sinx>abs(cosx) inequation

Given the inequality:
$$\sin{\left(x \right)} > \left|{\cos{\left(x \right)}}\right|$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(x \right)} = \left|{\cos{\left(x \right)}}\right|$$
Solve:
$$x_{1} = -36.9137136796801$$
$$x_{2} = 25.9181393921158$$
$$x_{3} = -16.4933614313464$$
$$x_{4} = -80.8960108299372$$
$$x_{5} = 52.621676947629$$
$$x_{6} = 96.6039740978861$$
$$x_{7} = -22.776546738526$$
$$x_{8} = 33.7721210260903$$
$$x_{9} = 95.0331777710912$$
$$x_{10} = -93.4623814442964$$
$$x_{11} = -11.7809724509617$$
$$x_{12} = 102.887159405066$$
$$x_{13} = 69.9004365423729$$
$$x_{14} = 2.35619449019234$$
$$x_{15} = -18.0641577581413$$
$$x_{16} = -74.6128255227576$$
$$x_{17} = 0.785398163397448$$
$$x_{18} = 58.9048622548086$$
$$x_{19} = -66.7588438887831$$
$$x_{20} = 88.7499924639117$$
$$x_{21} = 46.3384916404494$$
$$x_{22} = -3.92699081698724$$
$$x_{23} = 84.037603483527$$
$$x_{24} = 90.3207887907066$$
$$x_{25} = 13.3517687777566$$
$$x_{26} = 82.4668071567321$$
$$x_{27} = 63.6172512351933$$
$$x_{28} = -85.6083998103219$$
$$x_{29} = -98.174770424681$$
$$x_{30} = 19.6349540849362$$
$$x_{31} = -49.4800842940392$$
$$x_{32} = 65.1880475619882$$
$$x_{33} = 14.9225651045515$$
$$x_{34} = 40.0553063332699$$
$$x_{35} = 51.0508806208341$$
$$x_{36} = 71.4712328691678$$
$$x_{37} = 44.7676953136546$$
$$x_{38} = -99.7455667514759$$
$$x_{39} = -79.3252145031423$$
$$x_{40} = -91.8915851175014$$
$$x_{41} = 76.1836218495525$$
$$x_{42} = -68.329640215578$$
$$x_{43} = -60.4756585816035$$
$$x_{44} = 38.484510006475$$
$$x_{45} = 21.2057504117311$$
$$x_{46} = -30.6305283725005$$
$$x_{47} = 7.06858347057703$$
$$x_{48} = 77.7544181763474$$
$$x_{49} = -35.3429173528852$$
$$x_{50} = -795.608339521615$$
$$x_{51} = 57.3340659280137$$
$$x_{52} = -43.1968989868597$$
$$x_{53} = 107.59954838545$$
$$x_{54} = -24.3473430653209$$
$$x_{55} = -41.6261026600648$$
$$x_{56} = -3667.02402490269$$
$$x_{57} = -62.0464549083984$$
$$x_{58} = 27.4889357189107$$
$$x_{59} = -162.577419823272$$
$$x_{60} = 8.63937979737193$$
$$x_{61} = -87.1791961371168$$
$$x_{62} = -55.7632696012188$$
$$x_{63} = -5.49778714378214$$
$$x_{64} = -29.0597320457056$$
$$x_{65} = -10.2101761241668$$
$$x_{66} = 32.2013246992954$$
$$x_{67} = -73.0420291959627$$
$$x_{68} = -47.9092879672443$$
$$x_{69} = -54.1924732744239$$
$$x_{70} = -204.988920646734$$
$$x_{1} = -36.9137136796801$$
$$x_{2} = 25.9181393921158$$
$$x_{3} = -16.4933614313464$$
$$x_{4} = -80.8960108299372$$
$$x_{5} = 52.621676947629$$
$$x_{6} = 96.6039740978861$$
$$x_{7} = -22.776546738526$$
$$x_{8} = 33.7721210260903$$
$$x_{9} = 95.0331777710912$$
$$x_{10} = -93.4623814442964$$
$$x_{11} = -11.7809724509617$$
$$x_{12} = 102.887159405066$$
$$x_{13} = 69.9004365423729$$
$$x_{14} = 2.35619449019234$$
$$x_{15} = -18.0641577581413$$
$$x_{16} = -74.6128255227576$$
$$x_{17} = 0.785398163397448$$
$$x_{18} = 58.9048622548086$$
$$x_{19} = -66.7588438887831$$
$$x_{20} = 88.7499924639117$$
$$x_{21} = 46.3384916404494$$
$$x_{22} = -3.92699081698724$$
$$x_{23} = 84.037603483527$$
$$x_{24} = 90.3207887907066$$
$$x_{25} = 13.3517687777566$$
$$x_{26} = 82.4668071567321$$
$$x_{27} = 63.6172512351933$$
$$x_{28} = -85.6083998103219$$
$$x_{29} = -98.174770424681$$
$$x_{30} = 19.6349540849362$$
$$x_{31} = -49.4800842940392$$
$$x_{32} = 65.1880475619882$$
$$x_{33} = 14.9225651045515$$
$$x_{34} = 40.0553063332699$$
$$x_{35} = 51.0508806208341$$
$$x_{36} = 71.4712328691678$$
$$x_{37} = 44.7676953136546$$
$$x_{38} = -99.7455667514759$$
$$x_{39} = -79.3252145031423$$
$$x_{40} = -91.8915851175014$$
$$x_{41} = 76.1836218495525$$
$$x_{42} = -68.329640215578$$
$$x_{43} = -60.4756585816035$$
$$x_{44} = 38.484510006475$$
$$x_{45} = 21.2057504117311$$
$$x_{46} = -30.6305283725005$$
$$x_{47} = 7.06858347057703$$
$$x_{48} = 77.7544181763474$$
$$x_{49} = -35.3429173528852$$
$$x_{50} = -795.608339521615$$
$$x_{51} = 57.3340659280137$$
$$x_{52} = -43.1968989868597$$
$$x_{53} = 107.59954838545$$
$$x_{54} = -24.3473430653209$$
$$x_{55} = -41.6261026600648$$
$$x_{56} = -3667.02402490269$$
$$x_{57} = -62.0464549083984$$
$$x_{58} = 27.4889357189107$$
$$x_{59} = -162.577419823272$$
$$x_{60} = 8.63937979737193$$
$$x_{61} = -87.1791961371168$$
$$x_{62} = -55.7632696012188$$
$$x_{63} = -5.49778714378214$$
$$x_{64} = -29.0597320457056$$
$$x_{65} = -10.2101761241668$$
$$x_{66} = 32.2013246992954$$
$$x_{67} = -73.0420291959627$$
$$x_{68} = -47.9092879672443$$
$$x_{69} = -54.1924732744239$$
$$x_{70} = -204.988920646734$$
This roots
$$x_{56} = -3667.02402490269$$
$$x_{50} = -795.608339521615$$
$$x_{70} = -204.988920646734$$
$$x_{59} = -162.577419823272$$
$$x_{38} = -99.7455667514759$$
$$x_{29} = -98.174770424681$$
$$x_{10} = -93.4623814442964$$
$$x_{40} = -91.8915851175014$$
$$x_{61} = -87.1791961371168$$
$$x_{28} = -85.6083998103219$$
$$x_{4} = -80.8960108299372$$
$$x_{39} = -79.3252145031423$$
$$x_{16} = -74.6128255227576$$
$$x_{67} = -73.0420291959627$$
$$x_{42} = -68.329640215578$$
$$x_{19} = -66.7588438887831$$
$$x_{57} = -62.0464549083984$$
$$x_{43} = -60.4756585816035$$
$$x_{62} = -55.7632696012188$$
$$x_{69} = -54.1924732744239$$
$$x_{31} = -49.4800842940392$$
$$x_{68} = -47.9092879672443$$
$$x_{52} = -43.1968989868597$$
$$x_{55} = -41.6261026600648$$
$$x_{1} = -36.9137136796801$$
$$x_{49} = -35.3429173528852$$
$$x_{46} = -30.6305283725005$$
$$x_{64} = -29.0597320457056$$
$$x_{54} = -24.3473430653209$$
$$x_{7} = -22.776546738526$$
$$x_{15} = -18.0641577581413$$
$$x_{3} = -16.4933614313464$$
$$x_{11} = -11.7809724509617$$
$$x_{65} = -10.2101761241668$$
$$x_{63} = -5.49778714378214$$
$$x_{22} = -3.92699081698724$$
$$x_{17} = 0.785398163397448$$
$$x_{14} = 2.35619449019234$$
$$x_{47} = 7.06858347057703$$
$$x_{60} = 8.63937979737193$$
$$x_{25} = 13.3517687777566$$
$$x_{33} = 14.9225651045515$$
$$x_{30} = 19.6349540849362$$
$$x_{45} = 21.2057504117311$$
$$x_{2} = 25.9181393921158$$
$$x_{58} = 27.4889357189107$$
$$x_{66} = 32.2013246992954$$
$$x_{8} = 33.7721210260903$$
$$x_{44} = 38.484510006475$$
$$x_{34} = 40.0553063332699$$
$$x_{37} = 44.7676953136546$$
$$x_{21} = 46.3384916404494$$
$$x_{35} = 51.0508806208341$$
$$x_{5} = 52.621676947629$$
$$x_{51} = 57.3340659280137$$
$$x_{18} = 58.9048622548086$$
$$x_{27} = 63.6172512351933$$
$$x_{32} = 65.1880475619882$$
$$x_{13} = 69.9004365423729$$
$$x_{36} = 71.4712328691678$$
$$x_{41} = 76.1836218495525$$
$$x_{48} = 77.7544181763474$$
$$x_{26} = 82.4668071567321$$
$$x_{23} = 84.037603483527$$
$$x_{20} = 88.7499924639117$$
$$x_{24} = 90.3207887907066$$
$$x_{9} = 95.0331777710912$$
$$x_{6} = 96.6039740978861$$
$$x_{12} = 102.887159405066$$
$$x_{53} = 107.59954838545$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{56}$$
For example, let's take the point
$$x_{0} = x_{56} - \frac{1}{10}$$
=
$$-3667.02402490269 - \frac{1}{10}$$
=
$$-3667.12402490269$$
substitute to the expression
$$\sin{\left(x \right)} > \left|{\cos{\left(x \right)}}\right|$$
$$\sin{\left(-3667.12402490269 \right)} > \left|{\cos{\left(-3667.12402490269 \right)}}\right|$$

0.774167078476822 > 0.632981306677111

one of the solutions of our inequality is:
$$x < -3667.02402490269$$

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-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------
       x_56      x_50      x_70      x_59      x_38      x_29      x_10      x_40      x_61      x_28      x_4      x_39      x_16      x_67      x_42      x_19      x_57      x_43      x_62      x_69      x_31      x_68      x_52      x_55      x_1      x_49      x_46      x_64      x_54      x_7      x_15      x_3      x_11      x_65      x_63      x_22      x_17      x_14      x_47      x_60      x_25      x_33      x_30      x_45      x_2      x_58      x_66      x_8      x_44      x_34      x_37      x_21      x_35      x_5      x_51      x_18      x_27      x_32      x_13      x_36      x_41      x_48      x_26      x_23      x_20      x_24      x_9      x_6      x_12      x_53

Other solutions will get with the changeover to the next point
etc.
The answer:
$$x < -3667.02402490269$$
$$x > -795.608339521615 \wedge x < -204.988920646734$$
$$x > -162.577419823272 \wedge x < -99.7455667514759$$
$$x > -98.174770424681 \wedge x < -93.4623814442964$$
$$x > -91.8915851175014 \wedge x < -87.1791961371168$$
$$x > -85.6083998103219 \wedge x < -80.8960108299372$$
$$x > -79.3252145031423 \wedge x < -74.6128255227576$$
$$x > -73.0420291959627 \wedge x < -68.329640215578$$
$$x > -66.7588438887831 \wedge x < -62.0464549083984$$
$$x > -60.4756585816035 \wedge x < -55.7632696012188$$
$$x > -54.1924732744239 \wedge x < -49.4800842940392$$
$$x > -47.9092879672443 \wedge x < -43.1968989868597$$
$$x > -41.6261026600648 \wedge x < -36.9137136796801$$
$$x > -35.3429173528852 \wedge x < -30.6305283725005$$
$$x > -29.0597320457056 \wedge x < -24.3473430653209$$
$$x > -22.776546738526 \wedge x < -18.0641577581413$$
$$x > -16.4933614313464 \wedge x < -11.7809724509617$$
$$x > -10.2101761241668 \wedge x < -5.49778714378214$$
$$x > -3.92699081698724 \wedge x < 0.785398163397448$$
$$x > 2.35619449019234 \wedge x < 7.06858347057703$$
$$x > 8.63937979737193 \wedge x < 13.3517687777566$$
$$x > 14.9225651045515 \wedge x < 19.6349540849362$$
$$x > 21.2057504117311 \wedge x < 25.9181393921158$$
$$x > 27.4889357189107 \wedge x < 32.2013246992954$$
$$x > 33.7721210260903 \wedge x < 38.484510006475$$
$$x > 40.0553063332699 \wedge x < 44.7676953136546$$
$$x > 46.3384916404494 \wedge x < 51.0508806208341$$
$$x > 52.621676947629 \wedge x < 57.3340659280137$$
$$x > 58.9048622548086 \wedge x < 63.6172512351933$$
$$x > 65.1880475619882 \wedge x < 69.9004365423729$$
$$x > 71.4712328691678 \wedge x < 76.1836218495525$$
$$x > 77.7544181763474 \wedge x < 82.4668071567321$$
$$x > 84.037603483527 \wedge x < 88.7499924639117$$
$$x > 90.3207887907066 \wedge x < 95.0331777710912$$
$$x > 96.6039740978861 \wedge x < 102.887159405066$$
$$x > 107.59954838545$$