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-3)√x^2-√1<0
- (x^2-7|x|+10)/(x^2-6x+9)>=0
- 5x^2-2x^4+7>0
- 1−4x<2x+23−x−12
- Derivative of:
-
cos(t)
- Limit of the function:
-
cos(t)
-
1/7
- Integral of d{x}:
- cos(t)
-
Identical expressions
- cos(t)< one / seven
- co sinus of e of (t) less than 1 divide by 7
- co sinus of e of (t) less than one divide by seven
- cost<1/7
- cos(t)<1 divide by 7
-
Similar expressions
- cost>=-sqrt(2)/2
cos(t)<1/7 inequation
The solution
Detail solution
Given the inequality:
$$\cos{\left(t \right)} < \frac{1}{7}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(t \right)} = \frac{1}{7}$$
Solve:
Given the equation
$$\cos{\left(t \right)} = \frac{1}{7}$$
transform
$$\cos{\left(t \right)} - \frac{1}{7} = 0$$
$$\cos{\left(t \right)} - \frac{1}{7} = 0$$
Do replacement
$$w = \cos{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{1}{7}$$
We get the answer: w = 1/7
do backward replacement
$$\cos{\left(t \right)} = w$$
substitute w:
$$x_{1} = 73.9707749282655$$
$$x_{2} = 120.807969594302$$
$$x_{3} = 51.6929312153262$$
$$x_{4} = 29.9884777780084$$
$$x_{5} = -57.9761165225058$$
$$x_{6} = 83.1088577512241$$
$$x_{7} = -99.1035161569839$$
$$x_{8} = -67.6875896210859$$
$$x_{9} = 92.8203308498043$$
$$x_{10} = -42.5548483923676$$
$$x_{11} = -70.542487136865$$
$$x_{12} = 55.1212190067267$$
$$x_{13} = 17.4221071636492$$
$$x_{14} = 23.7052924708288$$
$$x_{15} = -80.2539602354451$$
$$x_{16} = -55.1212190067267$$
$$x_{17} = -36.271663085188$$
$$x_{18} = 48.8380336995472$$
$$x_{19} = 76.8256724440446$$
$$x_{20} = -29.9884777780084$$
$$x_{21} = -4.85573654929006$$
$$x_{22} = 61.4044043139063$$
$$x_{23} = -89.3920430584037$$
$$x_{24} = 95.6752283655833$$
$$x_{25} = -32.8433752937875$$
$$x_{26} = -45.4097459081466$$
$$x_{27} = 86.5371455426247$$
$$x_{28} = 7.71063406506912$$
$$x_{29} = 4.85573654929006$$
$$x_{30} = -17.4221071636492$$
$$x_{31} = 1.42744875788953$$
$$x_{32} = -26.5601899866079$$
$$x_{33} = -13.9938193722487$$
$$x_{34} = 20.2770046794283$$
$$x_{35} = -83.1088577512241$$
$$x_{36} = -23.7052924708288$$
$$x_{37} = -13252.6652615996$$
$$x_{38} = -7.71063406506912$$
$$x_{39} = -20.2770046794283$$
$$x_{40} = 67.6875896210859$$
$$x_{41} = -92.8203308498043$$
$$x_{42} = -76.8256724440446$$
$$x_{43} = -64.2593018296854$$
$$x_{44} = -51.6929312153262$$
$$x_{45} = 39.1265606009671$$
$$x_{46} = 45.4097459081466$$
$$x_{47} = 36.271663085188$$
$$x_{48} = 89.3920430584037$$
$$x_{49} = 64.2593018296854$$
$$x_{50} = 26.5601899866079$$
$$x_{51} = -1.42744875788953$$
$$x_{52} = -73.9707749282655$$
$$x_{53} = 13.9938193722487$$
$$x_{54} = -11.1389218564696$$
$$x_{55} = -61.4044043139063$$
$$x_{56} = 32.8433752937875$$
$$x_{57} = 99.1035161569839$$
$$x_{58} = -39.1265606009671$$
$$x_{59} = 70.542487136865$$
$$x_{60} = 11.1389218564696$$
$$x_{61} = -86.5371455426247$$
$$x_{62} = -12017630.0530054$$
$$x_{63} = -95.6752283655833$$
$$x_{64} = 42.5548483923676$$
$$x_{65} = 80.2539602354451$$
$$x_{66} = 57.9761165225058$$
$$x_{67} = -48.8380336995472$$
$$x_{1} = 73.9707749282655$$
$$x_{2} = 120.807969594302$$
$$x_{3} = 51.6929312153262$$
$$x_{4} = 29.9884777780084$$
$$x_{5} = -57.9761165225058$$
$$x_{6} = 83.1088577512241$$
$$x_{7} = -99.1035161569839$$
$$x_{8} = -67.6875896210859$$
$$x_{9} = 92.8203308498043$$
$$x_{10} = -42.5548483923676$$
$$x_{11} = -70.542487136865$$
$$x_{12} = 55.1212190067267$$
$$x_{13} = 17.4221071636492$$
$$x_{14} = 23.7052924708288$$
$$x_{15} = -80.2539602354451$$
$$x_{16} = -55.1212190067267$$
$$x_{17} = -36.271663085188$$
$$x_{18} = 48.8380336995472$$
$$x_{19} = 76.8256724440446$$
$$x_{20} = -29.9884777780084$$
$$x_{21} = -4.85573654929006$$
$$x_{22} = 61.4044043139063$$
$$x_{23} = -89.3920430584037$$
$$x_{24} = 95.6752283655833$$
$$x_{25} = -32.8433752937875$$
$$x_{26} = -45.4097459081466$$
$$x_{27} = 86.5371455426247$$
$$x_{28} = 7.71063406506912$$
$$x_{29} = 4.85573654929006$$
$$x_{30} = -17.4221071636492$$
$$x_{31} = 1.42744875788953$$
$$x_{32} = -26.5601899866079$$
$$x_{33} = -13.9938193722487$$
$$x_{34} = 20.2770046794283$$
$$x_{35} = -83.1088577512241$$
$$x_{36} = -23.7052924708288$$
$$x_{37} = -13252.6652615996$$
$$x_{38} = -7.71063406506912$$
$$x_{39} = -20.2770046794283$$
$$x_{40} = 67.6875896210859$$
$$x_{41} = -92.8203308498043$$
$$x_{42} = -76.8256724440446$$
$$x_{43} = -64.2593018296854$$
$$x_{44} = -51.6929312153262$$
$$x_{45} = 39.1265606009671$$
$$x_{46} = 45.4097459081466$$
$$x_{47} = 36.271663085188$$
$$x_{48} = 89.3920430584037$$
$$x_{49} = 64.2593018296854$$
$$x_{50} = 26.5601899866079$$
$$x_{51} = -1.42744875788953$$
$$x_{52} = -73.9707749282655$$
$$x_{53} = 13.9938193722487$$
$$x_{54} = -11.1389218564696$$
$$x_{55} = -61.4044043139063$$
$$x_{56} = 32.8433752937875$$
$$x_{57} = 99.1035161569839$$
$$x_{58} = -39.1265606009671$$
$$x_{59} = 70.542487136865$$
$$x_{60} = 11.1389218564696$$
$$x_{61} = -86.5371455426247$$
$$x_{62} = -12017630.0530054$$
$$x_{63} = -95.6752283655833$$
$$x_{64} = 42.5548483923676$$
$$x_{65} = 80.2539602354451$$
$$x_{66} = 57.9761165225058$$
$$x_{67} = -48.8380336995472$$
This roots
$$x_{62} = -12017630.0530054$$
$$x_{37} = -13252.6652615996$$
$$x_{7} = -99.1035161569839$$
$$x_{63} = -95.6752283655833$$
$$x_{41} = -92.8203308498043$$
$$x_{23} = -89.3920430584037$$
$$x_{61} = -86.5371455426247$$
$$x_{35} = -83.1088577512241$$
$$x_{15} = -80.2539602354451$$
$$x_{42} = -76.8256724440446$$
$$x_{52} = -73.9707749282655$$
$$x_{11} = -70.542487136865$$
$$x_{8} = -67.6875896210859$$
$$x_{43} = -64.2593018296854$$
$$x_{55} = -61.4044043139063$$
$$x_{5} = -57.9761165225058$$
$$x_{16} = -55.1212190067267$$
$$x_{44} = -51.6929312153262$$
$$x_{67} = -48.8380336995472$$
$$x_{26} = -45.4097459081466$$
$$x_{10} = -42.5548483923676$$
$$x_{58} = -39.1265606009671$$
$$x_{17} = -36.271663085188$$
$$x_{25} = -32.8433752937875$$
$$x_{20} = -29.9884777780084$$
$$x_{32} = -26.5601899866079$$
$$x_{36} = -23.7052924708288$$
$$x_{39} = -20.2770046794283$$
$$x_{30} = -17.4221071636492$$
$$x_{33} = -13.9938193722487$$
$$x_{54} = -11.1389218564696$$
$$x_{38} = -7.71063406506912$$
$$x_{21} = -4.85573654929006$$
$$x_{51} = -1.42744875788953$$
$$x_{31} = 1.42744875788953$$
$$x_{29} = 4.85573654929006$$
$$x_{28} = 7.71063406506912$$
$$x_{60} = 11.1389218564696$$
$$x_{53} = 13.9938193722487$$
$$x_{13} = 17.4221071636492$$
$$x_{34} = 20.2770046794283$$
$$x_{14} = 23.7052924708288$$
$$x_{50} = 26.5601899866079$$
$$x_{4} = 29.9884777780084$$
$$x_{56} = 32.8433752937875$$
$$x_{47} = 36.271663085188$$
$$x_{45} = 39.1265606009671$$
$$x_{64} = 42.5548483923676$$
$$x_{46} = 45.4097459081466$$
$$x_{18} = 48.8380336995472$$
$$x_{3} = 51.6929312153262$$
$$x_{12} = 55.1212190067267$$
$$x_{66} = 57.9761165225058$$
$$x_{22} = 61.4044043139063$$
$$x_{49} = 64.2593018296854$$
$$x_{40} = 67.6875896210859$$
$$x_{59} = 70.542487136865$$
$$x_{1} = 73.9707749282655$$
$$x_{19} = 76.8256724440446$$
$$x_{65} = 80.2539602354451$$
$$x_{6} = 83.1088577512241$$
$$x_{27} = 86.5371455426247$$
$$x_{48} = 89.3920430584037$$
$$x_{9} = 92.8203308498043$$
$$x_{24} = 95.6752283655833$$
$$x_{57} = 99.1035161569839$$
$$x_{2} = 120.807969594302$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{62}$$
For example, let's take the point
$$x_{0} = x_{62} - \frac{1}{10}$$
=
$$-12017630.0530054 + - \frac{1}{10}$$
=
$$-12017630.1530054$$
substitute to the expression
$$\cos{\left(t \right)} < \frac{1}{7}$$
$$\cos{\left(t \right)} < \frac{1}{7}$$
Then
$$x < -12017630.0530054$$
no execute
one of the solutions of our inequality is:
$$x > -12017630.0530054 \wedge x < -13252.6652615996$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -12017630.0530054 \wedge x < -13252.6652615996$$
$$x > -99.1035161569839 \wedge x < -95.6752283655833$$
$$x > -92.8203308498043 \wedge x < -89.3920430584037$$
$$x > -86.5371455426247 \wedge x < -83.1088577512241$$
$$x > -80.2539602354451 \wedge x < -76.8256724440446$$
$$x > -73.9707749282655 \wedge x < -70.542487136865$$
$$x > -67.6875896210859 \wedge x < -64.2593018296854$$
$$x > -61.4044043139063 \wedge x < -57.9761165225058$$
$$x > -55.1212190067267 \wedge x < -51.6929312153262$$
$$x > -48.8380336995472 \wedge x < -45.4097459081466$$
$$x > -42.5548483923676 \wedge x < -39.1265606009671$$
$$x > -36.271663085188 \wedge x < -32.8433752937875$$
$$x > -29.9884777780084 \wedge x < -26.5601899866079$$
$$x > -23.7052924708288 \wedge x < -20.2770046794283$$
$$x > -17.4221071636492 \wedge x < -13.9938193722487$$
$$x > -11.1389218564696 \wedge x < -7.71063406506912$$
$$x > -4.85573654929006 \wedge x < -1.42744875788953$$
$$x > 1.42744875788953 \wedge x < 4.85573654929006$$
$$x > 7.71063406506912 \wedge x < 11.1389218564696$$
$$x > 13.9938193722487 \wedge x < 17.4221071636492$$
$$x > 20.2770046794283 \wedge x < 23.7052924708288$$
$$x > 26.5601899866079 \wedge x < 29.9884777780084$$
$$x > 32.8433752937875 \wedge x < 36.271663085188$$
$$x > 39.1265606009671 \wedge x < 42.5548483923676$$
$$x > 45.4097459081466 \wedge x < 48.8380336995472$$
$$x > 51.6929312153262 \wedge x < 55.1212190067267$$
$$x > 57.9761165225058 \wedge x < 61.4044043139063$$
$$x > 64.2593018296854 \wedge x < 67.6875896210859$$
$$x > 70.542487136865 \wedge x < 73.9707749282655$$
$$x > 76.8256724440446 \wedge x < 80.2539602354451$$
$$x > 83.1088577512241 \wedge x < 86.5371455426247$$
$$x > 89.3920430584037 \wedge x < 92.8203308498043$$
$$x > 95.6752283655833 \wedge x < 99.1035161569839$$
$$x > 120.807969594302$$
$$\cos{\left(t \right)} < \frac{1}{7}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(t \right)} = \frac{1}{7}$$
Solve:
Given the equation
$$\cos{\left(t \right)} = \frac{1}{7}$$
transform
$$\cos{\left(t \right)} - \frac{1}{7} = 0$$
$$\cos{\left(t \right)} - \frac{1}{7} = 0$$
Do replacement
$$w = \cos{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{1}{7}$$
We get the answer: w = 1/7
do backward replacement
$$\cos{\left(t \right)} = w$$
substitute w:
$$x_{1} = 73.9707749282655$$
$$x_{2} = 120.807969594302$$
$$x_{3} = 51.6929312153262$$
$$x_{4} = 29.9884777780084$$
$$x_{5} = -57.9761165225058$$
$$x_{6} = 83.1088577512241$$
$$x_{7} = -99.1035161569839$$
$$x_{8} = -67.6875896210859$$
$$x_{9} = 92.8203308498043$$
$$x_{10} = -42.5548483923676$$
$$x_{11} = -70.542487136865$$
$$x_{12} = 55.1212190067267$$
$$x_{13} = 17.4221071636492$$
$$x_{14} = 23.7052924708288$$
$$x_{15} = -80.2539602354451$$
$$x_{16} = -55.1212190067267$$
$$x_{17} = -36.271663085188$$
$$x_{18} = 48.8380336995472$$
$$x_{19} = 76.8256724440446$$
$$x_{20} = -29.9884777780084$$
$$x_{21} = -4.85573654929006$$
$$x_{22} = 61.4044043139063$$
$$x_{23} = -89.3920430584037$$
$$x_{24} = 95.6752283655833$$
$$x_{25} = -32.8433752937875$$
$$x_{26} = -45.4097459081466$$
$$x_{27} = 86.5371455426247$$
$$x_{28} = 7.71063406506912$$
$$x_{29} = 4.85573654929006$$
$$x_{30} = -17.4221071636492$$
$$x_{31} = 1.42744875788953$$
$$x_{32} = -26.5601899866079$$
$$x_{33} = -13.9938193722487$$
$$x_{34} = 20.2770046794283$$
$$x_{35} = -83.1088577512241$$
$$x_{36} = -23.7052924708288$$
$$x_{37} = -13252.6652615996$$
$$x_{38} = -7.71063406506912$$
$$x_{39} = -20.2770046794283$$
$$x_{40} = 67.6875896210859$$
$$x_{41} = -92.8203308498043$$
$$x_{42} = -76.8256724440446$$
$$x_{43} = -64.2593018296854$$
$$x_{44} = -51.6929312153262$$
$$x_{45} = 39.1265606009671$$
$$x_{46} = 45.4097459081466$$
$$x_{47} = 36.271663085188$$
$$x_{48} = 89.3920430584037$$
$$x_{49} = 64.2593018296854$$
$$x_{50} = 26.5601899866079$$
$$x_{51} = -1.42744875788953$$
$$x_{52} = -73.9707749282655$$
$$x_{53} = 13.9938193722487$$
$$x_{54} = -11.1389218564696$$
$$x_{55} = -61.4044043139063$$
$$x_{56} = 32.8433752937875$$
$$x_{57} = 99.1035161569839$$
$$x_{58} = -39.1265606009671$$
$$x_{59} = 70.542487136865$$
$$x_{60} = 11.1389218564696$$
$$x_{61} = -86.5371455426247$$
$$x_{62} = -12017630.0530054$$
$$x_{63} = -95.6752283655833$$
$$x_{64} = 42.5548483923676$$
$$x_{65} = 80.2539602354451$$
$$x_{66} = 57.9761165225058$$
$$x_{67} = -48.8380336995472$$
$$x_{1} = 73.9707749282655$$
$$x_{2} = 120.807969594302$$
$$x_{3} = 51.6929312153262$$
$$x_{4} = 29.9884777780084$$
$$x_{5} = -57.9761165225058$$
$$x_{6} = 83.1088577512241$$
$$x_{7} = -99.1035161569839$$
$$x_{8} = -67.6875896210859$$
$$x_{9} = 92.8203308498043$$
$$x_{10} = -42.5548483923676$$
$$x_{11} = -70.542487136865$$
$$x_{12} = 55.1212190067267$$
$$x_{13} = 17.4221071636492$$
$$x_{14} = 23.7052924708288$$
$$x_{15} = -80.2539602354451$$
$$x_{16} = -55.1212190067267$$
$$x_{17} = -36.271663085188$$
$$x_{18} = 48.8380336995472$$
$$x_{19} = 76.8256724440446$$
$$x_{20} = -29.9884777780084$$
$$x_{21} = -4.85573654929006$$
$$x_{22} = 61.4044043139063$$
$$x_{23} = -89.3920430584037$$
$$x_{24} = 95.6752283655833$$
$$x_{25} = -32.8433752937875$$
$$x_{26} = -45.4097459081466$$
$$x_{27} = 86.5371455426247$$
$$x_{28} = 7.71063406506912$$
$$x_{29} = 4.85573654929006$$
$$x_{30} = -17.4221071636492$$
$$x_{31} = 1.42744875788953$$
$$x_{32} = -26.5601899866079$$
$$x_{33} = -13.9938193722487$$
$$x_{34} = 20.2770046794283$$
$$x_{35} = -83.1088577512241$$
$$x_{36} = -23.7052924708288$$
$$x_{37} = -13252.6652615996$$
$$x_{38} = -7.71063406506912$$
$$x_{39} = -20.2770046794283$$
$$x_{40} = 67.6875896210859$$
$$x_{41} = -92.8203308498043$$
$$x_{42} = -76.8256724440446$$
$$x_{43} = -64.2593018296854$$
$$x_{44} = -51.6929312153262$$
$$x_{45} = 39.1265606009671$$
$$x_{46} = 45.4097459081466$$
$$x_{47} = 36.271663085188$$
$$x_{48} = 89.3920430584037$$
$$x_{49} = 64.2593018296854$$
$$x_{50} = 26.5601899866079$$
$$x_{51} = -1.42744875788953$$
$$x_{52} = -73.9707749282655$$
$$x_{53} = 13.9938193722487$$
$$x_{54} = -11.1389218564696$$
$$x_{55} = -61.4044043139063$$
$$x_{56} = 32.8433752937875$$
$$x_{57} = 99.1035161569839$$
$$x_{58} = -39.1265606009671$$
$$x_{59} = 70.542487136865$$
$$x_{60} = 11.1389218564696$$
$$x_{61} = -86.5371455426247$$
$$x_{62} = -12017630.0530054$$
$$x_{63} = -95.6752283655833$$
$$x_{64} = 42.5548483923676$$
$$x_{65} = 80.2539602354451$$
$$x_{66} = 57.9761165225058$$
$$x_{67} = -48.8380336995472$$
This roots
$$x_{62} = -12017630.0530054$$
$$x_{37} = -13252.6652615996$$
$$x_{7} = -99.1035161569839$$
$$x_{63} = -95.6752283655833$$
$$x_{41} = -92.8203308498043$$
$$x_{23} = -89.3920430584037$$
$$x_{61} = -86.5371455426247$$
$$x_{35} = -83.1088577512241$$
$$x_{15} = -80.2539602354451$$
$$x_{42} = -76.8256724440446$$
$$x_{52} = -73.9707749282655$$
$$x_{11} = -70.542487136865$$
$$x_{8} = -67.6875896210859$$
$$x_{43} = -64.2593018296854$$
$$x_{55} = -61.4044043139063$$
$$x_{5} = -57.9761165225058$$
$$x_{16} = -55.1212190067267$$
$$x_{44} = -51.6929312153262$$
$$x_{67} = -48.8380336995472$$
$$x_{26} = -45.4097459081466$$
$$x_{10} = -42.5548483923676$$
$$x_{58} = -39.1265606009671$$
$$x_{17} = -36.271663085188$$
$$x_{25} = -32.8433752937875$$
$$x_{20} = -29.9884777780084$$
$$x_{32} = -26.5601899866079$$
$$x_{36} = -23.7052924708288$$
$$x_{39} = -20.2770046794283$$
$$x_{30} = -17.4221071636492$$
$$x_{33} = -13.9938193722487$$
$$x_{54} = -11.1389218564696$$
$$x_{38} = -7.71063406506912$$
$$x_{21} = -4.85573654929006$$
$$x_{51} = -1.42744875788953$$
$$x_{31} = 1.42744875788953$$
$$x_{29} = 4.85573654929006$$
$$x_{28} = 7.71063406506912$$
$$x_{60} = 11.1389218564696$$
$$x_{53} = 13.9938193722487$$
$$x_{13} = 17.4221071636492$$
$$x_{34} = 20.2770046794283$$
$$x_{14} = 23.7052924708288$$
$$x_{50} = 26.5601899866079$$
$$x_{4} = 29.9884777780084$$
$$x_{56} = 32.8433752937875$$
$$x_{47} = 36.271663085188$$
$$x_{45} = 39.1265606009671$$
$$x_{64} = 42.5548483923676$$
$$x_{46} = 45.4097459081466$$
$$x_{18} = 48.8380336995472$$
$$x_{3} = 51.6929312153262$$
$$x_{12} = 55.1212190067267$$
$$x_{66} = 57.9761165225058$$
$$x_{22} = 61.4044043139063$$
$$x_{49} = 64.2593018296854$$
$$x_{40} = 67.6875896210859$$
$$x_{59} = 70.542487136865$$
$$x_{1} = 73.9707749282655$$
$$x_{19} = 76.8256724440446$$
$$x_{65} = 80.2539602354451$$
$$x_{6} = 83.1088577512241$$
$$x_{27} = 86.5371455426247$$
$$x_{48} = 89.3920430584037$$
$$x_{9} = 92.8203308498043$$
$$x_{24} = 95.6752283655833$$
$$x_{57} = 99.1035161569839$$
$$x_{2} = 120.807969594302$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{62}$$
For example, let's take the point
$$x_{0} = x_{62} - \frac{1}{10}$$
=
$$-12017630.0530054 + - \frac{1}{10}$$
=
$$-12017630.1530054$$
substitute to the expression
$$\cos{\left(t \right)} < \frac{1}{7}$$
$$\cos{\left(t \right)} < \frac{1}{7}$$
cos(t) < 1/7
Then
$$x < -12017630.0530054$$
no execute
one of the solutions of our inequality is:
$$x > -12017630.0530054 \wedge x < -13252.6652615996$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------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-------
x62 x37 x7 x63 x41 x23 x61 x35 x15 x42 x52 x11 x8 x43 x55 x5 x16 x44 x67 x26 x10 x58 x17 x25 x20 x32 x36 x39 x30 x33 x54 x38 x21 x51 x31 x29 x28 x60 x53 x13 x34 x14 x50 x4 x56 x47 x45 x64 x46 x18 x3 x12 x66 x22 x49 x40 x59 x1 x19 x65 x6 x27 x48 x9 x24 x57 x2Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -12017630.0530054 \wedge x < -13252.6652615996$$
$$x > -99.1035161569839 \wedge x < -95.6752283655833$$
$$x > -92.8203308498043 \wedge x < -89.3920430584037$$
$$x > -86.5371455426247 \wedge x < -83.1088577512241$$
$$x > -80.2539602354451 \wedge x < -76.8256724440446$$
$$x > -73.9707749282655 \wedge x < -70.542487136865$$
$$x > -67.6875896210859 \wedge x < -64.2593018296854$$
$$x > -61.4044043139063 \wedge x < -57.9761165225058$$
$$x > -55.1212190067267 \wedge x < -51.6929312153262$$
$$x > -48.8380336995472 \wedge x < -45.4097459081466$$
$$x > -42.5548483923676 \wedge x < -39.1265606009671$$
$$x > -36.271663085188 \wedge x < -32.8433752937875$$
$$x > -29.9884777780084 \wedge x < -26.5601899866079$$
$$x > -23.7052924708288 \wedge x < -20.2770046794283$$
$$x > -17.4221071636492 \wedge x < -13.9938193722487$$
$$x > -11.1389218564696 \wedge x < -7.71063406506912$$
$$x > -4.85573654929006 \wedge x < -1.42744875788953$$
$$x > 1.42744875788953 \wedge x < 4.85573654929006$$
$$x > 7.71063406506912 \wedge x < 11.1389218564696$$
$$x > 13.9938193722487 \wedge x < 17.4221071636492$$
$$x > 20.2770046794283 \wedge x < 23.7052924708288$$
$$x > 26.5601899866079 \wedge x < 29.9884777780084$$
$$x > 32.8433752937875 \wedge x < 36.271663085188$$
$$x > 39.1265606009671 \wedge x < 42.5548483923676$$
$$x > 45.4097459081466 \wedge x < 48.8380336995472$$
$$x > 51.6929312153262 \wedge x < 55.1212190067267$$
$$x > 57.9761165225058 \wedge x < 61.4044043139063$$
$$x > 64.2593018296854 \wedge x < 67.6875896210859$$
$$x > 70.542487136865 \wedge x < 73.9707749282655$$
$$x > 76.8256724440446 \wedge x < 80.2539602354451$$
$$x > 83.1088577512241 \wedge x < 86.5371455426247$$
$$x > 89.3920430584037 \wedge x < 92.8203308498043$$
$$x > 95.6752283655833 \wedge x < 99.1035161569839$$
$$x > 120.807969594302$$
Rapid solution
[src]
/ / ___\ / ___\ \ And\t < - atan\4*\/ 3 / + 2*pi, atan\4*\/ 3 / < t/
$$t < - \operatorname{atan}{\left(4 \sqrt{3} \right)} + 2 \pi \wedge \operatorname{atan}{\left(4 \sqrt{3} \right)} < t$$
(atan(4*sqrt(3)) < t)∧(t < -atan(4*sqrt(3)) + 2*pi)
Rapid solution 2
[src]
/ ___\ / ___\ (atan\4*\/ 3 /, - atan\4*\/ 3 / + 2*pi)
$$x\ in\ \left(\operatorname{atan}{\left(4 \sqrt{3} \right)}, - \operatorname{atan}{\left(4 \sqrt{3} \right)} + 2 \pi\right)$$
x in Interval.open(atan(4*sqrt(3)), -atan(4*sqrt(3)) + 2*pi)