Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sin{\left(x \right)} \cos^{4}{\left(x \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
$$x_{2} = \frac{\pi}{2}$$
$$x_{3} = \pi$$
$$x_{4} = \frac{3 \pi}{2}$$
Numerical solution$$x_{1} = 72.2566310325652$$
$$x_{2} = 94.2477796076938$$
$$x_{3} = -23.5624592548809$$
$$x_{4} = 80.1097338230489$$
$$x_{5} = 48.6936384544703$$
$$x_{6} = -15.707963267949$$
$$x_{7} = -37.6991118430775$$
$$x_{8} = 95.8191542378595$$
$$x_{9} = 51.8368083468028$$
$$x_{10} = 64.402225324733$$
$$x_{11} = -29.8448010550122$$
$$x_{12} = -81.6814089933346$$
$$x_{13} = -51.83599882721$$
$$x_{14} = 14.1377544028184$$
$$x_{15} = 6.28318530717959$$
$$x_{16} = -1.57128845156238$$
$$x_{17} = 50.2654824574367$$
$$x_{18} = -86.3942476952527$$
$$x_{19} = -73.8271873469416$$
$$x_{20} = 42.4110538406422$$
$$x_{21} = -36.1278886571281$$
$$x_{22} = -14.1367137375758$$
$$x_{23} = 7.85446073245193$$
$$x_{24} = -80.1102398600213$$
$$x_{25} = 36.12756931678$$
$$x_{26} = 29.8456347584674$$
$$x_{27} = 58.1200321773123$$
$$x_{28} = -89.5359702676269$$
$$x_{29} = -87.9645943005142$$
$$x_{30} = 15.707963267949$$
$$x_{31} = 92.6759646251107$$
$$x_{32} = -67.5448001650043$$
$$x_{33} = 70.6848013733878$$
$$x_{34} = 73.8279815042637$$
$$x_{35} = -45.5536298267302$$
$$x_{36} = -58.1190640304595$$
$$x_{37} = -94.2477796076938$$
$$x_{38} = -21.9911485751286$$
$$x_{39} = -7.85359154756817$$
$$x_{40} = -72.2566310325652$$
$$x_{41} = 87.9645943005142$$
$$x_{42} = 86.3933970305611$$
$$x_{43} = 43.9822971502571$$
$$x_{44} = 28.2743338823081$$
$$x_{45} = -86.392754643863$$
$$x_{46} = -43.9822971502571$$
$$x_{47} = -20.4207948804258$$
$$x_{48} = 36.1277548171785$$
$$x_{49} = -95.8183697328683$$
$$x_{50} = 65.9734457253857$$
$$x_{51} = 80.1114818379005$$
$$x_{52} = -65.9734457253857$$
$$x_{53} = -64.4015912708019$$
$$x_{54} = 0$$
$$x_{55} = 20.4198825810465$$
$$x_{56} = -59.6902604182061$$
$$x_{57} = 36.1288287787813$$
$$x_{58} = 21.9911485751286$$
$$x_{59} = 58.1198687108489$$
$$x_{60} = 14.1376257184341$$
$$x_{61} = 26.7024758752468$$
$$x_{62} = -100.530964914873$$