|sinx|>0 inequation

Given the inequality:
$$\left|{\sin{\left(x \right)}}\right| > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{\sin{\left(x \right)}}\right| = 0$$
Solve:
Given the equation
$$\left|{\sin{\left(x \right)}}\right| = 0$$
transform
$$\left|{\sin{\left(x \right)}}\right| - 1 = 0$$
$$\left|{\sin{\left(x \right)}}\right| - 1 = 0$$
Do replacement
$$w = \left|{\sin{\left(x \right)}}\right|$$
Move free summands (without w)
from left part to right part, we given:
$$w = 1$$
We get the answer: w = 1
do backward replacement
$$\left|{\sin{\left(x \right)}}\right| = w$$
substitute w:
$$x_{1} = 43.9822971502571$$
$$x_{2} = -97.3893722612836$$
$$x_{3} = -43.9822971502571$$
$$x_{4} = -72.2566310325652$$
$$x_{5} = -3760.48640634698$$
$$x_{6} = 81.6814089933346$$
$$x_{7} = -31.4159265358979$$
$$x_{8} = -59.6902604182061$$
$$x_{9} = -78.5398163397448$$
$$x_{10} = 97.3893722612836$$
$$x_{11} = -25.1327412287183$$
$$x_{12} = 9.42477796076938$$
$$x_{13} = 84.8230016469244$$
$$x_{14} = -21.9911485751286$$
$$x_{15} = -94.2477796076938$$
$$x_{16} = 6.28318530717959$$
$$x_{17} = -50.2654824574367$$
$$x_{18} = 28.2743338823081$$
$$x_{19} = -75.398223686155$$
$$x_{20} = -28.2743338823081$$
$$x_{21} = -56.5486677646163$$
$$x_{22} = -65.9734457253857$$
$$x_{23} = -91.106186954104$$
$$x_{24} = -285.884931476671$$
$$x_{25} = 50.2654824574367$$
$$x_{26} = -69.1150383789755$$
$$x_{27} = -100.530964914873$$
$$x_{28} = 56.5486677646163$$
$$x_{29} = -87.9645943005142$$
$$x_{30} = 40.8407044966673$$
$$x_{31} = 18.8495559215388$$
$$x_{32} = 650.309679293087$$
$$x_{33} = 100.530964914873$$
$$x_{34} = 62.8318530717959$$
$$x_{35} = -53.4070751110265$$
$$x_{36} = 94.2477796076938$$
$$x_{37} = -3.14159265358979$$
$$x_{38} = 21.9911485751286$$
$$x_{39} = 12.5663706143592$$
$$x_{40} = -427.256600888212$$
$$x_{41} = 34.5575191894877$$
$$x_{42} = -15.707963267949$$
$$x_{43} = 53.4070751110265$$
$$x_{44} = 65.9734457253857$$
$$x_{45} = 87.9645943005142$$
$$x_{46} = 59.6902604182061$$
$$x_{47} = -6.28318530717959$$
$$x_{48} = 75.398223686155$$
$$x_{49} = -37.6991118430775$$
$$x_{50} = -12.5663706143592$$
$$x_{51} = 31.4159265358979$$
$$x_{52} = -81.6814089933346$$
$$x_{53} = 78.5398163397448$$
$$x_{54} = 15.707963267949$$
$$x_{55} = 72.2566310325652$$
$$x_{56} = 37.6991118430775$$
$$x_{57} = -47.1238898038469$$
$$x_{58} = 0$$
$$x_{59} = -9.42477796076938$$
$$x_{60} = -34.5575191894877$$
$$x_{1} = 43.9822971502571$$
$$x_{2} = -97.3893722612836$$
$$x_{3} = -43.9822971502571$$
$$x_{4} = -72.2566310325652$$
$$x_{5} = -3760.48640634698$$
$$x_{6} = 81.6814089933346$$
$$x_{7} = -31.4159265358979$$
$$x_{8} = -59.6902604182061$$
$$x_{9} = -78.5398163397448$$
$$x_{10} = 97.3893722612836$$
$$x_{11} = -25.1327412287183$$
$$x_{12} = 9.42477796076938$$
$$x_{13} = 84.8230016469244$$
$$x_{14} = -21.9911485751286$$
$$x_{15} = -94.2477796076938$$
$$x_{16} = 6.28318530717959$$
$$x_{17} = -50.2654824574367$$
$$x_{18} = 28.2743338823081$$
$$x_{19} = -75.398223686155$$
$$x_{20} = -28.2743338823081$$
$$x_{21} = -56.5486677646163$$
$$x_{22} = -65.9734457253857$$
$$x_{23} = -91.106186954104$$
$$x_{24} = -285.884931476671$$
$$x_{25} = 50.2654824574367$$
$$x_{26} = -69.1150383789755$$
$$x_{27} = -100.530964914873$$
$$x_{28} = 56.5486677646163$$
$$x_{29} = -87.9645943005142$$
$$x_{30} = 40.8407044966673$$
$$x_{31} = 18.8495559215388$$
$$x_{32} = 650.309679293087$$
$$x_{33} = 100.530964914873$$
$$x_{34} = 62.8318530717959$$
$$x_{35} = -53.4070751110265$$
$$x_{36} = 94.2477796076938$$
$$x_{37} = -3.14159265358979$$
$$x_{38} = 21.9911485751286$$
$$x_{39} = 12.5663706143592$$
$$x_{40} = -427.256600888212$$
$$x_{41} = 34.5575191894877$$
$$x_{42} = -15.707963267949$$
$$x_{43} = 53.4070751110265$$
$$x_{44} = 65.9734457253857$$
$$x_{45} = 87.9645943005142$$
$$x_{46} = 59.6902604182061$$
$$x_{47} = -6.28318530717959$$
$$x_{48} = 75.398223686155$$
$$x_{49} = -37.6991118430775$$
$$x_{50} = -12.5663706143592$$
$$x_{51} = 31.4159265358979$$
$$x_{52} = -81.6814089933346$$
$$x_{53} = 78.5398163397448$$
$$x_{54} = 15.707963267949$$
$$x_{55} = 72.2566310325652$$
$$x_{56} = 37.6991118430775$$
$$x_{57} = -47.1238898038469$$
$$x_{58} = 0$$
$$x_{59} = -9.42477796076938$$
$$x_{60} = -34.5575191894877$$
This roots
$$x_{5} = -3760.48640634698$$
$$x_{40} = -427.256600888212$$
$$x_{24} = -285.884931476671$$
$$x_{27} = -100.530964914873$$
$$x_{2} = -97.3893722612836$$
$$x_{15} = -94.2477796076938$$
$$x_{23} = -91.106186954104$$
$$x_{29} = -87.9645943005142$$
$$x_{52} = -81.6814089933346$$
$$x_{9} = -78.5398163397448$$
$$x_{19} = -75.398223686155$$
$$x_{4} = -72.2566310325652$$
$$x_{26} = -69.1150383789755$$
$$x_{22} = -65.9734457253857$$
$$x_{8} = -59.6902604182061$$
$$x_{21} = -56.5486677646163$$
$$x_{35} = -53.4070751110265$$
$$x_{17} = -50.2654824574367$$
$$x_{57} = -47.1238898038469$$
$$x_{3} = -43.9822971502571$$
$$x_{49} = -37.6991118430775$$
$$x_{60} = -34.5575191894877$$
$$x_{7} = -31.4159265358979$$
$$x_{20} = -28.2743338823081$$
$$x_{11} = -25.1327412287183$$
$$x_{14} = -21.9911485751286$$
$$x_{42} = -15.707963267949$$
$$x_{50} = -12.5663706143592$$
$$x_{59} = -9.42477796076938$$
$$x_{47} = -6.28318530717959$$
$$x_{37} = -3.14159265358979$$
$$x_{58} = 0$$
$$x_{16} = 6.28318530717959$$
$$x_{12} = 9.42477796076938$$
$$x_{39} = 12.5663706143592$$
$$x_{54} = 15.707963267949$$
$$x_{31} = 18.8495559215388$$
$$x_{38} = 21.9911485751286$$
$$x_{18} = 28.2743338823081$$
$$x_{51} = 31.4159265358979$$
$$x_{41} = 34.5575191894877$$
$$x_{56} = 37.6991118430775$$
$$x_{30} = 40.8407044966673$$
$$x_{1} = 43.9822971502571$$
$$x_{25} = 50.2654824574367$$
$$x_{43} = 53.4070751110265$$
$$x_{28} = 56.5486677646163$$
$$x_{46} = 59.6902604182061$$
$$x_{34} = 62.8318530717959$$
$$x_{44} = 65.9734457253857$$
$$x_{55} = 72.2566310325652$$
$$x_{48} = 75.398223686155$$
$$x_{53} = 78.5398163397448$$
$$x_{6} = 81.6814089933346$$
$$x_{13} = 84.8230016469244$$
$$x_{45} = 87.9645943005142$$
$$x_{36} = 94.2477796076938$$
$$x_{10} = 97.3893722612836$$
$$x_{33} = 100.530964914873$$
$$x_{32} = 650.309679293087$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{5}$$
For example, let's take the point
$$x_{0} = x_{5} - \frac{1}{10}$$
=
$$-3760.48640634698 + - \frac{1}{10}$$
=
$$-3760.58640634698$$
substitute to the expression
$$\left|{\sin{\left(x \right)}}\right| > 0$$
$$\left|{\sin{\left(-3760.58640634698 \right)}}\right| > 0$$

0.0998334166469064 > 0

one of the solutions of our inequality is:
$$x < -3760.48640634698$$

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Other solutions will get with the changeover to the next point
etc.
The answer:
$$x < -3760.48640634698$$
$$x > -427.256600888212 \wedge x < -285.884931476671$$
$$x > -100.530964914873 \wedge x < -97.3893722612836$$
$$x > -94.2477796076938 \wedge x < -91.106186954104$$
$$x > -87.9645943005142 \wedge x < -81.6814089933346$$
$$x > -78.5398163397448 \wedge x < -75.398223686155$$
$$x > -72.2566310325652 \wedge x < -69.1150383789755$$
$$x > -65.9734457253857 \wedge x < -59.6902604182061$$
$$x > -56.5486677646163 \wedge x < -53.4070751110265$$
$$x > -50.2654824574367 \wedge x < -47.1238898038469$$
$$x > -43.9822971502571 \wedge x < -37.6991118430775$$
$$x > -34.5575191894877 \wedge x < -31.4159265358979$$
$$x > -28.2743338823081 \wedge x < -25.1327412287183$$
$$x > -21.9911485751286 \wedge x < -15.707963267949$$
$$x > -12.5663706143592 \wedge x < -9.42477796076938$$
$$x > -6.28318530717959 \wedge x < -3.14159265358979$$
$$x > 0 \wedge x < 6.28318530717959$$
$$x > 9.42477796076938 \wedge x < 12.5663706143592$$
$$x > 15.707963267949 \wedge x < 18.8495559215388$$
$$x > 21.9911485751286 \wedge x < 28.2743338823081$$
$$x > 31.4159265358979 \wedge x < 34.5575191894877$$
$$x > 37.6991118430775 \wedge x < 40.8407044966673$$
$$x > 43.9822971502571 \wedge x < 50.2654824574367$$
$$x > 53.4070751110265 \wedge x < 56.5486677646163$$
$$x > 59.6902604182061 \wedge x < 62.8318530717959$$
$$x > 65.9734457253857 \wedge x < 72.2566310325652$$
$$x > 75.398223686155 \wedge x < 78.5398163397448$$
$$x > 81.6814089933346 \wedge x < 84.8230016469244$$
$$x > 87.9645943005142 \wedge x < 94.2477796076938$$
$$x > 97.3893722612836 \wedge x < 100.530964914873$$
$$x > 650.309679293087$$