El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(- \cos{\left(x \right)} + \frac{1}{2 \sin{\left(x \right)}}\right) - \sin{\left(x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = 2 \operatorname{atan}{\left(-1 + \sqrt{2} \sqrt{2 - \sqrt{2}} + \sqrt{2} \right)}$$
$$x_{2} = - 2 \operatorname{atan}{\left(1 + \sqrt{2} + \sqrt{2} \sqrt{\sqrt{2} + 2} \right)}$$
$$x_{3} = - 2 \operatorname{atan}{\left(- \sqrt{2} + 1 + \sqrt{2} \sqrt{2 - \sqrt{2}} \right)}$$
$$x_{4} = - 2 \operatorname{atan}{\left(- \sqrt{2} \sqrt{\sqrt{2} + 2} + 1 + \sqrt{2} \right)}$$
Solución numérica$$x_{1} = -73.4347282776614$$
$$x_{2} = -65.5807466436869$$
$$x_{3} = -29.4524311274043$$
$$x_{4} = -45.1603943953533$$
$$x_{5} = 71.0785337874691$$
$$x_{6} = 36.5210145979813$$
$$x_{7} = 17.6714586764426$$
$$x_{8} = 33.3794219443916$$
$$x_{9} = 82.0741080750334$$
$$x_{10} = -93.8550805259951$$
$$x_{11} = -38.8772090881737$$
$$x_{12} = -92.2842841992002$$
$$x_{13} = -82.8595062384308$$
$$x_{14} = 14.5298660228528$$
$$x_{15} = 66.3661448070844$$
$$x_{16} = 8.24668071567321$$
$$x_{17} = 75.7909227678538$$
$$x_{18} = 52.2289778659303$$
$$x_{19} = -87.5718952188155$$
$$x_{20} = -43.5895980685584$$
$$x_{21} = 60.0829594999048$$
$$x_{22} = -12.1736715326604$$
$$x_{23} = 74.2201264410589$$
$$x_{24} = 39.6626072515711$$
$$x_{25} = -100.138265833175$$
$$x_{26} = 53.7997741927252$$
$$x_{27} = -5.89048622548086$$
$$x_{28} = -51.4435797025329$$
$$x_{29} = -26.3108384738145$$
$$x_{30} = 42.8041999051609$$
$$x_{31} = -56.1559686829176$$
$$x_{32} = 80.5033117482384$$
$$x_{33} = -57.7267650097125$$
$$x_{34} = 49.0873852123405$$
$$x_{35} = -35.7356164345839$$
$$x_{36} = 11.388273369263$$
$$x_{37} = 31.8086256175967$$
$$x_{38} = 55.3705705195201$$
$$x_{39} = -16.8860605130451$$
$$x_{40} = 22.3838476568273$$
$$x_{41} = 5.10508806208341$$
$$x_{42} = 99.3528676697772$$
$$x_{43} = 83.6449044018282$$
$$x_{44} = -1.17809724509617$$
$$x_{45} = 1.96349540849362$$
$$x_{46} = -98.5674695063798$$
$$x_{47} = -60.8683576633022$$
$$x_{48} = 16.1006623496477$$
$$x_{49} = -76.5763209312512$$
$$x_{50} = 93.0696823625976$$
$$x_{51} = -54.5851723561227$$
$$x_{52} = -7.46128255227576$$
$$x_{53} = -4.31968989868597$$
$$x_{54} = 27.096236637212$$
$$x_{55} = 44.3749962319558$$
$$x_{56} = -78.1471172580461$$
$$x_{57} = -67.1515429704818$$
$$x_{58} = 61.6537558266997$$
$$x_{59} = 38.0918109247762$$
$$x_{60} = -48.3019870489431$$
$$x_{61} = 88.3572933822129$$
$$x_{62} = -27.8816348006094$$
$$x_{63} = 23.9546439836222$$
$$x_{64} = -89.1426915456104$$
$$x_{65} = -86.0010988920206$$
$$x_{66} = 9.8174770424681$$
$$x_{67} = 58.5121631731099$$
$$x_{68} = -21.5984494934298$$
$$x_{69} = -42.0188017417635$$
$$x_{70} = 45.9457925587507$$
$$x_{71} = 96.2112750161874$$
$$x_{72} = -10.6028752058656$$
$$x_{73} = -13.7444678594553$$
$$x_{74} = 20.8130513300324$$
$$x_{75} = -34.164820107789$$
$$x_{76} = -49.872783375738$$
$$x_{77} = 86.786497055418$$
$$x_{78} = -95.42587685279$$
$$x_{79} = 100.923663996572$$
$$x_{80} = 77.3617190946487$$
$$x_{81} = -64.009950316892$$
$$x_{82} = 64.7953484802895$$
$$x_{83} = -20.0276531666349$$
$$x_{84} = -23.1692458202247$$
$$x_{85} = 89.9280897090078$$
$$x_{86} = -70.2931356240716$$
$$x_{87} = 67.9369411338793$$
$$x_{88} = 30.2378292908018$$
$$x_{89} = -32.5940237809941$$
$$x_{90} = -71.8639319508665$$
$$x_{91} = -79.717913584841$$