i have a very confusing result, which i will not explain because i'd rather you try it yourself. consider:

x is an arbitrary vector in R^n-1 such that ||x|| < 2*pi
y is a vector in R^n, such that ||y|| == 1

given x, y is defined as:
y = (   sinc(||x||/2) * x^T/2,     cos(||x||/2)   )^T

(note that there is an error in HZ pg 625 in case you check this against it; the above is correct)

exercise: try to find the jacobian dy/dx.