Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sin^{10}{\left(x \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
$$x_{2} = \pi$$
Numerical solution$$x_{1} = -50.2324868643099$$
$$x_{2} = -78.4770869973023$$
$$x_{3} = -37.7050845774162$$
$$x_{4} = -72.2246959176148$$
$$x_{5} = 0$$
$$x_{6} = -75.4384341141264$$
$$x_{7} = -65.9767997500511$$
$$x_{8} = 78.5063807665967$$
$$x_{9} = 59.7284836024868$$
$$x_{10} = 34.5221271875178$$
$$x_{11} = 12.5300063809925$$
$$x_{12} = 21.9922667177402$$
$$x_{13} = 65.9767997500161$$
$$x_{14} = 28.2714767215875$$
$$x_{15} = 84.7607022787199$$
$$x_{16} = -15.7128978925504$$
$$x_{17} = -31.4542226523405$$
$$x_{18} = 100.498513288837$$
$$x_{19} = -9.46211027265062$$
$$x_{20} = 72.2558523684046$$
$$x_{21} = 81.7206614302856$$
$$x_{22} = -94.2169095008228$$
$$x_{23} = -81.6894562305931$$
$$x_{24} = -97.4205438221578$$
$$x_{25} = 6.26279749505248$$
$$x_{26} = 56.5142520241778$$
$$x_{27} = -97.4305329626649$$
$$x_{28} = -34.4931251477632$$
$$x_{29} = 6.2792892384702$$
$$x_{30} = -59.6972707217566$$
$$x_{31} = 15.7441111366748$$
$$x_{32} = -43.9845333346793$$
$$x_{33} = -28.2402825408958$$
$$x_{34} = -56.4851017371817$$
$$x_{35} = 50.2636644628673$$
$$x_{36} = -21.9922667177402$$
$$x_{37} = -6.24808314337863$$
$$x_{38} = -100.469080855946$$
$$x_{39} = 87.9603746328622$$
$$x_{40} = 40.7768097416968$$
$$x_{41} = -72.2774086724237$$
$$x_{42} = 62.7687524265754$$
$$x_{43} = 94.2480403442937$$
$$x_{44} = 37.7363001125115$$
$$x_{45} = 87.9690658629265$$
$$x_{46} = -12.5716694317032$$
$$x_{47} = 6.2418172277331$$
$$x_{48} = -87.9690658638002$$
$$x_{49} = -53.4463306387129$$
$$x_{50} = 18.7848743105356$$
$$x_{51} = 43.9845333346789$$