed between the given surfaces.
The elliptic cylinder and the planes and .
Set up (but do not evaluate) an iterated triple integral for the volume of the solid enclosed between the given surfaces.
The cylinders and .
Set up (but do not evaluate) an iterated triple integral for the volume of the solid enclosed between the given surfaces.
The cylinders and .
In each part, sketch the solid whose volume is given by the integral.
(a)
(c)
In each part, sketch the solid whose volume is given by the integral.
(a)
(c)
In each part, sketch the solid whose volume is given by the integral.
(a)
(c)
Cylindrical and Spherical Coordinates
r =!
x2 + y2
! = tan!1(y/x) (somtimes)
x = r cos !
y = r sin !
r = " sin #
x = " sin # cos !
y = " sin # sin !
z = " cos #
" =!
x2 + y2 + z2
Cylindrical and Spherical Coordinates
r =!
x2 + y2
! = tan!1(y/x) (somtimes)
x = r cos !
y = r sin !
r = " sin #
x = " sin # cos !
y = " sin # sin !
z = " cos #
" =!
x2 + y2 + z2
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical and Spherical Coordinates
r =!
x2 + y2
! = tan!1(y/x) (somtimes)
x = r cos !
y = r sin !
r = " sin #
x = " sin # cos !
y = " sin # sin !
z = " cos #
" =!
x2 + y2 + z2
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical and Spherical Coordinates
r =!
x2 + y2
! = tan!1(y/x) (somtimes)
x = r cos !
y = r sin !
r = " sin #
x = " sin # cos !
y = " sin # sin !
z = " cos #
" =!
x2 + y2 + z2
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical coordinates are really just the same as polarcoordinates (with a z).
There is no real reason to pretend like we are doing any-thing but polar coordinates except to complicate mattersfor students struggling with Calculus.
Spherical coordinates are a di!erent matter (literally).
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical Coordinates
r =!
x2 + y2
! = tan!1(y/x) (sometimes)
z = z
x = r cos !
y = r sin !
z = z
r = " sin #
x = " sin # cos !
y = " sin # sin !
z = " cos #
" =!
x2 + y2 + z2
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical Coordinates
r =!
x2 + y2
! = tan!1(y/x) (sometimes)
z = z
x = r cos !
y = r sin !
z = z
r = " sin #
x = " sin # cos !
y = " sin # sin !
z = " cos #
" =!
x2 + y2 + z2
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical Coordinates
r =!
x2 + y2
! = tan!1(y/x) (sometimes)
z = z
x = r cos !
y = r sin !
z = z
r = " sin #
x = " sin # cos !
y = " sin # sin !
z = " cos #
" =!
x2 + y2 + z2
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical Coordinates
r =!
x2 + y2
! = tan!1(y/x) (sometimes)
z = z
x = r cos !
y = r sin !
z = z
r = " sin #
x = " sin # cos !
y = " sin # sin !
z = " cos #
" =!
x2 + y2 + z2
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical Coordinates
r =!
x2 + y2
! = tan!1(y/x) (sometimes)
z = z
x = r cos !
y = r sin !
z = z
r = " sin #
x = " sin # cos !
y = " sin # sin !
z = " cos #
" =!
x2 + y2 + z2
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical Coordinates
r =!
x2 + y2
! = tan!1(y/x) (somtimes)
z = z
x = r cos !
y = r sin !
z = z
r = " sin #
x = " sin # cos !
y = " sin # sin !
z = " cos #
" =!
x2 + y2 + z2
r =!
x2 + y2
! = tan!1(y/x) (sometimes)
z = z
x = r cos !
y = r sin !
z = z
r = " sin #
x = " sin # cos !
y = " sin # sin !
z = " cos #
" =!
x2 + y2 + z2
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical Coordinates
r =!
x2 + y2
! = tan!1(y/x) (somtimes)
z = z
x = r cos !
y = r sin !
z = z
r = " sin #
x = " sin # cos !
y = " sin # sin !
z = " cos #
" =!
x2 + y2 + z2
r =!
x2 + y2
! = tan!1(y/x) (sometimes)
z = z
x = r cos !
y = r sin !
z = z
r = " sin #
x = " sin # cos !
y = " sin # sin !
z = " cos #
" =!
x2 + y2 + z2
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical Coordinates
r =!
x2 + y2
! = tan!1(y/x) (somtimes)
z = z
x = r cos !
y = r sin !
z = z
r = " sin #
x = " sin # cos !
y = " sin # sin !
z = " cos #
" =!
x2 + y2 + z2
Don’t forget me.
Don’t forget me.
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical Coordinates
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical CoordinatesSpherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical CoordinatesSpherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Don’t forget me.
What are r and !?
r = distance from z-axis
! = angle from positive x-axis
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical CoordinatesSpherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Don’t forget me.
What are r and !?
r = distance from z-axis
! = angle from positive x-axis
Don’t forget me.
What are r and !?
r = distance from z-axis
! = angle from positive x-axis
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical CoordinatesSpherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Don’t forget me.
What are r and !?
r = distance from z-axis
! = angle from positive x-axis
Don’t forget me.
What are r and !?
r = distance from z-axis
! = angle from positive x-axis
Don’t forget me.
What are r and !?
r = distance from z-axis
! = angle from positive x-axis
dV = "2 sin # d" d# d!
0 ! ! < 2$ 0 ! # ! $
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical CoordinatesSpherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Don’t forget me.
What are r and !?
r = distance from z-axis
! = angle from positive x-axis
Don’t forget me.
What are r and !?
r = distance from z-axis
! = angle from positive x-axis
Don’t forget me.
What are r and !?
r = distance from z-axis
! = angle from positive x-axis
dV = "2 sin # d" d# d!
0 ! ! < 2$ 0 ! # ! $
Don’t forget me.
What are r and !?
r = distance from z-axis
! = angle from positive x-axis
dV = "2 sin # d" d# d!
0 ! ! < 2$ 0 ! # ! $
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical CoordinatesSpherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Spherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
Conversion Formulas
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical CoordinatesSpherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Spherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
Conversion Formulas
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Spherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
Conversion Formulas
! =!
x2 + y2 + z2
r = ! sin "
z = ! cos "
x = ! sin " cos #
y = ! sin " sin #
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical CoordinatesSpherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Spherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
Conversion Formulas
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Spherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
Conversion Formulas
! =!
x2 + y2 + z2
r = ! sin "
z = ! cos "
x = ! sin " cos #
y = ! sin " sin #
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical CoordinatesSpherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Spherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
Conversion Formulas
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Spherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
Conversion Formulas
! =!
x2 + y2 + z2
r = ! sin "
z = ! cos "
x = ! sin " cos #
y = ! sin " sin #
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical CoordinatesSpherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Spherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
Conversion Formulas
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Spherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
Conversion Formulas
! =!
x2 + y2 + z2
r = ! sin "
z = ! cos "
x = ! sin " cos #
y = ! sin " sin #
Cylindrical coordinates are really just the sameas polar coordinates (with a z).
There is no real reason to pretend like we aredoing anything but polar coordinates except tocomplicate matters for students struggling withCalculus.
Spherical coordinates are a di!erent matter (lit-erally).
Cylindrical Coordinates
Spherical CoordinatesSpherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Spherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
Conversion Formulas
! =!
x2 + y2 + z2
r = ! sin "
x = ! sin " cos #
y = ! sin " sin #
z = ! cos "
Spherical Coordinates
! = distance from origin
" = angle from positive z-axis
# = same as before
Conversion Formulas
! =!
x2 + y2 + z2
r = ! sin "
z = ! cos "
x = ! sin " cos #
y = ! sin " sin #
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Don’t forget me.
What are r and !?
r = distance from z-axis
! = angle from positive x-axis
dV = "2 sin # d" d# d!
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.
Examples
Convert(x, y, z) = (1, 1, 0)
to cylindrical and spherical coordinates.
Convert(x, y, z) = (!1, !1, 0))
to cylindrical and spherical coordinates.
Convert(x, y, z) = (3, 4, !12))
to cylindrical and spherical coordinates.