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
- Integral of d{x}:
-
cost
- Derivative of:
-
cost
-
1/3
- Sum of series:
-
1/3
- Limit of the function:
- 1/3
-
Identical expressions
- cost< one / three
- co sinus of e of t less than 1 divide by 3
- co sinus of e of t less than one divide by three
- cost<1 divide by 3
-
Similar expressions
- log(1)/3*(x+1)-log(1)/3*(x-1)>=log(1)/3*(x)
- cos(t)<1/5
- cos(t)<=1/2
- cos(t)<=0
cost<1/3 inequation
The solution
Detail solution
Given the inequality:
$$\cos{\left(t \right)} < \frac{1}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(t \right)} = \frac{1}{3}$$
Solve:
Given the equation
$$\cos{\left(t \right)} = \frac{1}{3}$$
transform
$$\cos{\left(t \right)} - \frac{1}{3} = 0$$
$$\cos{\left(t \right)} - \frac{1}{3} = 0$$
Do replacement
$$w = \cos{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{1}{3}$$
We get the answer: w = 1/3
do backward replacement
$$\cos{\left(t \right)} = w$$
substitute w:
$$x_{1} = -86.7336348831734$$
$$x_{2} = -49.0345230400959$$
$$x_{3} = -61.6008936544551$$
$$x_{4} = 42.7513377329163$$
$$x_{5} = -99.3000054975326$$
$$x_{6} = -30.1849671185572$$
$$x_{7} = 5.05222588983881$$
$$x_{8} = -51.4964418747775$$
$$x_{9} = -101.761924332214$$
$$x_{10} = 20.0805153388795$$
$$x_{11} = -38.9300712604183$$
$$x_{12} = -55.3177083472755$$
$$x_{13} = 36.4681524257367$$
$$x_{14} = 86.7336348831734$$
$$x_{15} = -80.4504495759938$$
$$x_{16} = 11.3354111970184$$
$$x_{17} = 32.6468859532387$$
$$x_{18} = -36.4681524257367$$
$$x_{19} = -57.7796271819571$$
$$x_{20} = 93.016820190353$$
$$x_{21} = 23.9017818113776$$
$$x_{22} = -26.3637006460591$$
$$x_{23} = 76.6291831034958$$
$$x_{24} = -325.494676555998$$
$$x_{25} = -13.7973300316999$$
$$x_{26} = -32.6468859532387$$
$$x_{27} = 95.4787390250346$$
$$x_{28} = 30.1849671185572$$
$$x_{29} = -93.016820190353$$
$$x_{30} = -17.618596504198$$
$$x_{31} = 67.8840789616347$$
$$x_{32} = 17.618596504198$$
$$x_{33} = 82.9123684106754$$
$$x_{34} = 45.2132565675979$$
$$x_{35} = 51.4964418747775$$
$$x_{36} = 7.51414472452036$$
$$x_{37} = 61.6008936544551$$
$$x_{38} = -67.8840789616347$$
$$x_{39} = 64.0628124891366$$
$$x_{40} = 38.9300712604183$$
$$x_{41} = -64.0628124891366$$
$$x_{42} = 70.3459977963162$$
$$x_{43} = 13.7973300316999$$
$$x_{44} = 89.195553717855$$
$$x_{45} = -76.6291831034958$$
$$x_{46} = -1.23095941734077$$
$$x_{47} = -7.51414472452036$$
$$x_{48} = -82.9123684106754$$
$$x_{49} = 99.3000054975326$$
$$x_{50} = 74.1672642688143$$
$$x_{51} = 1.23095941734077$$
$$x_{52} = -11.3354111970184$$
$$x_{53} = 80.4504495759938$$
$$x_{54} = -23.9017818113776$$
$$x_{55} = -5.05222588983881$$
$$x_{56} = -20.0805153388795$$
$$x_{57} = -45.2132565675979$$
$$x_{58} = 26.3637006460591$$
$$x_{59} = 57.7796271819571$$
$$x_{60} = -95.4787390250346$$
$$x_{61} = 55.3177083472755$$
$$x_{62} = 49.0345230400959$$
$$x_{63} = -42.7513377329163$$
$$x_{64} = -89.195553717855$$
$$x_{65} = -70.3459977963162$$
$$x_{66} = -74.1672642688143$$
$$x_{1} = -86.7336348831734$$
$$x_{2} = -49.0345230400959$$
$$x_{3} = -61.6008936544551$$
$$x_{4} = 42.7513377329163$$
$$x_{5} = -99.3000054975326$$
$$x_{6} = -30.1849671185572$$
$$x_{7} = 5.05222588983881$$
$$x_{8} = -51.4964418747775$$
$$x_{9} = -101.761924332214$$
$$x_{10} = 20.0805153388795$$
$$x_{11} = -38.9300712604183$$
$$x_{12} = -55.3177083472755$$
$$x_{13} = 36.4681524257367$$
$$x_{14} = 86.7336348831734$$
$$x_{15} = -80.4504495759938$$
$$x_{16} = 11.3354111970184$$
$$x_{17} = 32.6468859532387$$
$$x_{18} = -36.4681524257367$$
$$x_{19} = -57.7796271819571$$
$$x_{20} = 93.016820190353$$
$$x_{21} = 23.9017818113776$$
$$x_{22} = -26.3637006460591$$
$$x_{23} = 76.6291831034958$$
$$x_{24} = -325.494676555998$$
$$x_{25} = -13.7973300316999$$
$$x_{26} = -32.6468859532387$$
$$x_{27} = 95.4787390250346$$
$$x_{28} = 30.1849671185572$$
$$x_{29} = -93.016820190353$$
$$x_{30} = -17.618596504198$$
$$x_{31} = 67.8840789616347$$
$$x_{32} = 17.618596504198$$
$$x_{33} = 82.9123684106754$$
$$x_{34} = 45.2132565675979$$
$$x_{35} = 51.4964418747775$$
$$x_{36} = 7.51414472452036$$
$$x_{37} = 61.6008936544551$$
$$x_{38} = -67.8840789616347$$
$$x_{39} = 64.0628124891366$$
$$x_{40} = 38.9300712604183$$
$$x_{41} = -64.0628124891366$$
$$x_{42} = 70.3459977963162$$
$$x_{43} = 13.7973300316999$$
$$x_{44} = 89.195553717855$$
$$x_{45} = -76.6291831034958$$
$$x_{46} = -1.23095941734077$$
$$x_{47} = -7.51414472452036$$
$$x_{48} = -82.9123684106754$$
$$x_{49} = 99.3000054975326$$
$$x_{50} = 74.1672642688143$$
$$x_{51} = 1.23095941734077$$
$$x_{52} = -11.3354111970184$$
$$x_{53} = 80.4504495759938$$
$$x_{54} = -23.9017818113776$$
$$x_{55} = -5.05222588983881$$
$$x_{56} = -20.0805153388795$$
$$x_{57} = -45.2132565675979$$
$$x_{58} = 26.3637006460591$$
$$x_{59} = 57.7796271819571$$
$$x_{60} = -95.4787390250346$$
$$x_{61} = 55.3177083472755$$
$$x_{62} = 49.0345230400959$$
$$x_{63} = -42.7513377329163$$
$$x_{64} = -89.195553717855$$
$$x_{65} = -70.3459977963162$$
$$x_{66} = -74.1672642688143$$
This roots
$$x_{24} = -325.494676555998$$
$$x_{9} = -101.761924332214$$
$$x_{5} = -99.3000054975326$$
$$x_{60} = -95.4787390250346$$
$$x_{29} = -93.016820190353$$
$$x_{64} = -89.195553717855$$
$$x_{1} = -86.7336348831734$$
$$x_{48} = -82.9123684106754$$
$$x_{15} = -80.4504495759938$$
$$x_{45} = -76.6291831034958$$
$$x_{66} = -74.1672642688143$$
$$x_{65} = -70.3459977963162$$
$$x_{38} = -67.8840789616347$$
$$x_{41} = -64.0628124891366$$
$$x_{3} = -61.6008936544551$$
$$x_{19} = -57.7796271819571$$
$$x_{12} = -55.3177083472755$$
$$x_{8} = -51.4964418747775$$
$$x_{2} = -49.0345230400959$$
$$x_{57} = -45.2132565675979$$
$$x_{63} = -42.7513377329163$$
$$x_{11} = -38.9300712604183$$
$$x_{18} = -36.4681524257367$$
$$x_{26} = -32.6468859532387$$
$$x_{6} = -30.1849671185572$$
$$x_{22} = -26.3637006460591$$
$$x_{54} = -23.9017818113776$$
$$x_{56} = -20.0805153388795$$
$$x_{30} = -17.618596504198$$
$$x_{25} = -13.7973300316999$$
$$x_{52} = -11.3354111970184$$
$$x_{47} = -7.51414472452036$$
$$x_{55} = -5.05222588983881$$
$$x_{46} = -1.23095941734077$$
$$x_{51} = 1.23095941734077$$
$$x_{7} = 5.05222588983881$$
$$x_{36} = 7.51414472452036$$
$$x_{16} = 11.3354111970184$$
$$x_{43} = 13.7973300316999$$
$$x_{32} = 17.618596504198$$
$$x_{10} = 20.0805153388795$$
$$x_{21} = 23.9017818113776$$
$$x_{58} = 26.3637006460591$$
$$x_{28} = 30.1849671185572$$
$$x_{17} = 32.6468859532387$$
$$x_{13} = 36.4681524257367$$
$$x_{40} = 38.9300712604183$$
$$x_{4} = 42.7513377329163$$
$$x_{34} = 45.2132565675979$$
$$x_{62} = 49.0345230400959$$
$$x_{35} = 51.4964418747775$$
$$x_{61} = 55.3177083472755$$
$$x_{59} = 57.7796271819571$$
$$x_{37} = 61.6008936544551$$
$$x_{39} = 64.0628124891366$$
$$x_{31} = 67.8840789616347$$
$$x_{42} = 70.3459977963162$$
$$x_{50} = 74.1672642688143$$
$$x_{23} = 76.6291831034958$$
$$x_{53} = 80.4504495759938$$
$$x_{33} = 82.9123684106754$$
$$x_{14} = 86.7336348831734$$
$$x_{44} = 89.195553717855$$
$$x_{20} = 93.016820190353$$
$$x_{27} = 95.4787390250346$$
$$x_{49} = 99.3000054975326$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{24}$$
For example, let's take the point
$$x_{0} = x_{24} - \frac{1}{10}$$
=
$$-325.494676555998 + - \frac{1}{10}$$
=
$$-325.594676555998$$
substitute to the expression
$$\cos{\left(t \right)} < \frac{1}{3}$$
$$\cos{\left(t \right)} < \frac{1}{3}$$
Then
$$x < -325.494676555998$$
no execute
one of the solutions of our inequality is:
$$x > -325.494676555998 \wedge x < -101.761924332214$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -325.494676555998 \wedge x < -101.761924332214$$
$$x > -99.3000054975326 \wedge x < -95.4787390250346$$
$$x > -93.016820190353 \wedge x < -89.195553717855$$
$$x > -86.7336348831734 \wedge x < -82.9123684106754$$
$$x > -80.4504495759938 \wedge x < -76.6291831034958$$
$$x > -74.1672642688143 \wedge x < -70.3459977963162$$
$$x > -67.8840789616347 \wedge x < -64.0628124891366$$
$$x > -61.6008936544551 \wedge x < -57.7796271819571$$
$$x > -55.3177083472755 \wedge x < -51.4964418747775$$
$$x > -49.0345230400959 \wedge x < -45.2132565675979$$
$$x > -42.7513377329163 \wedge x < -38.9300712604183$$
$$x > -36.4681524257367 \wedge x < -32.6468859532387$$
$$x > -30.1849671185572 \wedge x < -26.3637006460591$$
$$x > -23.9017818113776 \wedge x < -20.0805153388795$$
$$x > -17.618596504198 \wedge x < -13.7973300316999$$
$$x > -11.3354111970184 \wedge x < -7.51414472452036$$
$$x > -5.05222588983881 \wedge x < -1.23095941734077$$
$$x > 1.23095941734077 \wedge x < 5.05222588983881$$
$$x > 7.51414472452036 \wedge x < 11.3354111970184$$
$$x > 13.7973300316999 \wedge x < 17.618596504198$$
$$x > 20.0805153388795 \wedge x < 23.9017818113776$$
$$x > 26.3637006460591 \wedge x < 30.1849671185572$$
$$x > 32.6468859532387 \wedge x < 36.4681524257367$$
$$x > 38.9300712604183 \wedge x < 42.7513377329163$$
$$x > 45.2132565675979 \wedge x < 49.0345230400959$$
$$x > 51.4964418747775 \wedge x < 55.3177083472755$$
$$x > 57.7796271819571 \wedge x < 61.6008936544551$$
$$x > 64.0628124891366 \wedge x < 67.8840789616347$$
$$x > 70.3459977963162 \wedge x < 74.1672642688143$$
$$x > 76.6291831034958 \wedge x < 80.4504495759938$$
$$x > 82.9123684106754 \wedge x < 86.7336348831734$$
$$x > 89.195553717855 \wedge x < 93.016820190353$$
$$x > 95.4787390250346 \wedge x < 99.3000054975326$$
$$\cos{\left(t \right)} < \frac{1}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(t \right)} = \frac{1}{3}$$
Solve:
Given the equation
$$\cos{\left(t \right)} = \frac{1}{3}$$
transform
$$\cos{\left(t \right)} - \frac{1}{3} = 0$$
$$\cos{\left(t \right)} - \frac{1}{3} = 0$$
Do replacement
$$w = \cos{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{1}{3}$$
We get the answer: w = 1/3
do backward replacement
$$\cos{\left(t \right)} = w$$
substitute w:
$$x_{1} = -86.7336348831734$$
$$x_{2} = -49.0345230400959$$
$$x_{3} = -61.6008936544551$$
$$x_{4} = 42.7513377329163$$
$$x_{5} = -99.3000054975326$$
$$x_{6} = -30.1849671185572$$
$$x_{7} = 5.05222588983881$$
$$x_{8} = -51.4964418747775$$
$$x_{9} = -101.761924332214$$
$$x_{10} = 20.0805153388795$$
$$x_{11} = -38.9300712604183$$
$$x_{12} = -55.3177083472755$$
$$x_{13} = 36.4681524257367$$
$$x_{14} = 86.7336348831734$$
$$x_{15} = -80.4504495759938$$
$$x_{16} = 11.3354111970184$$
$$x_{17} = 32.6468859532387$$
$$x_{18} = -36.4681524257367$$
$$x_{19} = -57.7796271819571$$
$$x_{20} = 93.016820190353$$
$$x_{21} = 23.9017818113776$$
$$x_{22} = -26.3637006460591$$
$$x_{23} = 76.6291831034958$$
$$x_{24} = -325.494676555998$$
$$x_{25} = -13.7973300316999$$
$$x_{26} = -32.6468859532387$$
$$x_{27} = 95.4787390250346$$
$$x_{28} = 30.1849671185572$$
$$x_{29} = -93.016820190353$$
$$x_{30} = -17.618596504198$$
$$x_{31} = 67.8840789616347$$
$$x_{32} = 17.618596504198$$
$$x_{33} = 82.9123684106754$$
$$x_{34} = 45.2132565675979$$
$$x_{35} = 51.4964418747775$$
$$x_{36} = 7.51414472452036$$
$$x_{37} = 61.6008936544551$$
$$x_{38} = -67.8840789616347$$
$$x_{39} = 64.0628124891366$$
$$x_{40} = 38.9300712604183$$
$$x_{41} = -64.0628124891366$$
$$x_{42} = 70.3459977963162$$
$$x_{43} = 13.7973300316999$$
$$x_{44} = 89.195553717855$$
$$x_{45} = -76.6291831034958$$
$$x_{46} = -1.23095941734077$$
$$x_{47} = -7.51414472452036$$
$$x_{48} = -82.9123684106754$$
$$x_{49} = 99.3000054975326$$
$$x_{50} = 74.1672642688143$$
$$x_{51} = 1.23095941734077$$
$$x_{52} = -11.3354111970184$$
$$x_{53} = 80.4504495759938$$
$$x_{54} = -23.9017818113776$$
$$x_{55} = -5.05222588983881$$
$$x_{56} = -20.0805153388795$$
$$x_{57} = -45.2132565675979$$
$$x_{58} = 26.3637006460591$$
$$x_{59} = 57.7796271819571$$
$$x_{60} = -95.4787390250346$$
$$x_{61} = 55.3177083472755$$
$$x_{62} = 49.0345230400959$$
$$x_{63} = -42.7513377329163$$
$$x_{64} = -89.195553717855$$
$$x_{65} = -70.3459977963162$$
$$x_{66} = -74.1672642688143$$
$$x_{1} = -86.7336348831734$$
$$x_{2} = -49.0345230400959$$
$$x_{3} = -61.6008936544551$$
$$x_{4} = 42.7513377329163$$
$$x_{5} = -99.3000054975326$$
$$x_{6} = -30.1849671185572$$
$$x_{7} = 5.05222588983881$$
$$x_{8} = -51.4964418747775$$
$$x_{9} = -101.761924332214$$
$$x_{10} = 20.0805153388795$$
$$x_{11} = -38.9300712604183$$
$$x_{12} = -55.3177083472755$$
$$x_{13} = 36.4681524257367$$
$$x_{14} = 86.7336348831734$$
$$x_{15} = -80.4504495759938$$
$$x_{16} = 11.3354111970184$$
$$x_{17} = 32.6468859532387$$
$$x_{18} = -36.4681524257367$$
$$x_{19} = -57.7796271819571$$
$$x_{20} = 93.016820190353$$
$$x_{21} = 23.9017818113776$$
$$x_{22} = -26.3637006460591$$
$$x_{23} = 76.6291831034958$$
$$x_{24} = -325.494676555998$$
$$x_{25} = -13.7973300316999$$
$$x_{26} = -32.6468859532387$$
$$x_{27} = 95.4787390250346$$
$$x_{28} = 30.1849671185572$$
$$x_{29} = -93.016820190353$$
$$x_{30} = -17.618596504198$$
$$x_{31} = 67.8840789616347$$
$$x_{32} = 17.618596504198$$
$$x_{33} = 82.9123684106754$$
$$x_{34} = 45.2132565675979$$
$$x_{35} = 51.4964418747775$$
$$x_{36} = 7.51414472452036$$
$$x_{37} = 61.6008936544551$$
$$x_{38} = -67.8840789616347$$
$$x_{39} = 64.0628124891366$$
$$x_{40} = 38.9300712604183$$
$$x_{41} = -64.0628124891366$$
$$x_{42} = 70.3459977963162$$
$$x_{43} = 13.7973300316999$$
$$x_{44} = 89.195553717855$$
$$x_{45} = -76.6291831034958$$
$$x_{46} = -1.23095941734077$$
$$x_{47} = -7.51414472452036$$
$$x_{48} = -82.9123684106754$$
$$x_{49} = 99.3000054975326$$
$$x_{50} = 74.1672642688143$$
$$x_{51} = 1.23095941734077$$
$$x_{52} = -11.3354111970184$$
$$x_{53} = 80.4504495759938$$
$$x_{54} = -23.9017818113776$$
$$x_{55} = -5.05222588983881$$
$$x_{56} = -20.0805153388795$$
$$x_{57} = -45.2132565675979$$
$$x_{58} = 26.3637006460591$$
$$x_{59} = 57.7796271819571$$
$$x_{60} = -95.4787390250346$$
$$x_{61} = 55.3177083472755$$
$$x_{62} = 49.0345230400959$$
$$x_{63} = -42.7513377329163$$
$$x_{64} = -89.195553717855$$
$$x_{65} = -70.3459977963162$$
$$x_{66} = -74.1672642688143$$
This roots
$$x_{24} = -325.494676555998$$
$$x_{9} = -101.761924332214$$
$$x_{5} = -99.3000054975326$$
$$x_{60} = -95.4787390250346$$
$$x_{29} = -93.016820190353$$
$$x_{64} = -89.195553717855$$
$$x_{1} = -86.7336348831734$$
$$x_{48} = -82.9123684106754$$
$$x_{15} = -80.4504495759938$$
$$x_{45} = -76.6291831034958$$
$$x_{66} = -74.1672642688143$$
$$x_{65} = -70.3459977963162$$
$$x_{38} = -67.8840789616347$$
$$x_{41} = -64.0628124891366$$
$$x_{3} = -61.6008936544551$$
$$x_{19} = -57.7796271819571$$
$$x_{12} = -55.3177083472755$$
$$x_{8} = -51.4964418747775$$
$$x_{2} = -49.0345230400959$$
$$x_{57} = -45.2132565675979$$
$$x_{63} = -42.7513377329163$$
$$x_{11} = -38.9300712604183$$
$$x_{18} = -36.4681524257367$$
$$x_{26} = -32.6468859532387$$
$$x_{6} = -30.1849671185572$$
$$x_{22} = -26.3637006460591$$
$$x_{54} = -23.9017818113776$$
$$x_{56} = -20.0805153388795$$
$$x_{30} = -17.618596504198$$
$$x_{25} = -13.7973300316999$$
$$x_{52} = -11.3354111970184$$
$$x_{47} = -7.51414472452036$$
$$x_{55} = -5.05222588983881$$
$$x_{46} = -1.23095941734077$$
$$x_{51} = 1.23095941734077$$
$$x_{7} = 5.05222588983881$$
$$x_{36} = 7.51414472452036$$
$$x_{16} = 11.3354111970184$$
$$x_{43} = 13.7973300316999$$
$$x_{32} = 17.618596504198$$
$$x_{10} = 20.0805153388795$$
$$x_{21} = 23.9017818113776$$
$$x_{58} = 26.3637006460591$$
$$x_{28} = 30.1849671185572$$
$$x_{17} = 32.6468859532387$$
$$x_{13} = 36.4681524257367$$
$$x_{40} = 38.9300712604183$$
$$x_{4} = 42.7513377329163$$
$$x_{34} = 45.2132565675979$$
$$x_{62} = 49.0345230400959$$
$$x_{35} = 51.4964418747775$$
$$x_{61} = 55.3177083472755$$
$$x_{59} = 57.7796271819571$$
$$x_{37} = 61.6008936544551$$
$$x_{39} = 64.0628124891366$$
$$x_{31} = 67.8840789616347$$
$$x_{42} = 70.3459977963162$$
$$x_{50} = 74.1672642688143$$
$$x_{23} = 76.6291831034958$$
$$x_{53} = 80.4504495759938$$
$$x_{33} = 82.9123684106754$$
$$x_{14} = 86.7336348831734$$
$$x_{44} = 89.195553717855$$
$$x_{20} = 93.016820190353$$
$$x_{27} = 95.4787390250346$$
$$x_{49} = 99.3000054975326$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{24}$$
For example, let's take the point
$$x_{0} = x_{24} - \frac{1}{10}$$
=
$$-325.494676555998 + - \frac{1}{10}$$
=
$$-325.594676555998$$
substitute to the expression
$$\cos{\left(t \right)} < \frac{1}{3}$$
$$\cos{\left(t \right)} < \frac{1}{3}$$
cos(t) < 1/3
Then
$$x < -325.494676555998$$
no execute
one of the solutions of our inequality is:
$$x > -325.494676555998 \wedge x < -101.761924332214$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------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-------
x24 x9 x5 x60 x29 x64 x1 x48 x15 x45 x66 x65 x38 x41 x3 x19 x12 x8 x2 x57 x63 x11 x18 x26 x6 x22 x54 x56 x30 x25 x52 x47 x55 x46 x51 x7 x36 x16 x43 x32 x10 x21 x58 x28 x17 x13 x40 x4 x34 x62 x35 x61 x59 x37 x39 x31 x42 x50 x23 x53 x33 x14 x44 x20 x27 x49Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -325.494676555998 \wedge x < -101.761924332214$$
$$x > -99.3000054975326 \wedge x < -95.4787390250346$$
$$x > -93.016820190353 \wedge x < -89.195553717855$$
$$x > -86.7336348831734 \wedge x < -82.9123684106754$$
$$x > -80.4504495759938 \wedge x < -76.6291831034958$$
$$x > -74.1672642688143 \wedge x < -70.3459977963162$$
$$x > -67.8840789616347 \wedge x < -64.0628124891366$$
$$x > -61.6008936544551 \wedge x < -57.7796271819571$$
$$x > -55.3177083472755 \wedge x < -51.4964418747775$$
$$x > -49.0345230400959 \wedge x < -45.2132565675979$$
$$x > -42.7513377329163 \wedge x < -38.9300712604183$$
$$x > -36.4681524257367 \wedge x < -32.6468859532387$$
$$x > -30.1849671185572 \wedge x < -26.3637006460591$$
$$x > -23.9017818113776 \wedge x < -20.0805153388795$$
$$x > -17.618596504198 \wedge x < -13.7973300316999$$
$$x > -11.3354111970184 \wedge x < -7.51414472452036$$
$$x > -5.05222588983881 \wedge x < -1.23095941734077$$
$$x > 1.23095941734077 \wedge x < 5.05222588983881$$
$$x > 7.51414472452036 \wedge x < 11.3354111970184$$
$$x > 13.7973300316999 \wedge x < 17.618596504198$$
$$x > 20.0805153388795 \wedge x < 23.9017818113776$$
$$x > 26.3637006460591 \wedge x < 30.1849671185572$$
$$x > 32.6468859532387 \wedge x < 36.4681524257367$$
$$x > 38.9300712604183 \wedge x < 42.7513377329163$$
$$x > 45.2132565675979 \wedge x < 49.0345230400959$$
$$x > 51.4964418747775 \wedge x < 55.3177083472755$$
$$x > 57.7796271819571 \wedge x < 61.6008936544551$$
$$x > 64.0628124891366 \wedge x < 67.8840789616347$$
$$x > 70.3459977963162 \wedge x < 74.1672642688143$$
$$x > 76.6291831034958 \wedge x < 80.4504495759938$$
$$x > 82.9123684106754 \wedge x < 86.7336348831734$$
$$x > 89.195553717855 \wedge x < 93.016820190353$$
$$x > 95.4787390250346 \wedge x < 99.3000054975326$$
Rapid solution
[src]
/ / ___\ / ___\ \ And\t < - atan\2*\/ 2 / + 2*pi, atan\2*\/ 2 / < t/
$$t < - \operatorname{atan}{\left(2 \sqrt{2} \right)} + 2 \pi \wedge \operatorname{atan}{\left(2 \sqrt{2} \right)} < t$$
(atan(2*sqrt(2)) < t)∧(t < -atan(2*sqrt(2)) + 2*pi)
Rapid solution 2
[src]
/ ___\ / ___\ (atan\2*\/ 2 /, - atan\2*\/ 2 / + 2*pi)
$$x\ in\ \left(\operatorname{atan}{\left(2 \sqrt{2} \right)}, - \operatorname{atan}{\left(2 \sqrt{2} \right)} + 2 \pi\right)$$
x in Interval.open(atan(2*sqrt(2)), -atan(2*sqrt(2)) + 2*pi)