Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- |x+2|*3-x/-x-1<=0
- (1/5)^(x-1)-(1/5)^x<=100
- (4+x)/(4-x)<3
- 22x+2-42x>3
- Derivative of:
-
cos(t)
- Limit of the function:
-
cos(t)
- Integral of d{x}:
- cos(t)
- Canonical form:
- =0
-
Identical expressions
- cos(t)<= zero
- co sinus of e of (t) less than or equal to 0
- co sinus of e of (t) less than or equal to zero
- cost<=0
- cos(t)<=O
-
Similar expressions
- cost<1/3
- cost>√3/2
cos(t)<=0 inequation
The solution
Detail solution
Given the inequality:
$$\cos{\left(t \right)} \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(t \right)} = 0$$
Solve:
Given the equation
$$\cos{\left(t \right)} = 0$$
transform
$$\cos{\left(t \right)} - 1 = 0$$
$$\cos{\left(t \right)} - 1 = 0$$
Do replacement
$$w = \cos{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = 1$$
We get the answer: w = 1
do backward replacement
$$\cos{\left(t \right)} = w$$
substitute w:
$$x_{1} = 48.6946861306418$$
$$x_{2} = 54.9778714378214$$
$$x_{3} = -98.9601685880785$$
$$x_{4} = 67.5442420521806$$
$$x_{5} = 76.9690200129499$$
$$x_{6} = 36.1283155162826$$
$$x_{7} = 58.1194640914112$$
$$x_{8} = 14.1371669411541$$
$$x_{9} = -29.845130209103$$
$$x_{10} = 61.261056745001$$
$$x_{11} = -36.1283155162826$$
$$x_{12} = -4.71238898038469$$
$$x_{13} = -39.2699081698724$$
$$x_{14} = 1.5707963267949$$
$$x_{15} = -168.075206967054$$
$$x_{16} = -14.1371669411541$$
$$x_{17} = -64.4026493985908$$
$$x_{18} = -67.5442420521806$$
$$x_{19} = 92.6769832808989$$
$$x_{20} = -51.8362787842316$$
$$x_{21} = -86.3937979737193$$
$$x_{22} = 42.4115008234622$$
$$x_{23} = -17.2787595947439$$
$$x_{24} = -45.553093477052$$
$$x_{25} = -89.5353906273091$$
$$x_{26} = -1.5707963267949$$
$$x_{27} = 39.2699081698724$$
$$x_{28} = 23.5619449019235$$
$$x_{29} = 7.85398163397448$$
$$x_{30} = -58.1194640914112$$
$$x_{31} = -61.261056745001$$
$$x_{32} = -73.8274273593601$$
$$x_{33} = 73.8274273593601$$
$$x_{34} = 29.845130209103$$
$$x_{35} = 4.71238898038469$$
$$x_{36} = 86.3937979737193$$
$$x_{37} = 64.4026493985908$$
$$x_{38} = 89.5353906273091$$
$$x_{39} = -20.4203522483337$$
$$x_{40} = -387.986692718339$$
$$x_{41} = -26.7035375555132$$
$$x_{42} = 98.9601685880785$$
$$x_{43} = 51.8362787842316$$
$$x_{44} = 83.2522053201295$$
$$x_{45} = -48.6946861306418$$
$$x_{46} = -54.9778714378214$$
$$x_{47} = 70.6858347057703$$
$$x_{48} = -95.8185759344887$$
$$x_{49} = 26.7035375555132$$
$$x_{50} = 80.1106126665397$$
$$x_{51} = -23.5619449019235$$
$$x_{52} = -7.85398163397448$$
$$x_{53} = -83.2522053201295$$
$$x_{54} = -76.9690200129499$$
$$x_{55} = -42.4115008234622$$
$$x_{56} = -32.9867228626928$$
$$x_{57} = 17.2787595947439$$
$$x_{58} = 32.9867228626928$$
$$x_{59} = 20.4203522483337$$
$$x_{60} = -70.6858347057703$$
$$x_{61} = -10.9955742875643$$
$$x_{62} = -92.6769832808989$$
$$x_{63} = 45.553093477052$$
$$x_{64} = 10.9955742875643$$
$$x_{65} = -80.1106126665397$$
$$x_{66} = 95.8185759344887$$
$$x_{67} = -2266.65909956504$$
$$x_{1} = 48.6946861306418$$
$$x_{2} = 54.9778714378214$$
$$x_{3} = -98.9601685880785$$
$$x_{4} = 67.5442420521806$$
$$x_{5} = 76.9690200129499$$
$$x_{6} = 36.1283155162826$$
$$x_{7} = 58.1194640914112$$
$$x_{8} = 14.1371669411541$$
$$x_{9} = -29.845130209103$$
$$x_{10} = 61.261056745001$$
$$x_{11} = -36.1283155162826$$
$$x_{12} = -4.71238898038469$$
$$x_{13} = -39.2699081698724$$
$$x_{14} = 1.5707963267949$$
$$x_{15} = -168.075206967054$$
$$x_{16} = -14.1371669411541$$
$$x_{17} = -64.4026493985908$$
$$x_{18} = -67.5442420521806$$
$$x_{19} = 92.6769832808989$$
$$x_{20} = -51.8362787842316$$
$$x_{21} = -86.3937979737193$$
$$x_{22} = 42.4115008234622$$
$$x_{23} = -17.2787595947439$$
$$x_{24} = -45.553093477052$$
$$x_{25} = -89.5353906273091$$
$$x_{26} = -1.5707963267949$$
$$x_{27} = 39.2699081698724$$
$$x_{28} = 23.5619449019235$$
$$x_{29} = 7.85398163397448$$
$$x_{30} = -58.1194640914112$$
$$x_{31} = -61.261056745001$$
$$x_{32} = -73.8274273593601$$
$$x_{33} = 73.8274273593601$$
$$x_{34} = 29.845130209103$$
$$x_{35} = 4.71238898038469$$
$$x_{36} = 86.3937979737193$$
$$x_{37} = 64.4026493985908$$
$$x_{38} = 89.5353906273091$$
$$x_{39} = -20.4203522483337$$
$$x_{40} = -387.986692718339$$
$$x_{41} = -26.7035375555132$$
$$x_{42} = 98.9601685880785$$
$$x_{43} = 51.8362787842316$$
$$x_{44} = 83.2522053201295$$
$$x_{45} = -48.6946861306418$$
$$x_{46} = -54.9778714378214$$
$$x_{47} = 70.6858347057703$$
$$x_{48} = -95.8185759344887$$
$$x_{49} = 26.7035375555132$$
$$x_{50} = 80.1106126665397$$
$$x_{51} = -23.5619449019235$$
$$x_{52} = -7.85398163397448$$
$$x_{53} = -83.2522053201295$$
$$x_{54} = -76.9690200129499$$
$$x_{55} = -42.4115008234622$$
$$x_{56} = -32.9867228626928$$
$$x_{57} = 17.2787595947439$$
$$x_{58} = 32.9867228626928$$
$$x_{59} = 20.4203522483337$$
$$x_{60} = -70.6858347057703$$
$$x_{61} = -10.9955742875643$$
$$x_{62} = -92.6769832808989$$
$$x_{63} = 45.553093477052$$
$$x_{64} = 10.9955742875643$$
$$x_{65} = -80.1106126665397$$
$$x_{66} = 95.8185759344887$$
$$x_{67} = -2266.65909956504$$
This roots
$$x_{67} = -2266.65909956504$$
$$x_{40} = -387.986692718339$$
$$x_{15} = -168.075206967054$$
$$x_{3} = -98.9601685880785$$
$$x_{48} = -95.8185759344887$$
$$x_{62} = -92.6769832808989$$
$$x_{25} = -89.5353906273091$$
$$x_{21} = -86.3937979737193$$
$$x_{53} = -83.2522053201295$$
$$x_{65} = -80.1106126665397$$
$$x_{54} = -76.9690200129499$$
$$x_{32} = -73.8274273593601$$
$$x_{60} = -70.6858347057703$$
$$x_{18} = -67.5442420521806$$
$$x_{17} = -64.4026493985908$$
$$x_{31} = -61.261056745001$$
$$x_{30} = -58.1194640914112$$
$$x_{46} = -54.9778714378214$$
$$x_{20} = -51.8362787842316$$
$$x_{45} = -48.6946861306418$$
$$x_{24} = -45.553093477052$$
$$x_{55} = -42.4115008234622$$
$$x_{13} = -39.2699081698724$$
$$x_{11} = -36.1283155162826$$
$$x_{56} = -32.9867228626928$$
$$x_{9} = -29.845130209103$$
$$x_{41} = -26.7035375555132$$
$$x_{51} = -23.5619449019235$$
$$x_{39} = -20.4203522483337$$
$$x_{23} = -17.2787595947439$$
$$x_{16} = -14.1371669411541$$
$$x_{61} = -10.9955742875643$$
$$x_{52} = -7.85398163397448$$
$$x_{12} = -4.71238898038469$$
$$x_{26} = -1.5707963267949$$
$$x_{14} = 1.5707963267949$$
$$x_{35} = 4.71238898038469$$
$$x_{29} = 7.85398163397448$$
$$x_{64} = 10.9955742875643$$
$$x_{8} = 14.1371669411541$$
$$x_{57} = 17.2787595947439$$
$$x_{59} = 20.4203522483337$$
$$x_{28} = 23.5619449019235$$
$$x_{49} = 26.7035375555132$$
$$x_{34} = 29.845130209103$$
$$x_{58} = 32.9867228626928$$
$$x_{6} = 36.1283155162826$$
$$x_{27} = 39.2699081698724$$
$$x_{22} = 42.4115008234622$$
$$x_{63} = 45.553093477052$$
$$x_{1} = 48.6946861306418$$
$$x_{43} = 51.8362787842316$$
$$x_{2} = 54.9778714378214$$
$$x_{7} = 58.1194640914112$$
$$x_{10} = 61.261056745001$$
$$x_{37} = 64.4026493985908$$
$$x_{4} = 67.5442420521806$$
$$x_{47} = 70.6858347057703$$
$$x_{33} = 73.8274273593601$$
$$x_{5} = 76.9690200129499$$
$$x_{50} = 80.1106126665397$$
$$x_{44} = 83.2522053201295$$
$$x_{36} = 86.3937979737193$$
$$x_{38} = 89.5353906273091$$
$$x_{19} = 92.6769832808989$$
$$x_{66} = 95.8185759344887$$
$$x_{42} = 98.9601685880785$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{67}$$
For example, let's take the point
$$x_{0} = x_{67} - \frac{1}{10}$$
=
$$-2266.65909956504 + - \frac{1}{10}$$
=
$$-2266.75909956504$$
substitute to the expression
$$\cos{\left(t \right)} \leq 0$$
$$\cos{\left(t \right)} \leq 0$$
Then
$$x \leq -2266.65909956504$$
no execute
one of the solutions of our inequality is:
$$x \geq -2266.65909956504 \wedge x \leq -387.986692718339$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \geq -2266.65909956504 \wedge x \leq -387.986692718339$$
$$x \geq -168.075206967054 \wedge x \leq -98.9601685880785$$
$$x \geq -95.8185759344887 \wedge x \leq -92.6769832808989$$
$$x \geq -89.5353906273091 \wedge x \leq -86.3937979737193$$
$$x \geq -83.2522053201295 \wedge x \leq -80.1106126665397$$
$$x \geq -76.9690200129499 \wedge x \leq -73.8274273593601$$
$$x \geq -70.6858347057703 \wedge x \leq -67.5442420521806$$
$$x \geq -64.4026493985908 \wedge x \leq -61.261056745001$$
$$x \geq -58.1194640914112 \wedge x \leq -54.9778714378214$$
$$x \geq -51.8362787842316 \wedge x \leq -48.6946861306418$$
$$x \geq -45.553093477052 \wedge x \leq -42.4115008234622$$
$$x \geq -39.2699081698724 \wedge x \leq -36.1283155162826$$
$$x \geq -32.9867228626928 \wedge x \leq -29.845130209103$$
$$x \geq -26.7035375555132 \wedge x \leq -23.5619449019235$$
$$x \geq -20.4203522483337 \wedge x \leq -17.2787595947439$$
$$x \geq -14.1371669411541 \wedge x \leq -10.9955742875643$$
$$x \geq -7.85398163397448 \wedge x \leq -4.71238898038469$$
$$x \geq -1.5707963267949 \wedge x \leq 1.5707963267949$$
$$x \geq 4.71238898038469 \wedge x \leq 7.85398163397448$$
$$x \geq 10.9955742875643 \wedge x \leq 14.1371669411541$$
$$x \geq 17.2787595947439 \wedge x \leq 20.4203522483337$$
$$x \geq 23.5619449019235 \wedge x \leq 26.7035375555132$$
$$x \geq 29.845130209103 \wedge x \leq 32.9867228626928$$
$$x \geq 36.1283155162826 \wedge x \leq 39.2699081698724$$
$$x \geq 42.4115008234622 \wedge x \leq 45.553093477052$$
$$x \geq 48.6946861306418 \wedge x \leq 51.8362787842316$$
$$x \geq 54.9778714378214 \wedge x \leq 58.1194640914112$$
$$x \geq 61.261056745001 \wedge x \leq 64.4026493985908$$
$$x \geq 67.5442420521806 \wedge x \leq 70.6858347057703$$
$$x \geq 73.8274273593601 \wedge x \leq 76.9690200129499$$
$$x \geq 80.1106126665397 \wedge x \leq 83.2522053201295$$
$$x \geq 86.3937979737193 \wedge x \leq 89.5353906273091$$
$$x \geq 92.6769832808989 \wedge x \leq 95.8185759344887$$
$$x \geq 98.9601685880785$$
$$\cos{\left(t \right)} \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(t \right)} = 0$$
Solve:
Given the equation
$$\cos{\left(t \right)} = 0$$
transform
$$\cos{\left(t \right)} - 1 = 0$$
$$\cos{\left(t \right)} - 1 = 0$$
Do replacement
$$w = \cos{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = 1$$
We get the answer: w = 1
do backward replacement
$$\cos{\left(t \right)} = w$$
substitute w:
$$x_{1} = 48.6946861306418$$
$$x_{2} = 54.9778714378214$$
$$x_{3} = -98.9601685880785$$
$$x_{4} = 67.5442420521806$$
$$x_{5} = 76.9690200129499$$
$$x_{6} = 36.1283155162826$$
$$x_{7} = 58.1194640914112$$
$$x_{8} = 14.1371669411541$$
$$x_{9} = -29.845130209103$$
$$x_{10} = 61.261056745001$$
$$x_{11} = -36.1283155162826$$
$$x_{12} = -4.71238898038469$$
$$x_{13} = -39.2699081698724$$
$$x_{14} = 1.5707963267949$$
$$x_{15} = -168.075206967054$$
$$x_{16} = -14.1371669411541$$
$$x_{17} = -64.4026493985908$$
$$x_{18} = -67.5442420521806$$
$$x_{19} = 92.6769832808989$$
$$x_{20} = -51.8362787842316$$
$$x_{21} = -86.3937979737193$$
$$x_{22} = 42.4115008234622$$
$$x_{23} = -17.2787595947439$$
$$x_{24} = -45.553093477052$$
$$x_{25} = -89.5353906273091$$
$$x_{26} = -1.5707963267949$$
$$x_{27} = 39.2699081698724$$
$$x_{28} = 23.5619449019235$$
$$x_{29} = 7.85398163397448$$
$$x_{30} = -58.1194640914112$$
$$x_{31} = -61.261056745001$$
$$x_{32} = -73.8274273593601$$
$$x_{33} = 73.8274273593601$$
$$x_{34} = 29.845130209103$$
$$x_{35} = 4.71238898038469$$
$$x_{36} = 86.3937979737193$$
$$x_{37} = 64.4026493985908$$
$$x_{38} = 89.5353906273091$$
$$x_{39} = -20.4203522483337$$
$$x_{40} = -387.986692718339$$
$$x_{41} = -26.7035375555132$$
$$x_{42} = 98.9601685880785$$
$$x_{43} = 51.8362787842316$$
$$x_{44} = 83.2522053201295$$
$$x_{45} = -48.6946861306418$$
$$x_{46} = -54.9778714378214$$
$$x_{47} = 70.6858347057703$$
$$x_{48} = -95.8185759344887$$
$$x_{49} = 26.7035375555132$$
$$x_{50} = 80.1106126665397$$
$$x_{51} = -23.5619449019235$$
$$x_{52} = -7.85398163397448$$
$$x_{53} = -83.2522053201295$$
$$x_{54} = -76.9690200129499$$
$$x_{55} = -42.4115008234622$$
$$x_{56} = -32.9867228626928$$
$$x_{57} = 17.2787595947439$$
$$x_{58} = 32.9867228626928$$
$$x_{59} = 20.4203522483337$$
$$x_{60} = -70.6858347057703$$
$$x_{61} = -10.9955742875643$$
$$x_{62} = -92.6769832808989$$
$$x_{63} = 45.553093477052$$
$$x_{64} = 10.9955742875643$$
$$x_{65} = -80.1106126665397$$
$$x_{66} = 95.8185759344887$$
$$x_{67} = -2266.65909956504$$
$$x_{1} = 48.6946861306418$$
$$x_{2} = 54.9778714378214$$
$$x_{3} = -98.9601685880785$$
$$x_{4} = 67.5442420521806$$
$$x_{5} = 76.9690200129499$$
$$x_{6} = 36.1283155162826$$
$$x_{7} = 58.1194640914112$$
$$x_{8} = 14.1371669411541$$
$$x_{9} = -29.845130209103$$
$$x_{10} = 61.261056745001$$
$$x_{11} = -36.1283155162826$$
$$x_{12} = -4.71238898038469$$
$$x_{13} = -39.2699081698724$$
$$x_{14} = 1.5707963267949$$
$$x_{15} = -168.075206967054$$
$$x_{16} = -14.1371669411541$$
$$x_{17} = -64.4026493985908$$
$$x_{18} = -67.5442420521806$$
$$x_{19} = 92.6769832808989$$
$$x_{20} = -51.8362787842316$$
$$x_{21} = -86.3937979737193$$
$$x_{22} = 42.4115008234622$$
$$x_{23} = -17.2787595947439$$
$$x_{24} = -45.553093477052$$
$$x_{25} = -89.5353906273091$$
$$x_{26} = -1.5707963267949$$
$$x_{27} = 39.2699081698724$$
$$x_{28} = 23.5619449019235$$
$$x_{29} = 7.85398163397448$$
$$x_{30} = -58.1194640914112$$
$$x_{31} = -61.261056745001$$
$$x_{32} = -73.8274273593601$$
$$x_{33} = 73.8274273593601$$
$$x_{34} = 29.845130209103$$
$$x_{35} = 4.71238898038469$$
$$x_{36} = 86.3937979737193$$
$$x_{37} = 64.4026493985908$$
$$x_{38} = 89.5353906273091$$
$$x_{39} = -20.4203522483337$$
$$x_{40} = -387.986692718339$$
$$x_{41} = -26.7035375555132$$
$$x_{42} = 98.9601685880785$$
$$x_{43} = 51.8362787842316$$
$$x_{44} = 83.2522053201295$$
$$x_{45} = -48.6946861306418$$
$$x_{46} = -54.9778714378214$$
$$x_{47} = 70.6858347057703$$
$$x_{48} = -95.8185759344887$$
$$x_{49} = 26.7035375555132$$
$$x_{50} = 80.1106126665397$$
$$x_{51} = -23.5619449019235$$
$$x_{52} = -7.85398163397448$$
$$x_{53} = -83.2522053201295$$
$$x_{54} = -76.9690200129499$$
$$x_{55} = -42.4115008234622$$
$$x_{56} = -32.9867228626928$$
$$x_{57} = 17.2787595947439$$
$$x_{58} = 32.9867228626928$$
$$x_{59} = 20.4203522483337$$
$$x_{60} = -70.6858347057703$$
$$x_{61} = -10.9955742875643$$
$$x_{62} = -92.6769832808989$$
$$x_{63} = 45.553093477052$$
$$x_{64} = 10.9955742875643$$
$$x_{65} = -80.1106126665397$$
$$x_{66} = 95.8185759344887$$
$$x_{67} = -2266.65909956504$$
This roots
$$x_{67} = -2266.65909956504$$
$$x_{40} = -387.986692718339$$
$$x_{15} = -168.075206967054$$
$$x_{3} = -98.9601685880785$$
$$x_{48} = -95.8185759344887$$
$$x_{62} = -92.6769832808989$$
$$x_{25} = -89.5353906273091$$
$$x_{21} = -86.3937979737193$$
$$x_{53} = -83.2522053201295$$
$$x_{65} = -80.1106126665397$$
$$x_{54} = -76.9690200129499$$
$$x_{32} = -73.8274273593601$$
$$x_{60} = -70.6858347057703$$
$$x_{18} = -67.5442420521806$$
$$x_{17} = -64.4026493985908$$
$$x_{31} = -61.261056745001$$
$$x_{30} = -58.1194640914112$$
$$x_{46} = -54.9778714378214$$
$$x_{20} = -51.8362787842316$$
$$x_{45} = -48.6946861306418$$
$$x_{24} = -45.553093477052$$
$$x_{55} = -42.4115008234622$$
$$x_{13} = -39.2699081698724$$
$$x_{11} = -36.1283155162826$$
$$x_{56} = -32.9867228626928$$
$$x_{9} = -29.845130209103$$
$$x_{41} = -26.7035375555132$$
$$x_{51} = -23.5619449019235$$
$$x_{39} = -20.4203522483337$$
$$x_{23} = -17.2787595947439$$
$$x_{16} = -14.1371669411541$$
$$x_{61} = -10.9955742875643$$
$$x_{52} = -7.85398163397448$$
$$x_{12} = -4.71238898038469$$
$$x_{26} = -1.5707963267949$$
$$x_{14} = 1.5707963267949$$
$$x_{35} = 4.71238898038469$$
$$x_{29} = 7.85398163397448$$
$$x_{64} = 10.9955742875643$$
$$x_{8} = 14.1371669411541$$
$$x_{57} = 17.2787595947439$$
$$x_{59} = 20.4203522483337$$
$$x_{28} = 23.5619449019235$$
$$x_{49} = 26.7035375555132$$
$$x_{34} = 29.845130209103$$
$$x_{58} = 32.9867228626928$$
$$x_{6} = 36.1283155162826$$
$$x_{27} = 39.2699081698724$$
$$x_{22} = 42.4115008234622$$
$$x_{63} = 45.553093477052$$
$$x_{1} = 48.6946861306418$$
$$x_{43} = 51.8362787842316$$
$$x_{2} = 54.9778714378214$$
$$x_{7} = 58.1194640914112$$
$$x_{10} = 61.261056745001$$
$$x_{37} = 64.4026493985908$$
$$x_{4} = 67.5442420521806$$
$$x_{47} = 70.6858347057703$$
$$x_{33} = 73.8274273593601$$
$$x_{5} = 76.9690200129499$$
$$x_{50} = 80.1106126665397$$
$$x_{44} = 83.2522053201295$$
$$x_{36} = 86.3937979737193$$
$$x_{38} = 89.5353906273091$$
$$x_{19} = 92.6769832808989$$
$$x_{66} = 95.8185759344887$$
$$x_{42} = 98.9601685880785$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{67}$$
For example, let's take the point
$$x_{0} = x_{67} - \frac{1}{10}$$
=
$$-2266.65909956504 + - \frac{1}{10}$$
=
$$-2266.75909956504$$
substitute to the expression
$$\cos{\left(t \right)} \leq 0$$
$$\cos{\left(t \right)} \leq 0$$
cos(t) <= 0
Then
$$x \leq -2266.65909956504$$
no execute
one of the solutions of our inequality is:
$$x \geq -2266.65909956504 \wedge x \leq -387.986692718339$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
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x67 x40 x15 x3 x48 x62 x25 x21 x53 x65 x54 x32 x60 x18 x17 x31 x30 x46 x20 x45 x24 x55 x13 x11 x56 x9 x41 x51 x39 x23 x16 x61 x52 x12 x26 x14 x35 x29 x64 x8 x57 x59 x28 x49 x34 x58 x6 x27 x22 x63 x1 x43 x2 x7 x10 x37 x4 x47 x33 x5 x50 x44 x36 x38 x19 x66 x42Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \geq -2266.65909956504 \wedge x \leq -387.986692718339$$
$$x \geq -168.075206967054 \wedge x \leq -98.9601685880785$$
$$x \geq -95.8185759344887 \wedge x \leq -92.6769832808989$$
$$x \geq -89.5353906273091 \wedge x \leq -86.3937979737193$$
$$x \geq -83.2522053201295 \wedge x \leq -80.1106126665397$$
$$x \geq -76.9690200129499 \wedge x \leq -73.8274273593601$$
$$x \geq -70.6858347057703 \wedge x \leq -67.5442420521806$$
$$x \geq -64.4026493985908 \wedge x \leq -61.261056745001$$
$$x \geq -58.1194640914112 \wedge x \leq -54.9778714378214$$
$$x \geq -51.8362787842316 \wedge x \leq -48.6946861306418$$
$$x \geq -45.553093477052 \wedge x \leq -42.4115008234622$$
$$x \geq -39.2699081698724 \wedge x \leq -36.1283155162826$$
$$x \geq -32.9867228626928 \wedge x \leq -29.845130209103$$
$$x \geq -26.7035375555132 \wedge x \leq -23.5619449019235$$
$$x \geq -20.4203522483337 \wedge x \leq -17.2787595947439$$
$$x \geq -14.1371669411541 \wedge x \leq -10.9955742875643$$
$$x \geq -7.85398163397448 \wedge x \leq -4.71238898038469$$
$$x \geq -1.5707963267949 \wedge x \leq 1.5707963267949$$
$$x \geq 4.71238898038469 \wedge x \leq 7.85398163397448$$
$$x \geq 10.9955742875643 \wedge x \leq 14.1371669411541$$
$$x \geq 17.2787595947439 \wedge x \leq 20.4203522483337$$
$$x \geq 23.5619449019235 \wedge x \leq 26.7035375555132$$
$$x \geq 29.845130209103 \wedge x \leq 32.9867228626928$$
$$x \geq 36.1283155162826 \wedge x \leq 39.2699081698724$$
$$x \geq 42.4115008234622 \wedge x \leq 45.553093477052$$
$$x \geq 48.6946861306418 \wedge x \leq 51.8362787842316$$
$$x \geq 54.9778714378214 \wedge x \leq 58.1194640914112$$
$$x \geq 61.261056745001 \wedge x \leq 64.4026493985908$$
$$x \geq 67.5442420521806 \wedge x \leq 70.6858347057703$$
$$x \geq 73.8274273593601 \wedge x \leq 76.9690200129499$$
$$x \geq 80.1106126665397 \wedge x \leq 83.2522053201295$$
$$x \geq 86.3937979737193 \wedge x \leq 89.5353906273091$$
$$x \geq 92.6769832808989 \wedge x \leq 95.8185759344887$$
$$x \geq 98.9601685880785$$
Rapid solution
[src]
/pi 3*pi\ And|-- <= t, t <= ----| \2 2 /
$$\frac{\pi}{2} \leq t \wedge t \leq \frac{3 \pi}{2}$$
(pi/2 <= t)∧(t <= 3*pi/2)
Rapid solution 2
[src]
pi 3*pi [--, ----] 2 2
$$x\ in\ \left[\frac{\pi}{2}, \frac{3 \pi}{2}\right]$$
x in Interval(pi/2, 3*pi/2)