Trigonometry - textbook question. I have coordinates in X/Y/Z, which
are all points on the surface of a sphere radius 1. The coordinates
can also be put in longitude/latitude if necessary.

I want to rotate these coordinates on the sphere so that the central
coordinate is located at X=0,Y=0,Z=1. (or the North Pole Lat=90
long=?)

From memory this should be a matrix multiplication problem with
cos*sin answers?

I would like the solution in the form of 3 equations (newX=
fn(oldX/oldY/oldZ) etc if possible.

Hi, your explanation is not clear and confused. Since you need to
center move from (0,0,0) to (0,0 1). It is a tranlation instead of a
rotation.
 
 And, the trasformation
 x' = x
 y' = y
 z' = z - 1 will satisfy what you need.
 
 Yes, rotation relates to matrix multiplication such as

 [ cos x  -sin x 0 ]
 [ sin x  cos x  0 ]
 [ 0       0     1 ]
 it means rotating x angle about the z axis.

 Kenny

I apologise if I was not clear. I want to do more than rotate around
the Z axis.

An example would be, I have spherical coordinates of all the cities in
Europe.
The centre of these coordinates would be say somewhere in France.

I want to rotate the coordinates such that they are around the North
Pole - just like turning a globe but in Latitude and Longitude.
In polar coordinates it is rotation in two angles, something like
first rotating (minus longitude) then (90-latitude) degrees.

Furthermore, the rotation is around (0,0,0) for all the coordinates on
the sphere (which are distance 1 from the spherical centre).

As a further example, I have a ball with a smiley face painted on one
side in many dots including one dot for the nose. eg all the
coordinates of the smiley face might be X>0 with varying Y and Z. I
want to rotate the ball around the centre of the ball such that the
nose 'dot' of the smiley face is pointing up, and apply the same
rotation formula to all the other dots too getting their new X/Y/Z
numbers.

It is a spherical rotation from XYZ to X1Y1Z1 by 2 angles I need the
functions for.