Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$- \sin{\left(x \right)} + \cos^{2}{\left(x \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{2} \right)}$$
$$x_{2} = 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{2} + \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$
Numerical solution$$x_{1} = -269.51072877623$$
$$x_{2} = -91.7724263865965$$
$$x_{3} = 88.6308337330067$$
$$x_{4} = -55.8824283321238$$
$$x_{5} = 25.7989806612109$$
$$x_{6} = -5.61694587468707$$
$$x_{7} = -60.3564998506986$$
$$x_{8} = 94.9140190401863$$
$$x_{9} = 52.740835678534$$
$$x_{10} = 19.5157953540313$$
$$x_{11} = 8.75853852827686$$
$$x_{12} = -66.6396851578782$$
$$x_{13} = -41.5069439291598$$
$$x_{14} = 21.324909142636$$
$$x_{15} = 90.4399475216115$$
$$x_{16} = -35.2237586219802$$
$$x_{17} = 15.0417238354565$$
$$x_{18} = 77.8735769072523$$
$$x_{19} = -49.5992430249442$$
$$x_{20} = -37.032872410585$$
$$x_{21} = 38.36535127557$$
$$x_{22} = -3.80783208608231$$
$$x_{23} = -16.3742027004415$$
$$x_{24} = -18.1833164890462$$
$$x_{25} = 0.666239432492515$$
$$x_{26} = 27.6080944498156$$
$$x_{27} = 96.7231328287911$$
$$x_{28} = -72.9228704650578$$
$$x_{29} = -54.073314543519$$
$$x_{30} = -22.6573880076211$$
$$x_{31} = -47.7901292363394$$
$$x_{32} = 76.0644631186476$$
$$x_{33} = 44.6485365827496$$
$$x_{34} = 6.9494247396721$$
$$x_{35} = 82.3476484258271$$
$$x_{36} = -99.8647254823809$$
$$x_{37} = -93.5815401752013$$
$$x_{38} = -68.4487989464829$$
$$x_{39} = 65.3072062928931$$
$$x_{40} = -11.9001311818667$$
$$x_{41} = -10.0910173932619$$
$$x_{42} = 33.8912797569952$$
$$x_{43} = 50.9317218899292$$
$$x_{44} = -24.4665017962258$$
$$x_{45} = -98.0556116937761$$
$$x_{46} = 46.4576503713544$$
$$x_{47} = -79.2060557722373$$
$$x_{48} = -43.3160577177646$$
$$x_{49} = -81.0151695608421$$
$$x_{50} = 63.4980925042884$$
$$x_{51} = -85.4892410794169$$
$$x_{52} = 2.47535322109728$$
$$x_{53} = -30.7496871034054$$
$$x_{54} = 32.0821659683904$$
$$x_{55} = 71.5903916000727$$
$$x_{56} = 40.1744650641748$$
$$x_{57} = 84.1567622144319$$
$$x_{58} = 103.006318135971$$
$$x_{59} = -62.1656136393034$$
$$x_{60} = 69.781277811468$$
$$x_{61} = -87.2983548680217$$