Mister Exam
cos(t)≤-√2/2 inequation
The solution
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-\/ 2
cos(t) <= -------
2
$$\cos{\left(t \right)} \leq \frac{\left(-1\right) \sqrt{2}}{2}$$
cos(t) <= (-sqrt(2))/2
Detail solution
Given the inequality:
$$\cos{\left(t \right)} \leq \frac{\left(-1\right) \sqrt{2}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(t \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Solve:
$$x_{1} = -79.3252145031423$$
$$x_{2} = -66.7588438887831$$
$$x_{3} = -73.0420291959627$$
$$x_{4} = -85.6083998103219$$
$$x_{5} = -21.2057504117311$$
$$x_{6} = -10.2101761241668$$
$$x_{7} = -335.36501577071$$
$$x_{8} = 41.6261026600648$$
$$x_{9} = -29.0597320457056$$
$$x_{10} = 90.3207887907066$$
$$x_{11} = -35.3429173528852$$
$$x_{12} = 21.2057504117311$$
$$x_{13} = 2.35619449019234$$
$$x_{14} = 8.63937979737193$$
$$x_{15} = -60.4756585816035$$
$$x_{16} = -52.621676947629$$
$$x_{17} = 255.254403104171$$
$$x_{18} = 79.3252145031423$$
$$x_{19} = 3.92699081698724$$
$$x_{20} = 35.3429173528852$$
$$x_{21} = -46.3384916404494$$
$$x_{22} = 60.4756585816035$$
$$x_{23} = -27.4889357189107$$
$$x_{24} = -2.35619449019234$$
$$x_{25} = 29.0597320457056$$
$$x_{26} = 71.4712328691678$$
$$x_{27} = -90.3207887907066$$
$$x_{28} = 39349.2333843756$$
$$x_{29} = 14.9225651045515$$
$$x_{30} = 47.9092879672443$$
$$x_{31} = -77.7544181763474$$
$$x_{32} = 33.7721210260903$$
$$x_{33} = 73.0420291959627$$
$$x_{34} = 77.7544181763474$$
$$x_{35} = -54.1924732744239$$
$$x_{36} = 54.1924732744239$$
$$x_{37} = 46.3384916404494$$
$$x_{38} = -47.9092879672443$$
$$x_{39} = -65.1880475619882$$
$$x_{40} = 2584.745355741$$
$$x_{41} = 96.6039740978861$$
$$x_{42} = 66.7588438887831$$
$$x_{43} = -96.6039740978861$$
$$x_{44} = 65.1880475619882$$
$$x_{45} = 104.457955731861$$
$$x_{46} = 85.6083998103219$$
$$x_{47} = 16.4933614313464$$
$$x_{48} = -71.4712328691678$$
$$x_{49} = -8.63937979737193$$
$$x_{50} = -3.92699081698724$$
$$x_{51} = 27.4889357189107$$
$$x_{52} = 98.174770424681$$
$$x_{53} = 52.621676947629$$
$$x_{54} = -14.9225651045515$$
$$x_{55} = -40.0553063332699$$
$$x_{56} = 22.776546738526$$
$$x_{57} = -41.6261026600648$$
$$x_{58} = -16.4933614313464$$
$$x_{59} = 40.0553063332699$$
$$x_{60} = 58.9048622548086$$
$$x_{61} = -58.9048622548086$$
$$x_{62} = -84.037603483527$$
$$x_{63} = 91.8915851175014$$
$$x_{64} = -33.7721210260903$$
$$x_{65} = 10.2101761241668$$
$$x_{66} = -22.776546738526$$
$$x_{67} = -98.174770424681$$
$$x_{68} = 84.037603483527$$
$$x_{69} = -91.8915851175014$$
$$x_{1} = -79.3252145031423$$
$$x_{2} = -66.7588438887831$$
$$x_{3} = -73.0420291959627$$
$$x_{4} = -85.6083998103219$$
$$x_{5} = -21.2057504117311$$
$$x_{6} = -10.2101761241668$$
$$x_{7} = -335.36501577071$$
$$x_{8} = 41.6261026600648$$
$$x_{9} = -29.0597320457056$$
$$x_{10} = 90.3207887907066$$
$$x_{11} = -35.3429173528852$$
$$x_{12} = 21.2057504117311$$
$$x_{13} = 2.35619449019234$$
$$x_{14} = 8.63937979737193$$
$$x_{15} = -60.4756585816035$$
$$x_{16} = -52.621676947629$$
$$x_{17} = 255.254403104171$$
$$x_{18} = 79.3252145031423$$
$$x_{19} = 3.92699081698724$$
$$x_{20} = 35.3429173528852$$
$$x_{21} = -46.3384916404494$$
$$x_{22} = 60.4756585816035$$
$$x_{23} = -27.4889357189107$$
$$x_{24} = -2.35619449019234$$
$$x_{25} = 29.0597320457056$$
$$x_{26} = 71.4712328691678$$
$$x_{27} = -90.3207887907066$$
$$x_{28} = 39349.2333843756$$
$$x_{29} = 14.9225651045515$$
$$x_{30} = 47.9092879672443$$
$$x_{31} = -77.7544181763474$$
$$x_{32} = 33.7721210260903$$
$$x_{33} = 73.0420291959627$$
$$x_{34} = 77.7544181763474$$
$$x_{35} = -54.1924732744239$$
$$x_{36} = 54.1924732744239$$
$$x_{37} = 46.3384916404494$$
$$x_{38} = -47.9092879672443$$
$$x_{39} = -65.1880475619882$$
$$x_{40} = 2584.745355741$$
$$x_{41} = 96.6039740978861$$
$$x_{42} = 66.7588438887831$$
$$x_{43} = -96.6039740978861$$
$$x_{44} = 65.1880475619882$$
$$x_{45} = 104.457955731861$$
$$x_{46} = 85.6083998103219$$
$$x_{47} = 16.4933614313464$$
$$x_{48} = -71.4712328691678$$
$$x_{49} = -8.63937979737193$$
$$x_{50} = -3.92699081698724$$
$$x_{51} = 27.4889357189107$$
$$x_{52} = 98.174770424681$$
$$x_{53} = 52.621676947629$$
$$x_{54} = -14.9225651045515$$
$$x_{55} = -40.0553063332699$$
$$x_{56} = 22.776546738526$$
$$x_{57} = -41.6261026600648$$
$$x_{58} = -16.4933614313464$$
$$x_{59} = 40.0553063332699$$
$$x_{60} = 58.9048622548086$$
$$x_{61} = -58.9048622548086$$
$$x_{62} = -84.037603483527$$
$$x_{63} = 91.8915851175014$$
$$x_{64} = -33.7721210260903$$
$$x_{65} = 10.2101761241668$$
$$x_{66} = -22.776546738526$$
$$x_{67} = -98.174770424681$$
$$x_{68} = 84.037603483527$$
$$x_{69} = -91.8915851175014$$
This roots
$$x_{7} = -335.36501577071$$
$$x_{67} = -98.174770424681$$
$$x_{43} = -96.6039740978861$$
$$x_{69} = -91.8915851175014$$
$$x_{27} = -90.3207887907066$$
$$x_{4} = -85.6083998103219$$
$$x_{62} = -84.037603483527$$
$$x_{1} = -79.3252145031423$$
$$x_{31} = -77.7544181763474$$
$$x_{3} = -73.0420291959627$$
$$x_{48} = -71.4712328691678$$
$$x_{2} = -66.7588438887831$$
$$x_{39} = -65.1880475619882$$
$$x_{15} = -60.4756585816035$$
$$x_{61} = -58.9048622548086$$
$$x_{35} = -54.1924732744239$$
$$x_{16} = -52.621676947629$$
$$x_{38} = -47.9092879672443$$
$$x_{21} = -46.3384916404494$$
$$x_{57} = -41.6261026600648$$
$$x_{55} = -40.0553063332699$$
$$x_{11} = -35.3429173528852$$
$$x_{64} = -33.7721210260903$$
$$x_{9} = -29.0597320457056$$
$$x_{23} = -27.4889357189107$$
$$x_{66} = -22.776546738526$$
$$x_{5} = -21.2057504117311$$
$$x_{58} = -16.4933614313464$$
$$x_{54} = -14.9225651045515$$
$$x_{6} = -10.2101761241668$$
$$x_{49} = -8.63937979737193$$
$$x_{50} = -3.92699081698724$$
$$x_{24} = -2.35619449019234$$
$$x_{13} = 2.35619449019234$$
$$x_{19} = 3.92699081698724$$
$$x_{14} = 8.63937979737193$$
$$x_{65} = 10.2101761241668$$
$$x_{29} = 14.9225651045515$$
$$x_{47} = 16.4933614313464$$
$$x_{12} = 21.2057504117311$$
$$x_{56} = 22.776546738526$$
$$x_{51} = 27.4889357189107$$
$$x_{25} = 29.0597320457056$$
$$x_{32} = 33.7721210260903$$
$$x_{20} = 35.3429173528852$$
$$x_{59} = 40.0553063332699$$
$$x_{8} = 41.6261026600648$$
$$x_{37} = 46.3384916404494$$
$$x_{30} = 47.9092879672443$$
$$x_{53} = 52.621676947629$$
$$x_{36} = 54.1924732744239$$
$$x_{60} = 58.9048622548086$$
$$x_{22} = 60.4756585816035$$
$$x_{44} = 65.1880475619882$$
$$x_{42} = 66.7588438887831$$
$$x_{26} = 71.4712328691678$$
$$x_{33} = 73.0420291959627$$
$$x_{34} = 77.7544181763474$$
$$x_{18} = 79.3252145031423$$
$$x_{68} = 84.037603483527$$
$$x_{46} = 85.6083998103219$$
$$x_{10} = 90.3207887907066$$
$$x_{63} = 91.8915851175014$$
$$x_{41} = 96.6039740978861$$
$$x_{52} = 98.174770424681$$
$$x_{45} = 104.457955731861$$
$$x_{17} = 255.254403104171$$
$$x_{40} = 2584.745355741$$
$$x_{28} = 39349.2333843756$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{7}$$
For example, let's take the point
$$x_{0} = x_{7} - \frac{1}{10}$$
=
$$-335.36501577071 + - \frac{1}{10}$$
=
$$-335.46501577071$$
substitute to the expression
$$\cos{\left(t \right)} \leq \frac{\left(-1\right) \sqrt{2}}{2}$$
$$\cos{\left(t \right)} \leq \frac{\left(-1\right) \sqrt{2}}{2}$$
Then
$$x \leq -335.36501577071$$
no execute
one of the solutions of our inequality is:
$$x \geq -335.36501577071 \wedge x \leq -98.174770424681$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \geq -335.36501577071 \wedge x \leq -98.174770424681$$
$$x \geq -96.6039740978861 \wedge x \leq -91.8915851175014$$
$$x \geq -90.3207887907066 \wedge x \leq -85.6083998103219$$
$$x \geq -84.037603483527 \wedge x \leq -79.3252145031423$$
$$x \geq -77.7544181763474 \wedge x \leq -73.0420291959627$$
$$x \geq -71.4712328691678 \wedge x \leq -66.7588438887831$$
$$x \geq -65.1880475619882 \wedge x \leq -60.4756585816035$$
$$x \geq -58.9048622548086 \wedge x \leq -54.1924732744239$$
$$x \geq -52.621676947629 \wedge x \leq -47.9092879672443$$
$$x \geq -46.3384916404494 \wedge x \leq -41.6261026600648$$
$$x \geq -40.0553063332699 \wedge x \leq -35.3429173528852$$
$$x \geq -33.7721210260903 \wedge x \leq -29.0597320457056$$
$$x \geq -27.4889357189107 \wedge x \leq -22.776546738526$$
$$x \geq -21.2057504117311 \wedge x \leq -16.4933614313464$$
$$x \geq -14.9225651045515 \wedge x \leq -10.2101761241668$$
$$x \geq -8.63937979737193 \wedge x \leq -3.92699081698724$$
$$x \geq -2.35619449019234 \wedge x \leq 2.35619449019234$$
$$x \geq 3.92699081698724 \wedge x \leq 8.63937979737193$$
$$x \geq 10.2101761241668 \wedge x \leq 14.9225651045515$$
$$x \geq 16.4933614313464 \wedge x \leq 21.2057504117311$$
$$x \geq 22.776546738526 \wedge x \leq 27.4889357189107$$
$$x \geq 29.0597320457056 \wedge x \leq 33.7721210260903$$
$$x \geq 35.3429173528852 \wedge x \leq 40.0553063332699$$
$$x \geq 41.6261026600648 \wedge x \leq 46.3384916404494$$
$$x \geq 47.9092879672443 \wedge x \leq 52.621676947629$$
$$x \geq 54.1924732744239 \wedge x \leq 58.9048622548086$$
$$x \geq 60.4756585816035 \wedge x \leq 65.1880475619882$$
$$x \geq 66.7588438887831 \wedge x \leq 71.4712328691678$$
$$x \geq 73.0420291959627 \wedge x \leq 77.7544181763474$$
$$x \geq 79.3252145031423 \wedge x \leq 84.037603483527$$
$$x \geq 85.6083998103219 \wedge x \leq 90.3207887907066$$
$$x \geq 91.8915851175014 \wedge x \leq 96.6039740978861$$
$$x \geq 98.174770424681 \wedge x \leq 104.457955731861$$
$$x \geq 255.254403104171 \wedge x \leq 2584.745355741$$
$$x \geq 39349.2333843756$$
$$\cos{\left(t \right)} \leq \frac{\left(-1\right) \sqrt{2}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(t \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Solve:
$$x_{1} = -79.3252145031423$$
$$x_{2} = -66.7588438887831$$
$$x_{3} = -73.0420291959627$$
$$x_{4} = -85.6083998103219$$
$$x_{5} = -21.2057504117311$$
$$x_{6} = -10.2101761241668$$
$$x_{7} = -335.36501577071$$
$$x_{8} = 41.6261026600648$$
$$x_{9} = -29.0597320457056$$
$$x_{10} = 90.3207887907066$$
$$x_{11} = -35.3429173528852$$
$$x_{12} = 21.2057504117311$$
$$x_{13} = 2.35619449019234$$
$$x_{14} = 8.63937979737193$$
$$x_{15} = -60.4756585816035$$
$$x_{16} = -52.621676947629$$
$$x_{17} = 255.254403104171$$
$$x_{18} = 79.3252145031423$$
$$x_{19} = 3.92699081698724$$
$$x_{20} = 35.3429173528852$$
$$x_{21} = -46.3384916404494$$
$$x_{22} = 60.4756585816035$$
$$x_{23} = -27.4889357189107$$
$$x_{24} = -2.35619449019234$$
$$x_{25} = 29.0597320457056$$
$$x_{26} = 71.4712328691678$$
$$x_{27} = -90.3207887907066$$
$$x_{28} = 39349.2333843756$$
$$x_{29} = 14.9225651045515$$
$$x_{30} = 47.9092879672443$$
$$x_{31} = -77.7544181763474$$
$$x_{32} = 33.7721210260903$$
$$x_{33} = 73.0420291959627$$
$$x_{34} = 77.7544181763474$$
$$x_{35} = -54.1924732744239$$
$$x_{36} = 54.1924732744239$$
$$x_{37} = 46.3384916404494$$
$$x_{38} = -47.9092879672443$$
$$x_{39} = -65.1880475619882$$
$$x_{40} = 2584.745355741$$
$$x_{41} = 96.6039740978861$$
$$x_{42} = 66.7588438887831$$
$$x_{43} = -96.6039740978861$$
$$x_{44} = 65.1880475619882$$
$$x_{45} = 104.457955731861$$
$$x_{46} = 85.6083998103219$$
$$x_{47} = 16.4933614313464$$
$$x_{48} = -71.4712328691678$$
$$x_{49} = -8.63937979737193$$
$$x_{50} = -3.92699081698724$$
$$x_{51} = 27.4889357189107$$
$$x_{52} = 98.174770424681$$
$$x_{53} = 52.621676947629$$
$$x_{54} = -14.9225651045515$$
$$x_{55} = -40.0553063332699$$
$$x_{56} = 22.776546738526$$
$$x_{57} = -41.6261026600648$$
$$x_{58} = -16.4933614313464$$
$$x_{59} = 40.0553063332699$$
$$x_{60} = 58.9048622548086$$
$$x_{61} = -58.9048622548086$$
$$x_{62} = -84.037603483527$$
$$x_{63} = 91.8915851175014$$
$$x_{64} = -33.7721210260903$$
$$x_{65} = 10.2101761241668$$
$$x_{66} = -22.776546738526$$
$$x_{67} = -98.174770424681$$
$$x_{68} = 84.037603483527$$
$$x_{69} = -91.8915851175014$$
$$x_{1} = -79.3252145031423$$
$$x_{2} = -66.7588438887831$$
$$x_{3} = -73.0420291959627$$
$$x_{4} = -85.6083998103219$$
$$x_{5} = -21.2057504117311$$
$$x_{6} = -10.2101761241668$$
$$x_{7} = -335.36501577071$$
$$x_{8} = 41.6261026600648$$
$$x_{9} = -29.0597320457056$$
$$x_{10} = 90.3207887907066$$
$$x_{11} = -35.3429173528852$$
$$x_{12} = 21.2057504117311$$
$$x_{13} = 2.35619449019234$$
$$x_{14} = 8.63937979737193$$
$$x_{15} = -60.4756585816035$$
$$x_{16} = -52.621676947629$$
$$x_{17} = 255.254403104171$$
$$x_{18} = 79.3252145031423$$
$$x_{19} = 3.92699081698724$$
$$x_{20} = 35.3429173528852$$
$$x_{21} = -46.3384916404494$$
$$x_{22} = 60.4756585816035$$
$$x_{23} = -27.4889357189107$$
$$x_{24} = -2.35619449019234$$
$$x_{25} = 29.0597320457056$$
$$x_{26} = 71.4712328691678$$
$$x_{27} = -90.3207887907066$$
$$x_{28} = 39349.2333843756$$
$$x_{29} = 14.9225651045515$$
$$x_{30} = 47.9092879672443$$
$$x_{31} = -77.7544181763474$$
$$x_{32} = 33.7721210260903$$
$$x_{33} = 73.0420291959627$$
$$x_{34} = 77.7544181763474$$
$$x_{35} = -54.1924732744239$$
$$x_{36} = 54.1924732744239$$
$$x_{37} = 46.3384916404494$$
$$x_{38} = -47.9092879672443$$
$$x_{39} = -65.1880475619882$$
$$x_{40} = 2584.745355741$$
$$x_{41} = 96.6039740978861$$
$$x_{42} = 66.7588438887831$$
$$x_{43} = -96.6039740978861$$
$$x_{44} = 65.1880475619882$$
$$x_{45} = 104.457955731861$$
$$x_{46} = 85.6083998103219$$
$$x_{47} = 16.4933614313464$$
$$x_{48} = -71.4712328691678$$
$$x_{49} = -8.63937979737193$$
$$x_{50} = -3.92699081698724$$
$$x_{51} = 27.4889357189107$$
$$x_{52} = 98.174770424681$$
$$x_{53} = 52.621676947629$$
$$x_{54} = -14.9225651045515$$
$$x_{55} = -40.0553063332699$$
$$x_{56} = 22.776546738526$$
$$x_{57} = -41.6261026600648$$
$$x_{58} = -16.4933614313464$$
$$x_{59} = 40.0553063332699$$
$$x_{60} = 58.9048622548086$$
$$x_{61} = -58.9048622548086$$
$$x_{62} = -84.037603483527$$
$$x_{63} = 91.8915851175014$$
$$x_{64} = -33.7721210260903$$
$$x_{65} = 10.2101761241668$$
$$x_{66} = -22.776546738526$$
$$x_{67} = -98.174770424681$$
$$x_{68} = 84.037603483527$$
$$x_{69} = -91.8915851175014$$
This roots
$$x_{7} = -335.36501577071$$
$$x_{67} = -98.174770424681$$
$$x_{43} = -96.6039740978861$$
$$x_{69} = -91.8915851175014$$
$$x_{27} = -90.3207887907066$$
$$x_{4} = -85.6083998103219$$
$$x_{62} = -84.037603483527$$
$$x_{1} = -79.3252145031423$$
$$x_{31} = -77.7544181763474$$
$$x_{3} = -73.0420291959627$$
$$x_{48} = -71.4712328691678$$
$$x_{2} = -66.7588438887831$$
$$x_{39} = -65.1880475619882$$
$$x_{15} = -60.4756585816035$$
$$x_{61} = -58.9048622548086$$
$$x_{35} = -54.1924732744239$$
$$x_{16} = -52.621676947629$$
$$x_{38} = -47.9092879672443$$
$$x_{21} = -46.3384916404494$$
$$x_{57} = -41.6261026600648$$
$$x_{55} = -40.0553063332699$$
$$x_{11} = -35.3429173528852$$
$$x_{64} = -33.7721210260903$$
$$x_{9} = -29.0597320457056$$
$$x_{23} = -27.4889357189107$$
$$x_{66} = -22.776546738526$$
$$x_{5} = -21.2057504117311$$
$$x_{58} = -16.4933614313464$$
$$x_{54} = -14.9225651045515$$
$$x_{6} = -10.2101761241668$$
$$x_{49} = -8.63937979737193$$
$$x_{50} = -3.92699081698724$$
$$x_{24} = -2.35619449019234$$
$$x_{13} = 2.35619449019234$$
$$x_{19} = 3.92699081698724$$
$$x_{14} = 8.63937979737193$$
$$x_{65} = 10.2101761241668$$
$$x_{29} = 14.9225651045515$$
$$x_{47} = 16.4933614313464$$
$$x_{12} = 21.2057504117311$$
$$x_{56} = 22.776546738526$$
$$x_{51} = 27.4889357189107$$
$$x_{25} = 29.0597320457056$$
$$x_{32} = 33.7721210260903$$
$$x_{20} = 35.3429173528852$$
$$x_{59} = 40.0553063332699$$
$$x_{8} = 41.6261026600648$$
$$x_{37} = 46.3384916404494$$
$$x_{30} = 47.9092879672443$$
$$x_{53} = 52.621676947629$$
$$x_{36} = 54.1924732744239$$
$$x_{60} = 58.9048622548086$$
$$x_{22} = 60.4756585816035$$
$$x_{44} = 65.1880475619882$$
$$x_{42} = 66.7588438887831$$
$$x_{26} = 71.4712328691678$$
$$x_{33} = 73.0420291959627$$
$$x_{34} = 77.7544181763474$$
$$x_{18} = 79.3252145031423$$
$$x_{68} = 84.037603483527$$
$$x_{46} = 85.6083998103219$$
$$x_{10} = 90.3207887907066$$
$$x_{63} = 91.8915851175014$$
$$x_{41} = 96.6039740978861$$
$$x_{52} = 98.174770424681$$
$$x_{45} = 104.457955731861$$
$$x_{17} = 255.254403104171$$
$$x_{40} = 2584.745355741$$
$$x_{28} = 39349.2333843756$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{7}$$
For example, let's take the point
$$x_{0} = x_{7} - \frac{1}{10}$$
=
$$-335.36501577071 + - \frac{1}{10}$$
=
$$-335.46501577071$$
substitute to the expression
$$\cos{\left(t \right)} \leq \frac{\left(-1\right) \sqrt{2}}{2}$$
$$\cos{\left(t \right)} \leq \frac{\left(-1\right) \sqrt{2}}{2}$$
___
-\/ 2
cos(t) <= -------
2
Then
$$x \leq -335.36501577071$$
no execute
one of the solutions of our inequality is:
$$x \geq -335.36501577071 \wedge x \leq -98.174770424681$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
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x7 x67 x43 x69 x27 x4 x62 x1 x31 x3 x48 x2 x39 x15 x61 x35 x16 x38 x21 x57 x55 x11 x64 x9 x23 x66 x5 x58 x54 x6 x49 x50 x24 x13 x19 x14 x65 x29 x47 x12 x56 x51 x25 x32 x20 x59 x8 x37 x30 x53 x36 x60 x22 x44 x42 x26 x33 x34 x18 x68 x46 x10 x63 x41 x52 x45 x17 x40 x28Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \geq -335.36501577071 \wedge x \leq -98.174770424681$$
$$x \geq -96.6039740978861 \wedge x \leq -91.8915851175014$$
$$x \geq -90.3207887907066 \wedge x \leq -85.6083998103219$$
$$x \geq -84.037603483527 \wedge x \leq -79.3252145031423$$
$$x \geq -77.7544181763474 \wedge x \leq -73.0420291959627$$
$$x \geq -71.4712328691678 \wedge x \leq -66.7588438887831$$
$$x \geq -65.1880475619882 \wedge x \leq -60.4756585816035$$
$$x \geq -58.9048622548086 \wedge x \leq -54.1924732744239$$
$$x \geq -52.621676947629 \wedge x \leq -47.9092879672443$$
$$x \geq -46.3384916404494 \wedge x \leq -41.6261026600648$$
$$x \geq -40.0553063332699 \wedge x \leq -35.3429173528852$$
$$x \geq -33.7721210260903 \wedge x \leq -29.0597320457056$$
$$x \geq -27.4889357189107 \wedge x \leq -22.776546738526$$
$$x \geq -21.2057504117311 \wedge x \leq -16.4933614313464$$
$$x \geq -14.9225651045515 \wedge x \leq -10.2101761241668$$
$$x \geq -8.63937979737193 \wedge x \leq -3.92699081698724$$
$$x \geq -2.35619449019234 \wedge x \leq 2.35619449019234$$
$$x \geq 3.92699081698724 \wedge x \leq 8.63937979737193$$
$$x \geq 10.2101761241668 \wedge x \leq 14.9225651045515$$
$$x \geq 16.4933614313464 \wedge x \leq 21.2057504117311$$
$$x \geq 22.776546738526 \wedge x \leq 27.4889357189107$$
$$x \geq 29.0597320457056 \wedge x \leq 33.7721210260903$$
$$x \geq 35.3429173528852 \wedge x \leq 40.0553063332699$$
$$x \geq 41.6261026600648 \wedge x \leq 46.3384916404494$$
$$x \geq 47.9092879672443 \wedge x \leq 52.621676947629$$
$$x \geq 54.1924732744239 \wedge x \leq 58.9048622548086$$
$$x \geq 60.4756585816035 \wedge x \leq 65.1880475619882$$
$$x \geq 66.7588438887831 \wedge x \leq 71.4712328691678$$
$$x \geq 73.0420291959627 \wedge x \leq 77.7544181763474$$
$$x \geq 79.3252145031423 \wedge x \leq 84.037603483527$$
$$x \geq 85.6083998103219 \wedge x \leq 90.3207887907066$$
$$x \geq 91.8915851175014 \wedge x \leq 96.6039740978861$$
$$x \geq 98.174770424681 \wedge x \leq 104.457955731861$$
$$x \geq 255.254403104171 \wedge x \leq 2584.745355741$$
$$x \geq 39349.2333843756$$
Rapid solution 2
[src]
3*pi 5*pi [----, ----] 4 4
$$x\ in\ \left[\frac{3 \pi}{4}, \frac{5 \pi}{4}\right]$$
x in Interval(3*pi/4, 5*pi/4)
Rapid solution
[src]
/3*pi 5*pi\ And|---- <= x, x <= ----| \ 4 4 /
$$\frac{3 \pi}{4} \leq x \wedge x \leq \frac{5 \pi}{4}$$
(3*pi/4 <= x)∧(x <= 5*pi/4)