Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sin{\left(\frac{x}{3} \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
$$x_{2} = 3 \pi$$
Numerical solution$$x_{1} = 0$$
$$x_{2} = -18.8495559215388$$
$$x_{3} = -56.5486677646163$$
$$x_{4} = 47.1238898038469$$
$$x_{5} = 37.6991118430775$$
$$x_{6} = 65.9734457253857$$
$$x_{7} = -94.2477796076938$$
$$x_{8} = -75.398223686155$$
$$x_{9} = -9.42477796076938$$
$$x_{10} = -113.097335529233$$
$$x_{11} = -47.1238898038469$$
$$x_{12} = 28.2743338823081$$
$$x_{13} = -103.672557568463$$
$$x_{14} = -65.9734457253857$$
$$x_{15} = 94.2477796076938$$
$$x_{16} = 103.672557568463$$
$$x_{17} = 56.5486677646163$$
$$x_{18} = 84.8230016469244$$
$$x_{19} = 9.42477796076938$$
$$x_{20} = -84.8230016469244$$
$$x_{21} = 113.097335529233$$
$$x_{22} = 904.77868423386$$
$$x_{23} = -28.2743338823081$$
$$x_{24} = -37.6991118430775$$
$$x_{25} = 160.221225333079$$
$$x_{26} = 18.8495559215388$$
$$x_{27} = 75.398223686155$$