1. ## Wind vector rotation

As described here - http://www.aprweather.com/pages/wind.htm the "u" component refers to the east-west component of the wind and the "v" component is the north-south component. I have been given the "u" and "v" component with respect to an earth coordinate reference system in terms of latitude and longitude and I need to transform this pair of vector into a new coordinate system whose north pole is defined not relative to the earth's north pole but relative to a "imaginary" north pole.
What I do believe is that the wind vector pair must transform together(as shown below) but I am not sure about the transformation and how to go about calculating it.
uNew = u*cos(rot) - v*sin(rot)

vNew = u*sin(rot) + v*cos(rot)
I am basically rotating around the z axis on the xy - plane(lat lon plane)
A combined wind vector needs to be obtained by first calculating the magnitude and the direction. Then the components of this wind vector need to be rotated into the new coordinate frame.

Is this approach correct ?

The u and v are functions of latitude and longitude on the surface of a sphere. So the question is how to construct spherical triangles such that the angle of rotation "rot" between the true north and rotated north pole is calculated. Once the appropriate spherical triangles are constructed the angle of rotation can be determined. How can i do this ?