I have been trying to understand HOW one arrives at the equations
$z=−sin(c)$ of the loxodrome.
I can see that if the transformation to spherical coordinates is
then the "loxodromic equations" above are the derivative of the transformation with respect to $ϕ$ and then replacing $\theta$ with $t$ and $\phi$ with $c$.
Could someone make sense out of this? Thanks!