# Table and FindRoot of a 2 variable function of x and t : cos(x + 3t)

I am trying implement mathematica commands: Table and FindRoot, of a 2 variable function cos(x + 3t) to find all the x values where the cosine function meets the x axis, i.e. cos(x + 3t) == 0, and the times, t, when this happens. Can someone indicate how this can be accomplished, or if it is possible within mathematica?

xInit = 0;
xmin = -4 Pi;
xmax = 4 Pi;
dx = 0.1;

tmin = 0;
tmax = 10;

Astep[x_, t_] := Cos[x + 3 t]

Union[Table[x /. FindRoot[Astep[x, t] == 0, {x, xInit, xmin, xmax}, {t, 0, tmin, tmax}], {xInit, xmin + dx, xmax - dx, dx}], SameTest -> Equal]


The error messages are:

FindRoot::nveq: The number of equations does not match the number of variables in FindRoot[Astep[x,t]==0,{x,xInit,xmin,xmax},{t,0,tmin,tmax}].

ReplaceAll::reps: {FindRoot[Astep[x,t]==0,{x,xInit,xmin,xmax},{t,0,tmin,tmax}]} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing.

General::stop: Further output of FindRoot::nveq will be suppressed during this calculation.


Table[{t, x /. NSolve[{Astep[x, t] == 0, -4 Pi < x < 4 Pi}, x]}, {t,1, 10}]