Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sin^{4}{\left(x \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
$$x_{2} = \pi$$
Numerical solution$$x_{1} = -75.399135702077$$
$$x_{2} = 12.5655386528631$$
$$x_{3} = -100.530131852098$$
$$x_{4} = -31.4167988656097$$
$$x_{5} = -53.4079673694574$$
$$x_{6} = 56.5478768483803$$
$$x_{7} = -97.3903038626381$$
$$x_{8} = 100.530215717383$$
$$x_{9} = -15.7080840961257$$
$$x_{10} = -94.2470163876969$$
$$x_{11} = -28.2735039765954$$
$$x_{12} = 94.247786003435$$
$$x_{13} = -50.2646745128884$$
$$x_{14} = -6.28233370088717$$
$$x_{15} = 59.691175606583$$
$$x_{16} = -65.9735393756143$$
$$x_{17} = 72.2566119325769$$
$$x_{18} = 50.2654378689882$$
$$x_{19} = -87.9647198526024$$
$$x_{20} = -9.42563019128159$$
$$x_{21} = 97.3891235063633$$
$$x_{22} = 21.991179696756$$
$$x_{23} = 6.283089833683$$
$$x_{24} = -6.28329572483107$$
$$x_{25} = -78.5408115487035$$
$$x_{26} = -21.9911797014772$$
$$x_{27} = 78.5390461988625$$
$$x_{28} = 34.556707666247$$
$$x_{29} = 81.682344881864$$
$$x_{30} = 0$$
$$x_{31} = 37.7000060867127$$
$$x_{32} = -37.6992579404428$$
$$x_{33} = -59.6904316816828$$
$$x_{34} = -276.460396846785$$
$$x_{35} = 28.2742638291305$$
$$x_{36} = 43.982359365339$$
$$x_{37} = 87.964718403403$$
$$x_{38} = 65.9735389544475$$
$$x_{39} = 15.7088363188216$$
$$x_{40} = -72.2558453147736$$
$$x_{41} = -43.98235944366$$
$$x_{42} = 97.3894444037214$$
$$x_{43} = -81.681605304824$$