11.7 Cylindrical and Spherical coordinates
Recall that in R we introduced polar coordinates
to locate points in the plane
x Polar
where roost r
RE
y rsint tant
Yy
We can use similar ideas in 1R space
x y z r 0 Z
Cartesian Cylindrical
where r f are the polar coordinates of My
f
xy.tl
ilny ray is thedistance
to the Z axis
, Cylindrical
coordinates are useful to describe a surface
very
with rotational symmetry around the Z axis ↑Eze
like a surface of revolution around the z axis
Example
Consider the line 1 in the yz plane
y
zn yI
i
If we rotate this aroundthe Z axis we get a cylinder
ya
i
I
what is the equation of the surface
Cartesian Note thatthesurface is defined thedistance
by
to the z axis beingconstant andequal to 1
so MY 1 or
xty 1
Recall that in R we introduced polar coordinates
to locate points in the plane
x Polar
where roost r
RE
y rsint tant
Yy
We can use similar ideas in 1R space
x y z r 0 Z
Cartesian Cylindrical
where r f are the polar coordinates of My
f
xy.tl
ilny ray is thedistance
to the Z axis
, Cylindrical
coordinates are useful to describe a surface
very
with rotational symmetry around the Z axis ↑Eze
like a surface of revolution around the z axis
Example
Consider the line 1 in the yz plane
y
zn yI
i
If we rotate this aroundthe Z axis we get a cylinder
ya
i
I
what is the equation of the surface
Cartesian Note thatthesurface is defined thedistance
by
to the z axis beingconstant andequal to 1
so MY 1 or
xty 1
