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->=-16
- ln(4x-5)≥ln(3x-6)
- x^2*log(243)*(-x-3)≥log(3)*(x^2+6*x+9)
- sin(t)<-2:3
- Derivative of:
-
sin(t)
- Limit of the function:
-
sin(t)
- Integral of d{x}:
-
sin(t)
-
Identical expressions
- sin(t)<- two : three
- sinus of (t) less than minus 2:3
- sinus of (t) less than minus two : three
- sint<-2:3
-
Similar expressions
- 3-(1-x):2<=(2x-7):6+(7x-2):3
- (8x^2-2):(3-6x)>0
- sint<-√3/2
- (x-2):(3-x)>0
- sint<0
- (3x-2):(3-x)=<2
- sin(t)<+2:3
- sint≤1/2
sin(t)<-2:3 inequation
The solution
Detail solution
Given the inequality:
$$\sin{\left(t \right)} < - \frac{2}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(t \right)} = - \frac{2}{3}$$
Solve:
Given the equation
$$\sin{\left(t \right)} = - \frac{2}{3}$$
transform
$$\sin{\left(t \right)} + \frac{2}{3} = 0$$
$$\sin{\left(t \right)} + \frac{2}{3} = 0$$
Do replacement
$$w = \sin{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = - \frac{2}{3}$$
We get the answer: w = -2/3
do backward replacement
$$\sin{\left(t \right)} = w$$
substitute w:
$$x_{1} = 412.27836527649$$
$$x_{2} = 10.1545056169963$$
$$x_{3} = 93.5180519514668$$
$$x_{4} = 1216.52608459548$$
$$x_{5} = -32.1456541921249$$
$$x_{6} = -65.2437180691587$$
$$x_{7} = 30.686198879671$$
$$x_{8} = -107.54387787828$$
$$x_{9} = -302.322622400847$$
$$x_{10} = -77.8100886835179$$
$$x_{11} = -8.69505030454241$$
$$x_{12} = -38.4288394993045$$
$$x_{13} = 5.55345765095262$$
$$x_{14} = 16.4376909241759$$
$$x_{15} = -88.6943219567412$$
$$x_{16} = 18.1198282653118$$
$$x_{17} = -50.9952101136637$$
$$x_{18} = -57.2783954208432$$
$$x_{19} = 24.4030135724914$$
$$x_{20} = 55.8189401083893$$
$$x_{21} = -14.978235611722$$
$$x_{22} = 85.5527293031514$$
$$x_{23} = 72.9863586887922$$
$$x_{24} = -69.8447660352024$$
$$x_{25} = 11.8366429581322$$
$$x_{26} = 74.6684960299281$$
$$x_{27} = -33.8277915332608$$
$$x_{28} = -101.2606925711$$
$$x_{29} = -7.01291296340655$$
$$x_{30} = -0.729727656226966$$
$$x_{31} = -63.5615807280228$$
$$x_{32} = -84.0932739906975$$
$$x_{33} = 68.3853107227485$$
$$x_{34} = 60.419988074433$$
$$x_{35} = 99.8012372586464$$
$$x_{36} = -13.2960982705861$$
$$x_{37} = -58.9605327619791$$
$$x_{38} = -21.2614209189016$$
$$x_{39} = 29.0040615385351$$
$$x_{40} = 87.2348666442873$$
$$x_{41} = -2.41186499736283$$
$$x_{42} = 62.1021254155689$$
$$x_{43} = -27.5446062260812$$
$$x_{44} = -44.7120248064841$$
$$x_{45} = -94.9775072639208$$
$$x_{46} = 54.1368027672534$$
$$x_{47} = -25.8624688849453$$
$$x_{48} = 98.1190999175106$$
$$x_{49} = -836.393373511112$$
$$x_{50} = 3.87132030981676$$
$$x_{51} = -46.3941621476199$$
$$x_{52} = 22.7208762313555$$
$$x_{53} = 36.9693841868506$$
$$x_{54} = -90.376459297877$$
$$x_{55} = 175.199460944801$$
$$x_{56} = -82.4111366495616$$
$$x_{57} = 91.835914610331$$
$$x_{58} = -1755.42056570047$$
$$x_{59} = -19.5792835777657$$
$$x_{60} = 79.2695439959718$$
$$x_{61} = 49.5357548012097$$
$$x_{62} = 66.7031733816126$$
$$x_{63} = 80.9516813371077$$
$$x_{64} = -40.1109768404403$$
$$x_{65} = 47.8536174600739$$
$$x_{66} = -96.6596446050566$$
$$x_{67} = 43.2525694940301$$
$$x_{68} = -1979.9330994178$$
$$x_{69} = -71.5269033763383$$
$$x_{70} = 41.5704321528943$$
$$x_{71} = -52.6773474547995$$
$$x_{72} = 35.2872468457147$$
$$x_{73} = -76.127951342382$$
$$x_{1} = 412.27836527649$$
$$x_{2} = 10.1545056169963$$
$$x_{3} = 93.5180519514668$$
$$x_{4} = 1216.52608459548$$
$$x_{5} = -32.1456541921249$$
$$x_{6} = -65.2437180691587$$
$$x_{7} = 30.686198879671$$
$$x_{8} = -107.54387787828$$
$$x_{9} = -302.322622400847$$
$$x_{10} = -77.8100886835179$$
$$x_{11} = -8.69505030454241$$
$$x_{12} = -38.4288394993045$$
$$x_{13} = 5.55345765095262$$
$$x_{14} = 16.4376909241759$$
$$x_{15} = -88.6943219567412$$
$$x_{16} = 18.1198282653118$$
$$x_{17} = -50.9952101136637$$
$$x_{18} = -57.2783954208432$$
$$x_{19} = 24.4030135724914$$
$$x_{20} = 55.8189401083893$$
$$x_{21} = -14.978235611722$$
$$x_{22} = 85.5527293031514$$
$$x_{23} = 72.9863586887922$$
$$x_{24} = -69.8447660352024$$
$$x_{25} = 11.8366429581322$$
$$x_{26} = 74.6684960299281$$
$$x_{27} = -33.8277915332608$$
$$x_{28} = -101.2606925711$$
$$x_{29} = -7.01291296340655$$
$$x_{30} = -0.729727656226966$$
$$x_{31} = -63.5615807280228$$
$$x_{32} = -84.0932739906975$$
$$x_{33} = 68.3853107227485$$
$$x_{34} = 60.419988074433$$
$$x_{35} = 99.8012372586464$$
$$x_{36} = -13.2960982705861$$
$$x_{37} = -58.9605327619791$$
$$x_{38} = -21.2614209189016$$
$$x_{39} = 29.0040615385351$$
$$x_{40} = 87.2348666442873$$
$$x_{41} = -2.41186499736283$$
$$x_{42} = 62.1021254155689$$
$$x_{43} = -27.5446062260812$$
$$x_{44} = -44.7120248064841$$
$$x_{45} = -94.9775072639208$$
$$x_{46} = 54.1368027672534$$
$$x_{47} = -25.8624688849453$$
$$x_{48} = 98.1190999175106$$
$$x_{49} = -836.393373511112$$
$$x_{50} = 3.87132030981676$$
$$x_{51} = -46.3941621476199$$
$$x_{52} = 22.7208762313555$$
$$x_{53} = 36.9693841868506$$
$$x_{54} = -90.376459297877$$
$$x_{55} = 175.199460944801$$
$$x_{56} = -82.4111366495616$$
$$x_{57} = 91.835914610331$$
$$x_{58} = -1755.42056570047$$
$$x_{59} = -19.5792835777657$$
$$x_{60} = 79.2695439959718$$
$$x_{61} = 49.5357548012097$$
$$x_{62} = 66.7031733816126$$
$$x_{63} = 80.9516813371077$$
$$x_{64} = -40.1109768404403$$
$$x_{65} = 47.8536174600739$$
$$x_{66} = -96.6596446050566$$
$$x_{67} = 43.2525694940301$$
$$x_{68} = -1979.9330994178$$
$$x_{69} = -71.5269033763383$$
$$x_{70} = 41.5704321528943$$
$$x_{71} = -52.6773474547995$$
$$x_{72} = 35.2872468457147$$
$$x_{73} = -76.127951342382$$
This roots
$$x_{68} = -1979.9330994178$$
$$x_{58} = -1755.42056570047$$
$$x_{49} = -836.393373511112$$
$$x_{9} = -302.322622400847$$
$$x_{8} = -107.54387787828$$
$$x_{28} = -101.2606925711$$
$$x_{66} = -96.6596446050566$$
$$x_{45} = -94.9775072639208$$
$$x_{54} = -90.376459297877$$
$$x_{15} = -88.6943219567412$$
$$x_{32} = -84.0932739906975$$
$$x_{56} = -82.4111366495616$$
$$x_{10} = -77.8100886835179$$
$$x_{73} = -76.127951342382$$
$$x_{69} = -71.5269033763383$$
$$x_{24} = -69.8447660352024$$
$$x_{6} = -65.2437180691587$$
$$x_{31} = -63.5615807280228$$
$$x_{37} = -58.9605327619791$$
$$x_{18} = -57.2783954208432$$
$$x_{71} = -52.6773474547995$$
$$x_{17} = -50.9952101136637$$
$$x_{51} = -46.3941621476199$$
$$x_{44} = -44.7120248064841$$
$$x_{64} = -40.1109768404403$$
$$x_{12} = -38.4288394993045$$
$$x_{27} = -33.8277915332608$$
$$x_{5} = -32.1456541921249$$
$$x_{43} = -27.5446062260812$$
$$x_{47} = -25.8624688849453$$
$$x_{38} = -21.2614209189016$$
$$x_{59} = -19.5792835777657$$
$$x_{21} = -14.978235611722$$
$$x_{36} = -13.2960982705861$$
$$x_{11} = -8.69505030454241$$
$$x_{29} = -7.01291296340655$$
$$x_{41} = -2.41186499736283$$
$$x_{30} = -0.729727656226966$$
$$x_{50} = 3.87132030981676$$
$$x_{13} = 5.55345765095262$$
$$x_{2} = 10.1545056169963$$
$$x_{25} = 11.8366429581322$$
$$x_{14} = 16.4376909241759$$
$$x_{16} = 18.1198282653118$$
$$x_{52} = 22.7208762313555$$
$$x_{19} = 24.4030135724914$$
$$x_{39} = 29.0040615385351$$
$$x_{7} = 30.686198879671$$
$$x_{72} = 35.2872468457147$$
$$x_{53} = 36.9693841868506$$
$$x_{70} = 41.5704321528943$$
$$x_{67} = 43.2525694940301$$
$$x_{65} = 47.8536174600739$$
$$x_{61} = 49.5357548012097$$
$$x_{46} = 54.1368027672534$$
$$x_{20} = 55.8189401083893$$
$$x_{34} = 60.419988074433$$
$$x_{42} = 62.1021254155689$$
$$x_{62} = 66.7031733816126$$
$$x_{33} = 68.3853107227485$$
$$x_{23} = 72.9863586887922$$
$$x_{26} = 74.6684960299281$$
$$x_{60} = 79.2695439959718$$
$$x_{63} = 80.9516813371077$$
$$x_{22} = 85.5527293031514$$
$$x_{40} = 87.2348666442873$$
$$x_{57} = 91.835914610331$$
$$x_{3} = 93.5180519514668$$
$$x_{48} = 98.1190999175106$$
$$x_{35} = 99.8012372586464$$
$$x_{55} = 175.199460944801$$
$$x_{1} = 412.27836527649$$
$$x_{4} = 1216.52608459548$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{68}$$
For example, let's take the point
$$x_{0} = x_{68} - \frac{1}{10}$$
=
$$-1979.9330994178 + - \frac{1}{10}$$
=
$$-1980.0330994178$$
substitute to the expression
$$\sin{\left(t \right)} < - \frac{2}{3}$$
$$\sin{\left(t \right)} < - \frac{2}{3}$$
Then
$$x < -1979.9330994178$$
no execute
one of the solutions of our inequality is:
$$x > -1979.9330994178 \wedge x < -1755.42056570047$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -1979.9330994178 \wedge x < -1755.42056570047$$
$$x > -836.393373511112 \wedge x < -302.322622400847$$
$$x > -107.54387787828 \wedge x < -101.2606925711$$
$$x > -96.6596446050566 \wedge x < -94.9775072639208$$
$$x > -90.376459297877 \wedge x < -88.6943219567412$$
$$x > -84.0932739906975 \wedge x < -82.4111366495616$$
$$x > -77.8100886835179 \wedge x < -76.127951342382$$
$$x > -71.5269033763383 \wedge x < -69.8447660352024$$
$$x > -65.2437180691587 \wedge x < -63.5615807280228$$
$$x > -58.9605327619791 \wedge x < -57.2783954208432$$
$$x > -52.6773474547995 \wedge x < -50.9952101136637$$
$$x > -46.3941621476199 \wedge x < -44.7120248064841$$
$$x > -40.1109768404403 \wedge x < -38.4288394993045$$
$$x > -33.8277915332608 \wedge x < -32.1456541921249$$
$$x > -27.5446062260812 \wedge x < -25.8624688849453$$
$$x > -21.2614209189016 \wedge x < -19.5792835777657$$
$$x > -14.978235611722 \wedge x < -13.2960982705861$$
$$x > -8.69505030454241 \wedge x < -7.01291296340655$$
$$x > -2.41186499736283 \wedge x < -0.729727656226966$$
$$x > 3.87132030981676 \wedge x < 5.55345765095262$$
$$x > 10.1545056169963 \wedge x < 11.8366429581322$$
$$x > 16.4376909241759 \wedge x < 18.1198282653118$$
$$x > 22.7208762313555 \wedge x < 24.4030135724914$$
$$x > 29.0040615385351 \wedge x < 30.686198879671$$
$$x > 35.2872468457147 \wedge x < 36.9693841868506$$
$$x > 41.5704321528943 \wedge x < 43.2525694940301$$
$$x > 47.8536174600739 \wedge x < 49.5357548012097$$
$$x > 54.1368027672534 \wedge x < 55.8189401083893$$
$$x > 60.419988074433 \wedge x < 62.1021254155689$$
$$x > 66.7031733816126 \wedge x < 68.3853107227485$$
$$x > 72.9863586887922 \wedge x < 74.6684960299281$$
$$x > 79.2695439959718 \wedge x < 80.9516813371077$$
$$x > 85.5527293031514 \wedge x < 87.2348666442873$$
$$x > 91.835914610331 \wedge x < 93.5180519514668$$
$$x > 98.1190999175106 \wedge x < 99.8012372586464$$
$$x > 175.199460944801 \wedge x < 412.27836527649$$
$$x > 1216.52608459548$$
$$\sin{\left(t \right)} < - \frac{2}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(t \right)} = - \frac{2}{3}$$
Solve:
Given the equation
$$\sin{\left(t \right)} = - \frac{2}{3}$$
transform
$$\sin{\left(t \right)} + \frac{2}{3} = 0$$
$$\sin{\left(t \right)} + \frac{2}{3} = 0$$
Do replacement
$$w = \sin{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = - \frac{2}{3}$$
We get the answer: w = -2/3
do backward replacement
$$\sin{\left(t \right)} = w$$
substitute w:
$$x_{1} = 412.27836527649$$
$$x_{2} = 10.1545056169963$$
$$x_{3} = 93.5180519514668$$
$$x_{4} = 1216.52608459548$$
$$x_{5} = -32.1456541921249$$
$$x_{6} = -65.2437180691587$$
$$x_{7} = 30.686198879671$$
$$x_{8} = -107.54387787828$$
$$x_{9} = -302.322622400847$$
$$x_{10} = -77.8100886835179$$
$$x_{11} = -8.69505030454241$$
$$x_{12} = -38.4288394993045$$
$$x_{13} = 5.55345765095262$$
$$x_{14} = 16.4376909241759$$
$$x_{15} = -88.6943219567412$$
$$x_{16} = 18.1198282653118$$
$$x_{17} = -50.9952101136637$$
$$x_{18} = -57.2783954208432$$
$$x_{19} = 24.4030135724914$$
$$x_{20} = 55.8189401083893$$
$$x_{21} = -14.978235611722$$
$$x_{22} = 85.5527293031514$$
$$x_{23} = 72.9863586887922$$
$$x_{24} = -69.8447660352024$$
$$x_{25} = 11.8366429581322$$
$$x_{26} = 74.6684960299281$$
$$x_{27} = -33.8277915332608$$
$$x_{28} = -101.2606925711$$
$$x_{29} = -7.01291296340655$$
$$x_{30} = -0.729727656226966$$
$$x_{31} = -63.5615807280228$$
$$x_{32} = -84.0932739906975$$
$$x_{33} = 68.3853107227485$$
$$x_{34} = 60.419988074433$$
$$x_{35} = 99.8012372586464$$
$$x_{36} = -13.2960982705861$$
$$x_{37} = -58.9605327619791$$
$$x_{38} = -21.2614209189016$$
$$x_{39} = 29.0040615385351$$
$$x_{40} = 87.2348666442873$$
$$x_{41} = -2.41186499736283$$
$$x_{42} = 62.1021254155689$$
$$x_{43} = -27.5446062260812$$
$$x_{44} = -44.7120248064841$$
$$x_{45} = -94.9775072639208$$
$$x_{46} = 54.1368027672534$$
$$x_{47} = -25.8624688849453$$
$$x_{48} = 98.1190999175106$$
$$x_{49} = -836.393373511112$$
$$x_{50} = 3.87132030981676$$
$$x_{51} = -46.3941621476199$$
$$x_{52} = 22.7208762313555$$
$$x_{53} = 36.9693841868506$$
$$x_{54} = -90.376459297877$$
$$x_{55} = 175.199460944801$$
$$x_{56} = -82.4111366495616$$
$$x_{57} = 91.835914610331$$
$$x_{58} = -1755.42056570047$$
$$x_{59} = -19.5792835777657$$
$$x_{60} = 79.2695439959718$$
$$x_{61} = 49.5357548012097$$
$$x_{62} = 66.7031733816126$$
$$x_{63} = 80.9516813371077$$
$$x_{64} = -40.1109768404403$$
$$x_{65} = 47.8536174600739$$
$$x_{66} = -96.6596446050566$$
$$x_{67} = 43.2525694940301$$
$$x_{68} = -1979.9330994178$$
$$x_{69} = -71.5269033763383$$
$$x_{70} = 41.5704321528943$$
$$x_{71} = -52.6773474547995$$
$$x_{72} = 35.2872468457147$$
$$x_{73} = -76.127951342382$$
$$x_{1} = 412.27836527649$$
$$x_{2} = 10.1545056169963$$
$$x_{3} = 93.5180519514668$$
$$x_{4} = 1216.52608459548$$
$$x_{5} = -32.1456541921249$$
$$x_{6} = -65.2437180691587$$
$$x_{7} = 30.686198879671$$
$$x_{8} = -107.54387787828$$
$$x_{9} = -302.322622400847$$
$$x_{10} = -77.8100886835179$$
$$x_{11} = -8.69505030454241$$
$$x_{12} = -38.4288394993045$$
$$x_{13} = 5.55345765095262$$
$$x_{14} = 16.4376909241759$$
$$x_{15} = -88.6943219567412$$
$$x_{16} = 18.1198282653118$$
$$x_{17} = -50.9952101136637$$
$$x_{18} = -57.2783954208432$$
$$x_{19} = 24.4030135724914$$
$$x_{20} = 55.8189401083893$$
$$x_{21} = -14.978235611722$$
$$x_{22} = 85.5527293031514$$
$$x_{23} = 72.9863586887922$$
$$x_{24} = -69.8447660352024$$
$$x_{25} = 11.8366429581322$$
$$x_{26} = 74.6684960299281$$
$$x_{27} = -33.8277915332608$$
$$x_{28} = -101.2606925711$$
$$x_{29} = -7.01291296340655$$
$$x_{30} = -0.729727656226966$$
$$x_{31} = -63.5615807280228$$
$$x_{32} = -84.0932739906975$$
$$x_{33} = 68.3853107227485$$
$$x_{34} = 60.419988074433$$
$$x_{35} = 99.8012372586464$$
$$x_{36} = -13.2960982705861$$
$$x_{37} = -58.9605327619791$$
$$x_{38} = -21.2614209189016$$
$$x_{39} = 29.0040615385351$$
$$x_{40} = 87.2348666442873$$
$$x_{41} = -2.41186499736283$$
$$x_{42} = 62.1021254155689$$
$$x_{43} = -27.5446062260812$$
$$x_{44} = -44.7120248064841$$
$$x_{45} = -94.9775072639208$$
$$x_{46} = 54.1368027672534$$
$$x_{47} = -25.8624688849453$$
$$x_{48} = 98.1190999175106$$
$$x_{49} = -836.393373511112$$
$$x_{50} = 3.87132030981676$$
$$x_{51} = -46.3941621476199$$
$$x_{52} = 22.7208762313555$$
$$x_{53} = 36.9693841868506$$
$$x_{54} = -90.376459297877$$
$$x_{55} = 175.199460944801$$
$$x_{56} = -82.4111366495616$$
$$x_{57} = 91.835914610331$$
$$x_{58} = -1755.42056570047$$
$$x_{59} = -19.5792835777657$$
$$x_{60} = 79.2695439959718$$
$$x_{61} = 49.5357548012097$$
$$x_{62} = 66.7031733816126$$
$$x_{63} = 80.9516813371077$$
$$x_{64} = -40.1109768404403$$
$$x_{65} = 47.8536174600739$$
$$x_{66} = -96.6596446050566$$
$$x_{67} = 43.2525694940301$$
$$x_{68} = -1979.9330994178$$
$$x_{69} = -71.5269033763383$$
$$x_{70} = 41.5704321528943$$
$$x_{71} = -52.6773474547995$$
$$x_{72} = 35.2872468457147$$
$$x_{73} = -76.127951342382$$
This roots
$$x_{68} = -1979.9330994178$$
$$x_{58} = -1755.42056570047$$
$$x_{49} = -836.393373511112$$
$$x_{9} = -302.322622400847$$
$$x_{8} = -107.54387787828$$
$$x_{28} = -101.2606925711$$
$$x_{66} = -96.6596446050566$$
$$x_{45} = -94.9775072639208$$
$$x_{54} = -90.376459297877$$
$$x_{15} = -88.6943219567412$$
$$x_{32} = -84.0932739906975$$
$$x_{56} = -82.4111366495616$$
$$x_{10} = -77.8100886835179$$
$$x_{73} = -76.127951342382$$
$$x_{69} = -71.5269033763383$$
$$x_{24} = -69.8447660352024$$
$$x_{6} = -65.2437180691587$$
$$x_{31} = -63.5615807280228$$
$$x_{37} = -58.9605327619791$$
$$x_{18} = -57.2783954208432$$
$$x_{71} = -52.6773474547995$$
$$x_{17} = -50.9952101136637$$
$$x_{51} = -46.3941621476199$$
$$x_{44} = -44.7120248064841$$
$$x_{64} = -40.1109768404403$$
$$x_{12} = -38.4288394993045$$
$$x_{27} = -33.8277915332608$$
$$x_{5} = -32.1456541921249$$
$$x_{43} = -27.5446062260812$$
$$x_{47} = -25.8624688849453$$
$$x_{38} = -21.2614209189016$$
$$x_{59} = -19.5792835777657$$
$$x_{21} = -14.978235611722$$
$$x_{36} = -13.2960982705861$$
$$x_{11} = -8.69505030454241$$
$$x_{29} = -7.01291296340655$$
$$x_{41} = -2.41186499736283$$
$$x_{30} = -0.729727656226966$$
$$x_{50} = 3.87132030981676$$
$$x_{13} = 5.55345765095262$$
$$x_{2} = 10.1545056169963$$
$$x_{25} = 11.8366429581322$$
$$x_{14} = 16.4376909241759$$
$$x_{16} = 18.1198282653118$$
$$x_{52} = 22.7208762313555$$
$$x_{19} = 24.4030135724914$$
$$x_{39} = 29.0040615385351$$
$$x_{7} = 30.686198879671$$
$$x_{72} = 35.2872468457147$$
$$x_{53} = 36.9693841868506$$
$$x_{70} = 41.5704321528943$$
$$x_{67} = 43.2525694940301$$
$$x_{65} = 47.8536174600739$$
$$x_{61} = 49.5357548012097$$
$$x_{46} = 54.1368027672534$$
$$x_{20} = 55.8189401083893$$
$$x_{34} = 60.419988074433$$
$$x_{42} = 62.1021254155689$$
$$x_{62} = 66.7031733816126$$
$$x_{33} = 68.3853107227485$$
$$x_{23} = 72.9863586887922$$
$$x_{26} = 74.6684960299281$$
$$x_{60} = 79.2695439959718$$
$$x_{63} = 80.9516813371077$$
$$x_{22} = 85.5527293031514$$
$$x_{40} = 87.2348666442873$$
$$x_{57} = 91.835914610331$$
$$x_{3} = 93.5180519514668$$
$$x_{48} = 98.1190999175106$$
$$x_{35} = 99.8012372586464$$
$$x_{55} = 175.199460944801$$
$$x_{1} = 412.27836527649$$
$$x_{4} = 1216.52608459548$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{68}$$
For example, let's take the point
$$x_{0} = x_{68} - \frac{1}{10}$$
=
$$-1979.9330994178 + - \frac{1}{10}$$
=
$$-1980.0330994178$$
substitute to the expression
$$\sin{\left(t \right)} < - \frac{2}{3}$$
$$\sin{\left(t \right)} < - \frac{2}{3}$$
sin(t) < -2/3
Then
$$x < -1979.9330994178$$
no execute
one of the solutions of our inequality is:
$$x > -1979.9330994178 \wedge x < -1755.42056570047$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------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-------ο-------ο-------ο-------ο-------ο-------ο-------
x68 x58 x49 x9 x8 x28 x66 x45 x54 x15 x32 x56 x10 x73 x69 x24 x6 x31 x37 x18 x71 x17 x51 x44 x64 x12 x27 x5 x43 x47 x38 x59 x21 x36 x11 x29 x41 x30 x50 x13 x2 x25 x14 x16 x52 x19 x39 x7 x72 x53 x70 x67 x65 x61 x46 x20 x34 x42 x62 x33 x23 x26 x60 x63 x22 x40 x57 x3 x48 x35 x55 x1 x4Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -1979.9330994178 \wedge x < -1755.42056570047$$
$$x > -836.393373511112 \wedge x < -302.322622400847$$
$$x > -107.54387787828 \wedge x < -101.2606925711$$
$$x > -96.6596446050566 \wedge x < -94.9775072639208$$
$$x > -90.376459297877 \wedge x < -88.6943219567412$$
$$x > -84.0932739906975 \wedge x < -82.4111366495616$$
$$x > -77.8100886835179 \wedge x < -76.127951342382$$
$$x > -71.5269033763383 \wedge x < -69.8447660352024$$
$$x > -65.2437180691587 \wedge x < -63.5615807280228$$
$$x > -58.9605327619791 \wedge x < -57.2783954208432$$
$$x > -52.6773474547995 \wedge x < -50.9952101136637$$
$$x > -46.3941621476199 \wedge x < -44.7120248064841$$
$$x > -40.1109768404403 \wedge x < -38.4288394993045$$
$$x > -33.8277915332608 \wedge x < -32.1456541921249$$
$$x > -27.5446062260812 \wedge x < -25.8624688849453$$
$$x > -21.2614209189016 \wedge x < -19.5792835777657$$
$$x > -14.978235611722 \wedge x < -13.2960982705861$$
$$x > -8.69505030454241 \wedge x < -7.01291296340655$$
$$x > -2.41186499736283 \wedge x < -0.729727656226966$$
$$x > 3.87132030981676 \wedge x < 5.55345765095262$$
$$x > 10.1545056169963 \wedge x < 11.8366429581322$$
$$x > 16.4376909241759 \wedge x < 18.1198282653118$$
$$x > 22.7208762313555 \wedge x < 24.4030135724914$$
$$x > 29.0040615385351 \wedge x < 30.686198879671$$
$$x > 35.2872468457147 \wedge x < 36.9693841868506$$
$$x > 41.5704321528943 \wedge x < 43.2525694940301$$
$$x > 47.8536174600739 \wedge x < 49.5357548012097$$
$$x > 54.1368027672534 \wedge x < 55.8189401083893$$
$$x > 60.419988074433 \wedge x < 62.1021254155689$$
$$x > 66.7031733816126 \wedge x < 68.3853107227485$$
$$x > 72.9863586887922 \wedge x < 74.6684960299281$$
$$x > 79.2695439959718 \wedge x < 80.9516813371077$$
$$x > 85.5527293031514 \wedge x < 87.2348666442873$$
$$x > 91.835914610331 \wedge x < 93.5180519514668$$
$$x > 98.1190999175106 \wedge x < 99.8012372586464$$
$$x > 175.199460944801 \wedge x < 412.27836527649$$
$$x > 1216.52608459548$$
Rapid solution
[src]
/ / ___\ / ___\ \ | |2*\/ 5 | |2*\/ 5 | | And|t < - atan|-------| + 2*pi, pi + atan|-------| < t| \ \ 5 / \ 5 / /
$$t < - \operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)} + 2 \pi \wedge \operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)} + \pi < t$$
(pi + atan(2*sqrt(5)/5) < t)∧(t < -atan(2*sqrt(5)/5) + 2*pi)
Rapid solution 2
[src]
/ ___\ / ___\
|2*\/ 5 | |2*\/ 5 |
(pi + atan|-------|, - atan|-------| + 2*pi)
\ 5 / \ 5 /
$$x\ in\ \left(\operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)} + \pi, - \operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)} + 2 \pi\right)$$
x in Interval.open(atan(2*sqrt(5)/5) + pi, -atan(2*sqrt(5)/5) + 2*pi)