I'm struggling to understand the solution of the following question:
"The real electric field of the simplest monochromatic spherical wave in the source free vacuum which is allowed by Maxwell Theory is:"
$$E(r, \theta, \phi, t)= A \frac{\sin \theta}{r}[\cos (kr- \omega t)-(kr)^{-1} \sin{(kr- \omega t)}]n_{\phi}$$
"Show that the surfaces of constant phase are spheres"
The solution simply claims "The condition constant phase kr = ωt is the definition equation of a sphere". $k = \frac{2 \pi }{\lambda}$ is the wave number, $\omega = 2 \pi f$ the angular frequency, $t$ the time and $r$ the radius. I really have some troubles understanding how $k r= \omega t$ really describes a sphere. Any help/ hint would be greatly appreciated.