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^2-2x)>4-x
- (x+3)^2>(x−23)^2
- 3^(x+2)>81
- (x^2+5*x)/(x-6)>0
- Integral of d{x}:
-
cost
- Derivative of:
-
cost
-
Identical expressions
- cost<= one
- co sinus of e of t less than or equal to 1
- co sinus of e of t less than or equal to one
-
Similar expressions
- cos(t)<sqrt(3)/2
cost<=1 inequation
The solution
Detail solution
Given the inequality:
$$\cos{\left(t \right)} \leq 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(t \right)} = 1$$
Solve:
Given the equation
$$\cos{\left(t \right)} = 1$$
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:
$$x_{1} = 62.8318535568358$$
$$x_{2} = 37.6991115173992$$
$$x_{3} = -31.4159260507536$$
$$x_{4} = -37.6991113479743$$
$$x_{5} = -50.2654829667315$$
$$x_{6} = -18.8495563230046$$
$$x_{7} = 94.2477800892631$$
$$x_{8} = 100.530965157364$$
$$x_{9} = 31.4159268459961$$
$$x_{10} = -94.2477801171671$$
$$x_{11} = 12.5663710110881$$
$$x_{12} = -43.9822976246252$$
$$x_{13} = -94.2477797298079$$
$$x_{14} = -87.964593928489$$
$$x_{15} = -62.8318534787248$$
$$x_{16} = 81.6814084860076$$
$$x_{17} = 6.28318579821791$$
$$x_{18} = 100.530964759815$$
$$x_{19} = -75.3982238741744$$
$$x_{20} = 56.5486668532011$$
$$x_{21} = 87.964594335905$$
$$x_{22} = -56.5486682426592$$
$$x_{23} = -12.5663710889626$$
$$x_{24} = -43.9822971745392$$
$$x_{25} = 81.6814085860518$$
$$x_{26} = -56.5486674685864$$
$$x_{27} = -69.1150379045123$$
$$x_{28} = -62.831852673202$$
$$x_{29} = -25.1327407505866$$
$$x_{30} = 56.5486682809363$$
$$x_{31} = 50.2654824463392$$
$$x_{32} = -31.4159267157965$$
$$x_{33} = 56.5486680806249$$
$$x_{34} = 6.28318626747926$$
$$x_{35} = 37.6991120311338$$
$$x_{36} = -18.8495552124105$$
$$x_{37} = 69.115038794053$$
$$x_{38} = -87.9645947692094$$
$$x_{39} = 0$$
$$x_{40} = 87.9645946044253$$
$$x_{41} = -50.265482641087$$
$$x_{42} = 25.1327416384075$$
$$x_{43} = -12.5663703112531$$
$$x_{44} = -6.2831858160515$$
$$x_{45} = -75.3982231720141$$
$$x_{46} = -69.1150386869085$$
$$x_{47} = -25.1327415297174$$
$$x_{48} = 37.6991113348642$$
$$x_{49} = 69.1150379887504$$
$$x_{50} = 12.5663704426592$$
$$x_{51} = -6.2831851275477$$
$$x_{52} = 87.9645938121814$$
$$x_{53} = -37.6991121287155$$
$$x_{54} = -81.6814075578313$$
$$x_{55} = 3.40772025642919 \cdot 10^{-7}$$
$$x_{56} = -100.530964626003$$
$$x_{57} = -81.6814092565354$$
$$x_{58} = -18.8495555173448$$
$$x_{59} = -37.6991118772631$$
$$x_{60} = 75.3982232188727$$
$$x_{61} = -43.9822967932182$$
$$x_{62} = -31.4159260208155$$
$$x_{63} = -94.2477794452815$$
$$x_{64} = 6.28318528420851$$
$$x_{65} = 94.2477792651059$$
$$x_{66} = -81.6814090382277$$
$$x_{67} = 94.2477796093523$$
$$x_{68} = -6.28318555849548$$
$$x_{69} = 50.2654821322586$$
$$x_{70} = 25.1327408328211$$
$$x_{71} = -50.2654822863493$$
$$x_{72} = 62.8318527849002$$
$$x_{73} = 43.9822974733639$$
$$x_{74} = 81.6814091897036$$
$$x_{75} = 6.28318500093652$$
$$x_{76} = -81.6814084945807$$
$$x_{77} = 12.5663711301703$$
$$x_{78} = 43.9822971694647$$
$$x_{79} = 75.3982240031607$$
$$x_{80} = -75.3982231045728$$
$$x_{81} = 43.9822966661001$$
$$x_{82} = 31.4159260648825$$
$$x_{83} = 18.8495556275525$$
$$x_{84} = 18.8495564031971$$
$$x_{85} = 50.2654829439723$$
$$x_{86} = 56.5486676011951$$
$$x_{87} = -4.79511606158654 \cdot 10^{-7}$$
$$x_{88} = -87.9645943586158$$
$$x_{1} = 62.8318535568358$$
$$x_{2} = 37.6991115173992$$
$$x_{3} = -31.4159260507536$$
$$x_{4} = -37.6991113479743$$
$$x_{5} = -50.2654829667315$$
$$x_{6} = -18.8495563230046$$
$$x_{7} = 94.2477800892631$$
$$x_{8} = 100.530965157364$$
$$x_{9} = 31.4159268459961$$
$$x_{10} = -94.2477801171671$$
$$x_{11} = 12.5663710110881$$
$$x_{12} = -43.9822976246252$$
$$x_{13} = -94.2477797298079$$
$$x_{14} = -87.964593928489$$
$$x_{15} = -62.8318534787248$$
$$x_{16} = 81.6814084860076$$
$$x_{17} = 6.28318579821791$$
$$x_{18} = 100.530964759815$$
$$x_{19} = -75.3982238741744$$
$$x_{20} = 56.5486668532011$$
$$x_{21} = 87.964594335905$$
$$x_{22} = -56.5486682426592$$
$$x_{23} = -12.5663710889626$$
$$x_{24} = -43.9822971745392$$
$$x_{25} = 81.6814085860518$$
$$x_{26} = -56.5486674685864$$
$$x_{27} = -69.1150379045123$$
$$x_{28} = -62.831852673202$$
$$x_{29} = -25.1327407505866$$
$$x_{30} = 56.5486682809363$$
$$x_{31} = 50.2654824463392$$
$$x_{32} = -31.4159267157965$$
$$x_{33} = 56.5486680806249$$
$$x_{34} = 6.28318626747926$$
$$x_{35} = 37.6991120311338$$
$$x_{36} = -18.8495552124105$$
$$x_{37} = 69.115038794053$$
$$x_{38} = -87.9645947692094$$
$$x_{39} = 0$$
$$x_{40} = 87.9645946044253$$
$$x_{41} = -50.265482641087$$
$$x_{42} = 25.1327416384075$$
$$x_{43} = -12.5663703112531$$
$$x_{44} = -6.2831858160515$$
$$x_{45} = -75.3982231720141$$
$$x_{46} = -69.1150386869085$$
$$x_{47} = -25.1327415297174$$
$$x_{48} = 37.6991113348642$$
$$x_{49} = 69.1150379887504$$
$$x_{50} = 12.5663704426592$$
$$x_{51} = -6.2831851275477$$
$$x_{52} = 87.9645938121814$$
$$x_{53} = -37.6991121287155$$
$$x_{54} = -81.6814075578313$$
$$x_{55} = 3.40772025642919 \cdot 10^{-7}$$
$$x_{56} = -100.530964626003$$
$$x_{57} = -81.6814092565354$$
$$x_{58} = -18.8495555173448$$
$$x_{59} = -37.6991118772631$$
$$x_{60} = 75.3982232188727$$
$$x_{61} = -43.9822967932182$$
$$x_{62} = -31.4159260208155$$
$$x_{63} = -94.2477794452815$$
$$x_{64} = 6.28318528420851$$
$$x_{65} = 94.2477792651059$$
$$x_{66} = -81.6814090382277$$
$$x_{67} = 94.2477796093523$$
$$x_{68} = -6.28318555849548$$
$$x_{69} = 50.2654821322586$$
$$x_{70} = 25.1327408328211$$
$$x_{71} = -50.2654822863493$$
$$x_{72} = 62.8318527849002$$
$$x_{73} = 43.9822974733639$$
$$x_{74} = 81.6814091897036$$
$$x_{75} = 6.28318500093652$$
$$x_{76} = -81.6814084945807$$
$$x_{77} = 12.5663711301703$$
$$x_{78} = 43.9822971694647$$
$$x_{79} = 75.3982240031607$$
$$x_{80} = -75.3982231045728$$
$$x_{81} = 43.9822966661001$$
$$x_{82} = 31.4159260648825$$
$$x_{83} = 18.8495556275525$$
$$x_{84} = 18.8495564031971$$
$$x_{85} = 50.2654829439723$$
$$x_{86} = 56.5486676011951$$
$$x_{87} = -4.79511606158654 \cdot 10^{-7}$$
$$x_{88} = -87.9645943586158$$
This roots
$$x_{56} = -100.530964626003$$
$$x_{10} = -94.2477801171671$$
$$x_{13} = -94.2477797298079$$
$$x_{63} = -94.2477794452815$$
$$x_{38} = -87.9645947692094$$
$$x_{88} = -87.9645943586158$$
$$x_{14} = -87.964593928489$$
$$x_{57} = -81.6814092565354$$
$$x_{66} = -81.6814090382277$$
$$x_{76} = -81.6814084945807$$
$$x_{54} = -81.6814075578313$$
$$x_{19} = -75.3982238741744$$
$$x_{45} = -75.3982231720141$$
$$x_{80} = -75.3982231045728$$
$$x_{46} = -69.1150386869085$$
$$x_{27} = -69.1150379045123$$
$$x_{15} = -62.8318534787248$$
$$x_{28} = -62.831852673202$$
$$x_{22} = -56.5486682426592$$
$$x_{26} = -56.5486674685864$$
$$x_{5} = -50.2654829667315$$
$$x_{41} = -50.265482641087$$
$$x_{71} = -50.2654822863493$$
$$x_{12} = -43.9822976246252$$
$$x_{24} = -43.9822971745392$$
$$x_{61} = -43.9822967932182$$
$$x_{53} = -37.6991121287155$$
$$x_{59} = -37.6991118772631$$
$$x_{4} = -37.6991113479743$$
$$x_{32} = -31.4159267157965$$
$$x_{3} = -31.4159260507536$$
$$x_{62} = -31.4159260208155$$
$$x_{47} = -25.1327415297174$$
$$x_{29} = -25.1327407505866$$
$$x_{6} = -18.8495563230046$$
$$x_{58} = -18.8495555173448$$
$$x_{36} = -18.8495552124105$$
$$x_{23} = -12.5663710889626$$
$$x_{43} = -12.5663703112531$$
$$x_{44} = -6.2831858160515$$
$$x_{68} = -6.28318555849548$$
$$x_{51} = -6.2831851275477$$
$$x_{87} = -4.79511606158654 \cdot 10^{-7}$$
$$x_{39} = 0$$
$$x_{55} = 3.40772025642919 \cdot 10^{-7}$$
$$x_{75} = 6.28318500093652$$
$$x_{64} = 6.28318528420851$$
$$x_{17} = 6.28318579821791$$
$$x_{34} = 6.28318626747926$$
$$x_{50} = 12.5663704426592$$
$$x_{11} = 12.5663710110881$$
$$x_{77} = 12.5663711301703$$
$$x_{83} = 18.8495556275525$$
$$x_{84} = 18.8495564031971$$
$$x_{70} = 25.1327408328211$$
$$x_{42} = 25.1327416384075$$
$$x_{82} = 31.4159260648825$$
$$x_{9} = 31.4159268459961$$
$$x_{48} = 37.6991113348642$$
$$x_{2} = 37.6991115173992$$
$$x_{35} = 37.6991120311338$$
$$x_{81} = 43.9822966661001$$
$$x_{78} = 43.9822971694647$$
$$x_{73} = 43.9822974733639$$
$$x_{69} = 50.2654821322586$$
$$x_{31} = 50.2654824463392$$
$$x_{85} = 50.2654829439723$$
$$x_{20} = 56.5486668532011$$
$$x_{86} = 56.5486676011951$$
$$x_{33} = 56.5486680806249$$
$$x_{30} = 56.5486682809363$$
$$x_{72} = 62.8318527849002$$
$$x_{1} = 62.8318535568358$$
$$x_{49} = 69.1150379887504$$
$$x_{37} = 69.115038794053$$
$$x_{60} = 75.3982232188727$$
$$x_{79} = 75.3982240031607$$
$$x_{16} = 81.6814084860076$$
$$x_{25} = 81.6814085860518$$
$$x_{74} = 81.6814091897036$$
$$x_{52} = 87.9645938121814$$
$$x_{21} = 87.964594335905$$
$$x_{40} = 87.9645946044253$$
$$x_{65} = 94.2477792651059$$
$$x_{67} = 94.2477796093523$$
$$x_{7} = 94.2477800892631$$
$$x_{18} = 100.530964759815$$
$$x_{8} = 100.530965157364$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{56}$$
For example, let's take the point
$$x_{0} = x_{56} - \frac{1}{10}$$
=
$$-100.530964626003 + - \frac{1}{10}$$
=
$$-100.630964626003$$
substitute to the expression
$$\cos{\left(t \right)} \leq 1$$
$$\cos{\left(t \right)} \leq 1$$
Then
$$x \leq -100.530964626003$$
no execute
one of the solutions of our inequality is:
$$x \geq -100.530964626003 \wedge x \leq -94.2477801171671$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \geq -100.530964626003 \wedge x \leq -94.2477801171671$$
$$x \geq -94.2477797298079 \wedge x \leq -94.2477794452815$$
$$x \geq -87.9645947692094 \wedge x \leq -87.9645943586158$$
$$x \geq -87.964593928489 \wedge x \leq -81.6814092565354$$
$$x \geq -81.6814090382277 \wedge x \leq -81.6814084945807$$
$$x \geq -81.6814075578313 \wedge x \leq -75.3982238741744$$
$$x \geq -75.3982231720141 \wedge x \leq -75.3982231045728$$
$$x \geq -69.1150386869085 \wedge x \leq -69.1150379045123$$
$$x \geq -62.8318534787248 \wedge x \leq -62.831852673202$$
$$x \geq -56.5486682426592 \wedge x \leq -56.5486674685864$$
$$x \geq -50.2654829667315 \wedge x \leq -50.265482641087$$
$$x \geq -50.2654822863493 \wedge x \leq -43.9822976246252$$
$$x \geq -43.9822971745392 \wedge x \leq -43.9822967932182$$
$$x \geq -37.6991121287155 \wedge x \leq -37.6991118772631$$
$$x \geq -37.6991113479743 \wedge x \leq -31.4159267157965$$
$$x \geq -31.4159260507536 \wedge x \leq -31.4159260208155$$
$$x \geq -25.1327415297174 \wedge x \leq -25.1327407505866$$
$$x \geq -18.8495563230046 \wedge x \leq -18.8495555173448$$
$$x \geq -18.8495552124105 \wedge x \leq -12.5663710889626$$
$$x \geq -12.5663703112531 \wedge x \leq -6.2831858160515$$
$$x \geq -6.28318555849548 \wedge x \leq -6.2831851275477$$
$$x \geq -4.79511606158654 \cdot 10^{-7} \wedge x \leq 0$$
$$x \geq 3.40772025642919 \cdot 10^{-7} \wedge x \leq 6.28318500093652$$
$$x \geq 6.28318528420851 \wedge x \leq 6.28318579821791$$
$$x \geq 6.28318626747926 \wedge x \leq 12.5663704426592$$
$$x \geq 12.5663710110881 \wedge x \leq 12.5663711301703$$
$$x \geq 18.8495556275525 \wedge x \leq 18.8495564031971$$
$$x \geq 25.1327408328211 \wedge x \leq 25.1327416384075$$
$$x \geq 31.4159260648825 \wedge x \leq 31.4159268459961$$
$$x \geq 37.6991113348642 \wedge x \leq 37.6991115173992$$
$$x \geq 37.6991120311338 \wedge x \leq 43.9822966661001$$
$$x \geq 43.9822971694647 \wedge x \leq 43.9822974733639$$
$$x \geq 50.2654821322586 \wedge x \leq 50.2654824463392$$
$$x \geq 50.2654829439723 \wedge x \leq 56.5486668532011$$
$$x \geq 56.5486676011951 \wedge x \leq 56.5486680806249$$
$$x \geq 56.5486682809363 \wedge x \leq 62.8318527849002$$
$$x \geq 62.8318535568358 \wedge x \leq 69.1150379887504$$
$$x \geq 69.115038794053 \wedge x \leq 75.3982232188727$$
$$x \geq 75.3982240031607 \wedge x \leq 81.6814084860076$$
$$x \geq 81.6814085860518 \wedge x \leq 81.6814091897036$$
$$x \geq 87.9645938121814 \wedge x \leq 87.964594335905$$
$$x \geq 87.9645946044253 \wedge x \leq 94.2477792651059$$
$$x \geq 94.2477796093523 \wedge x \leq 94.2477800892631$$
$$x \geq 100.530964759815 \wedge x \leq 100.530965157364$$
$$\cos{\left(t \right)} \leq 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(t \right)} = 1$$
Solve:
Given the equation
$$\cos{\left(t \right)} = 1$$
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:
$$x_{1} = 62.8318535568358$$
$$x_{2} = 37.6991115173992$$
$$x_{3} = -31.4159260507536$$
$$x_{4} = -37.6991113479743$$
$$x_{5} = -50.2654829667315$$
$$x_{6} = -18.8495563230046$$
$$x_{7} = 94.2477800892631$$
$$x_{8} = 100.530965157364$$
$$x_{9} = 31.4159268459961$$
$$x_{10} = -94.2477801171671$$
$$x_{11} = 12.5663710110881$$
$$x_{12} = -43.9822976246252$$
$$x_{13} = -94.2477797298079$$
$$x_{14} = -87.964593928489$$
$$x_{15} = -62.8318534787248$$
$$x_{16} = 81.6814084860076$$
$$x_{17} = 6.28318579821791$$
$$x_{18} = 100.530964759815$$
$$x_{19} = -75.3982238741744$$
$$x_{20} = 56.5486668532011$$
$$x_{21} = 87.964594335905$$
$$x_{22} = -56.5486682426592$$
$$x_{23} = -12.5663710889626$$
$$x_{24} = -43.9822971745392$$
$$x_{25} = 81.6814085860518$$
$$x_{26} = -56.5486674685864$$
$$x_{27} = -69.1150379045123$$
$$x_{28} = -62.831852673202$$
$$x_{29} = -25.1327407505866$$
$$x_{30} = 56.5486682809363$$
$$x_{31} = 50.2654824463392$$
$$x_{32} = -31.4159267157965$$
$$x_{33} = 56.5486680806249$$
$$x_{34} = 6.28318626747926$$
$$x_{35} = 37.6991120311338$$
$$x_{36} = -18.8495552124105$$
$$x_{37} = 69.115038794053$$
$$x_{38} = -87.9645947692094$$
$$x_{39} = 0$$
$$x_{40} = 87.9645946044253$$
$$x_{41} = -50.265482641087$$
$$x_{42} = 25.1327416384075$$
$$x_{43} = -12.5663703112531$$
$$x_{44} = -6.2831858160515$$
$$x_{45} = -75.3982231720141$$
$$x_{46} = -69.1150386869085$$
$$x_{47} = -25.1327415297174$$
$$x_{48} = 37.6991113348642$$
$$x_{49} = 69.1150379887504$$
$$x_{50} = 12.5663704426592$$
$$x_{51} = -6.2831851275477$$
$$x_{52} = 87.9645938121814$$
$$x_{53} = -37.6991121287155$$
$$x_{54} = -81.6814075578313$$
$$x_{55} = 3.40772025642919 \cdot 10^{-7}$$
$$x_{56} = -100.530964626003$$
$$x_{57} = -81.6814092565354$$
$$x_{58} = -18.8495555173448$$
$$x_{59} = -37.6991118772631$$
$$x_{60} = 75.3982232188727$$
$$x_{61} = -43.9822967932182$$
$$x_{62} = -31.4159260208155$$
$$x_{63} = -94.2477794452815$$
$$x_{64} = 6.28318528420851$$
$$x_{65} = 94.2477792651059$$
$$x_{66} = -81.6814090382277$$
$$x_{67} = 94.2477796093523$$
$$x_{68} = -6.28318555849548$$
$$x_{69} = 50.2654821322586$$
$$x_{70} = 25.1327408328211$$
$$x_{71} = -50.2654822863493$$
$$x_{72} = 62.8318527849002$$
$$x_{73} = 43.9822974733639$$
$$x_{74} = 81.6814091897036$$
$$x_{75} = 6.28318500093652$$
$$x_{76} = -81.6814084945807$$
$$x_{77} = 12.5663711301703$$
$$x_{78} = 43.9822971694647$$
$$x_{79} = 75.3982240031607$$
$$x_{80} = -75.3982231045728$$
$$x_{81} = 43.9822966661001$$
$$x_{82} = 31.4159260648825$$
$$x_{83} = 18.8495556275525$$
$$x_{84} = 18.8495564031971$$
$$x_{85} = 50.2654829439723$$
$$x_{86} = 56.5486676011951$$
$$x_{87} = -4.79511606158654 \cdot 10^{-7}$$
$$x_{88} = -87.9645943586158$$
$$x_{1} = 62.8318535568358$$
$$x_{2} = 37.6991115173992$$
$$x_{3} = -31.4159260507536$$
$$x_{4} = -37.6991113479743$$
$$x_{5} = -50.2654829667315$$
$$x_{6} = -18.8495563230046$$
$$x_{7} = 94.2477800892631$$
$$x_{8} = 100.530965157364$$
$$x_{9} = 31.4159268459961$$
$$x_{10} = -94.2477801171671$$
$$x_{11} = 12.5663710110881$$
$$x_{12} = -43.9822976246252$$
$$x_{13} = -94.2477797298079$$
$$x_{14} = -87.964593928489$$
$$x_{15} = -62.8318534787248$$
$$x_{16} = 81.6814084860076$$
$$x_{17} = 6.28318579821791$$
$$x_{18} = 100.530964759815$$
$$x_{19} = -75.3982238741744$$
$$x_{20} = 56.5486668532011$$
$$x_{21} = 87.964594335905$$
$$x_{22} = -56.5486682426592$$
$$x_{23} = -12.5663710889626$$
$$x_{24} = -43.9822971745392$$
$$x_{25} = 81.6814085860518$$
$$x_{26} = -56.5486674685864$$
$$x_{27} = -69.1150379045123$$
$$x_{28} = -62.831852673202$$
$$x_{29} = -25.1327407505866$$
$$x_{30} = 56.5486682809363$$
$$x_{31} = 50.2654824463392$$
$$x_{32} = -31.4159267157965$$
$$x_{33} = 56.5486680806249$$
$$x_{34} = 6.28318626747926$$
$$x_{35} = 37.6991120311338$$
$$x_{36} = -18.8495552124105$$
$$x_{37} = 69.115038794053$$
$$x_{38} = -87.9645947692094$$
$$x_{39} = 0$$
$$x_{40} = 87.9645946044253$$
$$x_{41} = -50.265482641087$$
$$x_{42} = 25.1327416384075$$
$$x_{43} = -12.5663703112531$$
$$x_{44} = -6.2831858160515$$
$$x_{45} = -75.3982231720141$$
$$x_{46} = -69.1150386869085$$
$$x_{47} = -25.1327415297174$$
$$x_{48} = 37.6991113348642$$
$$x_{49} = 69.1150379887504$$
$$x_{50} = 12.5663704426592$$
$$x_{51} = -6.2831851275477$$
$$x_{52} = 87.9645938121814$$
$$x_{53} = -37.6991121287155$$
$$x_{54} = -81.6814075578313$$
$$x_{55} = 3.40772025642919 \cdot 10^{-7}$$
$$x_{56} = -100.530964626003$$
$$x_{57} = -81.6814092565354$$
$$x_{58} = -18.8495555173448$$
$$x_{59} = -37.6991118772631$$
$$x_{60} = 75.3982232188727$$
$$x_{61} = -43.9822967932182$$
$$x_{62} = -31.4159260208155$$
$$x_{63} = -94.2477794452815$$
$$x_{64} = 6.28318528420851$$
$$x_{65} = 94.2477792651059$$
$$x_{66} = -81.6814090382277$$
$$x_{67} = 94.2477796093523$$
$$x_{68} = -6.28318555849548$$
$$x_{69} = 50.2654821322586$$
$$x_{70} = 25.1327408328211$$
$$x_{71} = -50.2654822863493$$
$$x_{72} = 62.8318527849002$$
$$x_{73} = 43.9822974733639$$
$$x_{74} = 81.6814091897036$$
$$x_{75} = 6.28318500093652$$
$$x_{76} = -81.6814084945807$$
$$x_{77} = 12.5663711301703$$
$$x_{78} = 43.9822971694647$$
$$x_{79} = 75.3982240031607$$
$$x_{80} = -75.3982231045728$$
$$x_{81} = 43.9822966661001$$
$$x_{82} = 31.4159260648825$$
$$x_{83} = 18.8495556275525$$
$$x_{84} = 18.8495564031971$$
$$x_{85} = 50.2654829439723$$
$$x_{86} = 56.5486676011951$$
$$x_{87} = -4.79511606158654 \cdot 10^{-7}$$
$$x_{88} = -87.9645943586158$$
This roots
$$x_{56} = -100.530964626003$$
$$x_{10} = -94.2477801171671$$
$$x_{13} = -94.2477797298079$$
$$x_{63} = -94.2477794452815$$
$$x_{38} = -87.9645947692094$$
$$x_{88} = -87.9645943586158$$
$$x_{14} = -87.964593928489$$
$$x_{57} = -81.6814092565354$$
$$x_{66} = -81.6814090382277$$
$$x_{76} = -81.6814084945807$$
$$x_{54} = -81.6814075578313$$
$$x_{19} = -75.3982238741744$$
$$x_{45} = -75.3982231720141$$
$$x_{80} = -75.3982231045728$$
$$x_{46} = -69.1150386869085$$
$$x_{27} = -69.1150379045123$$
$$x_{15} = -62.8318534787248$$
$$x_{28} = -62.831852673202$$
$$x_{22} = -56.5486682426592$$
$$x_{26} = -56.5486674685864$$
$$x_{5} = -50.2654829667315$$
$$x_{41} = -50.265482641087$$
$$x_{71} = -50.2654822863493$$
$$x_{12} = -43.9822976246252$$
$$x_{24} = -43.9822971745392$$
$$x_{61} = -43.9822967932182$$
$$x_{53} = -37.6991121287155$$
$$x_{59} = -37.6991118772631$$
$$x_{4} = -37.6991113479743$$
$$x_{32} = -31.4159267157965$$
$$x_{3} = -31.4159260507536$$
$$x_{62} = -31.4159260208155$$
$$x_{47} = -25.1327415297174$$
$$x_{29} = -25.1327407505866$$
$$x_{6} = -18.8495563230046$$
$$x_{58} = -18.8495555173448$$
$$x_{36} = -18.8495552124105$$
$$x_{23} = -12.5663710889626$$
$$x_{43} = -12.5663703112531$$
$$x_{44} = -6.2831858160515$$
$$x_{68} = -6.28318555849548$$
$$x_{51} = -6.2831851275477$$
$$x_{87} = -4.79511606158654 \cdot 10^{-7}$$
$$x_{39} = 0$$
$$x_{55} = 3.40772025642919 \cdot 10^{-7}$$
$$x_{75} = 6.28318500093652$$
$$x_{64} = 6.28318528420851$$
$$x_{17} = 6.28318579821791$$
$$x_{34} = 6.28318626747926$$
$$x_{50} = 12.5663704426592$$
$$x_{11} = 12.5663710110881$$
$$x_{77} = 12.5663711301703$$
$$x_{83} = 18.8495556275525$$
$$x_{84} = 18.8495564031971$$
$$x_{70} = 25.1327408328211$$
$$x_{42} = 25.1327416384075$$
$$x_{82} = 31.4159260648825$$
$$x_{9} = 31.4159268459961$$
$$x_{48} = 37.6991113348642$$
$$x_{2} = 37.6991115173992$$
$$x_{35} = 37.6991120311338$$
$$x_{81} = 43.9822966661001$$
$$x_{78} = 43.9822971694647$$
$$x_{73} = 43.9822974733639$$
$$x_{69} = 50.2654821322586$$
$$x_{31} = 50.2654824463392$$
$$x_{85} = 50.2654829439723$$
$$x_{20} = 56.5486668532011$$
$$x_{86} = 56.5486676011951$$
$$x_{33} = 56.5486680806249$$
$$x_{30} = 56.5486682809363$$
$$x_{72} = 62.8318527849002$$
$$x_{1} = 62.8318535568358$$
$$x_{49} = 69.1150379887504$$
$$x_{37} = 69.115038794053$$
$$x_{60} = 75.3982232188727$$
$$x_{79} = 75.3982240031607$$
$$x_{16} = 81.6814084860076$$
$$x_{25} = 81.6814085860518$$
$$x_{74} = 81.6814091897036$$
$$x_{52} = 87.9645938121814$$
$$x_{21} = 87.964594335905$$
$$x_{40} = 87.9645946044253$$
$$x_{65} = 94.2477792651059$$
$$x_{67} = 94.2477796093523$$
$$x_{7} = 94.2477800892631$$
$$x_{18} = 100.530964759815$$
$$x_{8} = 100.530965157364$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{56}$$
For example, let's take the point
$$x_{0} = x_{56} - \frac{1}{10}$$
=
$$-100.530964626003 + - \frac{1}{10}$$
=
$$-100.630964626003$$
substitute to the expression
$$\cos{\left(t \right)} \leq 1$$
$$\cos{\left(t \right)} \leq 1$$
cos(t) <= 1
Then
$$x \leq -100.530964626003$$
no execute
one of the solutions of our inequality is:
$$x \geq -100.530964626003 \wedge x \leq -94.2477801171671$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------
x56 x10 x13 x63 x38 x88 x14 x57 x66 x76 x54 x19 x45 x80 x46 x27 x15 x28 x22 x26 x5 x41 x71 x12 x24 x61 x53 x59 x4 x32 x3 x62 x47 x29 x6 x58 x36 x23 x43 x44 x68 x51 x87 x39 x55 x75 x64 x17 x34 x50 x11 x77 x83 x84 x70 x42 x82 x9 x48 x2 x35 x81 x78 x73 x69 x31 x85 x20 x86 x33 x30 x72 x1 x49 x37 x60 x79 x16 x25 x74 x52 x21 x40 x65 x67 x7 x18 x8Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \geq -100.530964626003 \wedge x \leq -94.2477801171671$$
$$x \geq -94.2477797298079 \wedge x \leq -94.2477794452815$$
$$x \geq -87.9645947692094 \wedge x \leq -87.9645943586158$$
$$x \geq -87.964593928489 \wedge x \leq -81.6814092565354$$
$$x \geq -81.6814090382277 \wedge x \leq -81.6814084945807$$
$$x \geq -81.6814075578313 \wedge x \leq -75.3982238741744$$
$$x \geq -75.3982231720141 \wedge x \leq -75.3982231045728$$
$$x \geq -69.1150386869085 \wedge x \leq -69.1150379045123$$
$$x \geq -62.8318534787248 \wedge x \leq -62.831852673202$$
$$x \geq -56.5486682426592 \wedge x \leq -56.5486674685864$$
$$x \geq -50.2654829667315 \wedge x \leq -50.265482641087$$
$$x \geq -50.2654822863493 \wedge x \leq -43.9822976246252$$
$$x \geq -43.9822971745392 \wedge x \leq -43.9822967932182$$
$$x \geq -37.6991121287155 \wedge x \leq -37.6991118772631$$
$$x \geq -37.6991113479743 \wedge x \leq -31.4159267157965$$
$$x \geq -31.4159260507536 \wedge x \leq -31.4159260208155$$
$$x \geq -25.1327415297174 \wedge x \leq -25.1327407505866$$
$$x \geq -18.8495563230046 \wedge x \leq -18.8495555173448$$
$$x \geq -18.8495552124105 \wedge x \leq -12.5663710889626$$
$$x \geq -12.5663703112531 \wedge x \leq -6.2831858160515$$
$$x \geq -6.28318555849548 \wedge x \leq -6.2831851275477$$
$$x \geq -4.79511606158654 \cdot 10^{-7} \wedge x \leq 0$$
$$x \geq 3.40772025642919 \cdot 10^{-7} \wedge x \leq 6.28318500093652$$
$$x \geq 6.28318528420851 \wedge x \leq 6.28318579821791$$
$$x \geq 6.28318626747926 \wedge x \leq 12.5663704426592$$
$$x \geq 12.5663710110881 \wedge x \leq 12.5663711301703$$
$$x \geq 18.8495556275525 \wedge x \leq 18.8495564031971$$
$$x \geq 25.1327408328211 \wedge x \leq 25.1327416384075$$
$$x \geq 31.4159260648825 \wedge x \leq 31.4159268459961$$
$$x \geq 37.6991113348642 \wedge x \leq 37.6991115173992$$
$$x \geq 37.6991120311338 \wedge x \leq 43.9822966661001$$
$$x \geq 43.9822971694647 \wedge x \leq 43.9822974733639$$
$$x \geq 50.2654821322586 \wedge x \leq 50.2654824463392$$
$$x \geq 50.2654829439723 \wedge x \leq 56.5486668532011$$
$$x \geq 56.5486676011951 \wedge x \leq 56.5486680806249$$
$$x \geq 56.5486682809363 \wedge x \leq 62.8318527849002$$
$$x \geq 62.8318535568358 \wedge x \leq 69.1150379887504$$
$$x \geq 69.115038794053 \wedge x \leq 75.3982232188727$$
$$x \geq 75.3982240031607 \wedge x \leq 81.6814084860076$$
$$x \geq 81.6814085860518 \wedge x \leq 81.6814091897036$$
$$x \geq 87.9645938121814 \wedge x \leq 87.964594335905$$
$$x \geq 87.9645946044253 \wedge x \leq 94.2477792651059$$
$$x \geq 94.2477796093523 \wedge x \leq 94.2477800892631$$
$$x \geq 100.530964759815 \wedge x \leq 100.530965157364$$
Rapid solution
This inequality holds true always