fsolve() crash with given Interval

[parisse]

In radians your system becomes:

Code:

eq:=[-0.84=0.3912*cos(x)+0.3824*cos(y)+0.3606*cos(225/180*pi),0=0.3912*sin(x)+0.3824*sin(y)+0.3606*sin(225/180*pi)]

You can plot both curves, in Xcas

Code:

implicitplot(eq[0],[x=-0.4..5,y=-0.4..5]);implicitplot(eq[1],[x=-0.4..5,y=-0.4..5],color=red)

on the Prime in Adv Graphing or in Geometry with the implicitplot commands above.
It seems there are 2 intersection points in [0,2*pi]x[0,2*pi],

Code:

fsolve(eq,[x,y],[2.1,3.2]); fsolve(eq,[x,y],[3.2,2.1])

There is no way for a general system to find all solutions in a given rectangle, you must find initial guesses near intersection points then call fsolve with each initial point.
Approx solutions here [2.13760652067,3.33911049122] and [3.32352103537,2.12201706482].
This particular system could probably be solved by eliminating one variable using sin^2+cos^2=1.