If we had two waves perpendicular to each other, with equations:
$x=α \sin(ωt)$ (1)
$y=β \sin(ωt+π/2) ==> y=β \cos(ωt)$(2)
Now how can we find the path equation of a point when one wave interfere in an angle $π/4$ with the other?.
I found that the equation of a $\sin()$ function in $θ$ rad can be found here: http://mathman.biz/html/rotatingsine.html