Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- 14x+17x-18+35<3,10x+7
- (x^2+5*x)/(x-6)>0
- log2(x^3-x+10)>log2(x^3+5*x^2-6)
- 1-2/(|x|)<=23/x^2
- Integral of d{x}:
-
sint
- Derivative of:
-
sint
-
Identical expressions
- sint< one \ three
- sinus of t less than 1\3
- sinus of t less than one \ three
-
Similar expressions
- sin(t)>=1/2
- sin(t)>=0
- log(1/81(36-5x))log(8-x(1/9))>=1
- (sin2t)-((sin(t)+cos(t))^2)/(tg(t)+ctg(t))
- 5^log(x+1)(3*x^2+8*x+4)>=(x^2+3*x+2)^(log(x+1)25)
sint<1\3 inequation
The solution
Detail solution
Given the inequality:
$$\sin{\left(t \right)} < \frac{1}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(t \right)} = \frac{1}{3}$$
Solve:
Given the equation
$$\sin{\left(t \right)} = \frac{1}{3}$$
transform
$$\sin{\left(t \right)} - \frac{1}{3} = 0$$
$$\sin{\left(t \right)} - \frac{1}{3} = 0$$
Do replacement
$$w = \sin{\left(t \right)}$$
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
$$\sin{\left(t \right)} = w$$
substitute w:
$$x_{1} = 94.5876165171479$$
$$x_{2} = 21.6513116656744$$
$$x_{3} = 44.3221340597112$$
$$x_{4} = -56.2088308551622$$
$$x_{5} = -5.94334839772546$$
$$x_{6} = 172.447759037984$$
$$x_{7} = 78.1999794302907$$
$$x_{8} = 100.870801824328$$
$$x_{9} = -43.642460240803$$
$$x_{10} = 69.4548752884296$$
$$x_{11} = -24.7929043192642$$
$$x_{12} = 63.17168998125$$
$$x_{13} = 19.1893928309929$$
$$x_{14} = 53.0672382015724$$
$$x_{15} = 84.4831647374703$$
$$x_{16} = -18.5097190120846$$
$$x_{17} = -53.7469120204806$$
$$x_{18} = -9.7646148702235$$
$$x_{19} = 90.7663500446499$$
$$x_{20} = -112585.595763607$$
$$x_{21} = 75.7380605956092$$
$$x_{22} = 65.6336088159315$$
$$x_{23} = 27.934496972854$$
$$x_{24} = -34.8973560989418$$
$$x_{25} = -12.2265337049051$$
$$x_{26} = -60.0300973276602$$
$$x_{27} = 46.7840528943928$$
$$x_{28} = 59.350423508752$$
$$x_{29} = 40.5008675872132$$
$$x_{30} = -41.1805414061214$$
$$x_{31} = -87.6247573910601$$
$$x_{32} = -47.463726713301$$
$$x_{33} = -72.5964679420194$$
$$x_{34} = -68.7752014695213$$
$$x_{35} = -100.191128005419$$
$$x_{36} = -116.578765092276$$
$$x_{37} = -49.9256455479826$$
$$x_{38} = -78.879653249199$$
$$x_{39} = 97.0495353518295$$
$$x_{40} = 6.62302221663371$$
$$x_{41} = 9.08494105131526$$
$$x_{42} = 38.0389487525316$$
$$x_{43} = -66.3132826348398$$
$$x_{44} = -37.3592749336234$$
$$x_{45} = 34.2176822800336$$
$$x_{46} = 12.9062075238133$$
$$x_{47} = -3.48142956304392$$
$$x_{48} = -75.0583867767009$$
$$x_{49} = -85.1628385563785$$
$$x_{50} = -22.3309854845827$$
$$x_{51} = 2.80175574413567$$
$$x_{52} = -97.7292091707377$$
$$x_{53} = 951.562737128253$$
$$x_{54} = -81.3415720838805$$
$$x_{55} = 25.4725781381725$$
$$x_{56} = -28.6141707917623$$
$$x_{57} = -31.0760896264438$$
$$x_{58} = -93.9079426982397$$
$$x_{59} = 50.6053193668908$$
$$x_{60} = 15.3681263584948$$
$$x_{61} = -91.4460238635581$$
$$x_{62} = 0.339836909454122$$
$$x_{63} = 71.9167941231111$$
$$x_{64} = 88.3044312099683$$
$$x_{65} = 31.7557634453521$$
$$x_{66} = 82.0212459027887$$
$$x_{67} = 56.8885046740704$$
$$x_{68} = -16.0478001774031$$
$$x_{69} = -62.4920161623417$$
$$x_{1} = 94.5876165171479$$
$$x_{2} = 21.6513116656744$$
$$x_{3} = 44.3221340597112$$
$$x_{4} = -56.2088308551622$$
$$x_{5} = -5.94334839772546$$
$$x_{6} = 172.447759037984$$
$$x_{7} = 78.1999794302907$$
$$x_{8} = 100.870801824328$$
$$x_{9} = -43.642460240803$$
$$x_{10} = 69.4548752884296$$
$$x_{11} = -24.7929043192642$$
$$x_{12} = 63.17168998125$$
$$x_{13} = 19.1893928309929$$
$$x_{14} = 53.0672382015724$$
$$x_{15} = 84.4831647374703$$
$$x_{16} = -18.5097190120846$$
$$x_{17} = -53.7469120204806$$
$$x_{18} = -9.7646148702235$$
$$x_{19} = 90.7663500446499$$
$$x_{20} = -112585.595763607$$
$$x_{21} = 75.7380605956092$$
$$x_{22} = 65.6336088159315$$
$$x_{23} = 27.934496972854$$
$$x_{24} = -34.8973560989418$$
$$x_{25} = -12.2265337049051$$
$$x_{26} = -60.0300973276602$$
$$x_{27} = 46.7840528943928$$
$$x_{28} = 59.350423508752$$
$$x_{29} = 40.5008675872132$$
$$x_{30} = -41.1805414061214$$
$$x_{31} = -87.6247573910601$$
$$x_{32} = -47.463726713301$$
$$x_{33} = -72.5964679420194$$
$$x_{34} = -68.7752014695213$$
$$x_{35} = -100.191128005419$$
$$x_{36} = -116.578765092276$$
$$x_{37} = -49.9256455479826$$
$$x_{38} = -78.879653249199$$
$$x_{39} = 97.0495353518295$$
$$x_{40} = 6.62302221663371$$
$$x_{41} = 9.08494105131526$$
$$x_{42} = 38.0389487525316$$
$$x_{43} = -66.3132826348398$$
$$x_{44} = -37.3592749336234$$
$$x_{45} = 34.2176822800336$$
$$x_{46} = 12.9062075238133$$
$$x_{47} = -3.48142956304392$$
$$x_{48} = -75.0583867767009$$
$$x_{49} = -85.1628385563785$$
$$x_{50} = -22.3309854845827$$
$$x_{51} = 2.80175574413567$$
$$x_{52} = -97.7292091707377$$
$$x_{53} = 951.562737128253$$
$$x_{54} = -81.3415720838805$$
$$x_{55} = 25.4725781381725$$
$$x_{56} = -28.6141707917623$$
$$x_{57} = -31.0760896264438$$
$$x_{58} = -93.9079426982397$$
$$x_{59} = 50.6053193668908$$
$$x_{60} = 15.3681263584948$$
$$x_{61} = -91.4460238635581$$
$$x_{62} = 0.339836909454122$$
$$x_{63} = 71.9167941231111$$
$$x_{64} = 88.3044312099683$$
$$x_{65} = 31.7557634453521$$
$$x_{66} = 82.0212459027887$$
$$x_{67} = 56.8885046740704$$
$$x_{68} = -16.0478001774031$$
$$x_{69} = -62.4920161623417$$
This roots
$$x_{20} = -112585.595763607$$
$$x_{36} = -116.578765092276$$
$$x_{35} = -100.191128005419$$
$$x_{52} = -97.7292091707377$$
$$x_{58} = -93.9079426982397$$
$$x_{61} = -91.4460238635581$$
$$x_{31} = -87.6247573910601$$
$$x_{49} = -85.1628385563785$$
$$x_{54} = -81.3415720838805$$
$$x_{38} = -78.879653249199$$
$$x_{48} = -75.0583867767009$$
$$x_{33} = -72.5964679420194$$
$$x_{34} = -68.7752014695213$$
$$x_{43} = -66.3132826348398$$
$$x_{69} = -62.4920161623417$$
$$x_{26} = -60.0300973276602$$
$$x_{4} = -56.2088308551622$$
$$x_{17} = -53.7469120204806$$
$$x_{37} = -49.9256455479826$$
$$x_{32} = -47.463726713301$$
$$x_{9} = -43.642460240803$$
$$x_{30} = -41.1805414061214$$
$$x_{44} = -37.3592749336234$$
$$x_{24} = -34.8973560989418$$
$$x_{57} = -31.0760896264438$$
$$x_{56} = -28.6141707917623$$
$$x_{11} = -24.7929043192642$$
$$x_{50} = -22.3309854845827$$
$$x_{16} = -18.5097190120846$$
$$x_{68} = -16.0478001774031$$
$$x_{25} = -12.2265337049051$$
$$x_{18} = -9.7646148702235$$
$$x_{5} = -5.94334839772546$$
$$x_{47} = -3.48142956304392$$
$$x_{62} = 0.339836909454122$$
$$x_{51} = 2.80175574413567$$
$$x_{40} = 6.62302221663371$$
$$x_{41} = 9.08494105131526$$
$$x_{46} = 12.9062075238133$$
$$x_{60} = 15.3681263584948$$
$$x_{13} = 19.1893928309929$$
$$x_{2} = 21.6513116656744$$
$$x_{55} = 25.4725781381725$$
$$x_{23} = 27.934496972854$$
$$x_{65} = 31.7557634453521$$
$$x_{45} = 34.2176822800336$$
$$x_{42} = 38.0389487525316$$
$$x_{29} = 40.5008675872132$$
$$x_{3} = 44.3221340597112$$
$$x_{27} = 46.7840528943928$$
$$x_{59} = 50.6053193668908$$
$$x_{14} = 53.0672382015724$$
$$x_{67} = 56.8885046740704$$
$$x_{28} = 59.350423508752$$
$$x_{12} = 63.17168998125$$
$$x_{22} = 65.6336088159315$$
$$x_{10} = 69.4548752884296$$
$$x_{63} = 71.9167941231111$$
$$x_{21} = 75.7380605956092$$
$$x_{7} = 78.1999794302907$$
$$x_{66} = 82.0212459027887$$
$$x_{15} = 84.4831647374703$$
$$x_{64} = 88.3044312099683$$
$$x_{19} = 90.7663500446499$$
$$x_{1} = 94.5876165171479$$
$$x_{39} = 97.0495353518295$$
$$x_{8} = 100.870801824328$$
$$x_{6} = 172.447759037984$$
$$x_{53} = 951.562737128253$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{20}$$
For example, let's take the point
$$x_{0} = x_{20} - \frac{1}{10}$$
=
$$-112585.595763607 + - \frac{1}{10}$$
=
$$-112585.695763607$$
substitute to the expression
$$\sin{\left(t \right)} < \frac{1}{3}$$
$$\sin{\left(t \right)} < \frac{1}{3}$$
Then
$$x < -112585.595763607$$
no execute
one of the solutions of our inequality is:
$$x > -112585.595763607 \wedge x < -116.578765092276$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -112585.595763607 \wedge x < -116.578765092276$$
$$x > -100.191128005419 \wedge x < -97.7292091707377$$
$$x > -93.9079426982397 \wedge x < -91.4460238635581$$
$$x > -87.6247573910601 \wedge x < -85.1628385563785$$
$$x > -81.3415720838805 \wedge x < -78.879653249199$$
$$x > -75.0583867767009 \wedge x < -72.5964679420194$$
$$x > -68.7752014695213 \wedge x < -66.3132826348398$$
$$x > -62.4920161623417 \wedge x < -60.0300973276602$$
$$x > -56.2088308551622 \wedge x < -53.7469120204806$$
$$x > -49.9256455479826 \wedge x < -47.463726713301$$
$$x > -43.642460240803 \wedge x < -41.1805414061214$$
$$x > -37.3592749336234 \wedge x < -34.8973560989418$$
$$x > -31.0760896264438 \wedge x < -28.6141707917623$$
$$x > -24.7929043192642 \wedge x < -22.3309854845827$$
$$x > -18.5097190120846 \wedge x < -16.0478001774031$$
$$x > -12.2265337049051 \wedge x < -9.7646148702235$$
$$x > -5.94334839772546 \wedge x < -3.48142956304392$$
$$x > 0.339836909454122 \wedge x < 2.80175574413567$$
$$x > 6.62302221663371 \wedge x < 9.08494105131526$$
$$x > 12.9062075238133 \wedge x < 15.3681263584948$$
$$x > 19.1893928309929 \wedge x < 21.6513116656744$$
$$x > 25.4725781381725 \wedge x < 27.934496972854$$
$$x > 31.7557634453521 \wedge x < 34.2176822800336$$
$$x > 38.0389487525316 \wedge x < 40.5008675872132$$
$$x > 44.3221340597112 \wedge x < 46.7840528943928$$
$$x > 50.6053193668908 \wedge x < 53.0672382015724$$
$$x > 56.8885046740704 \wedge x < 59.350423508752$$
$$x > 63.17168998125 \wedge x < 65.6336088159315$$
$$x > 69.4548752884296 \wedge x < 71.9167941231111$$
$$x > 75.7380605956092 \wedge x < 78.1999794302907$$
$$x > 82.0212459027887 \wedge x < 84.4831647374703$$
$$x > 88.3044312099683 \wedge x < 90.7663500446499$$
$$x > 94.5876165171479 \wedge x < 97.0495353518295$$
$$x > 100.870801824328 \wedge x < 172.447759037984$$
$$x > 951.562737128253$$
$$\sin{\left(t \right)} < \frac{1}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(t \right)} = \frac{1}{3}$$
Solve:
Given the equation
$$\sin{\left(t \right)} = \frac{1}{3}$$
transform
$$\sin{\left(t \right)} - \frac{1}{3} = 0$$
$$\sin{\left(t \right)} - \frac{1}{3} = 0$$
Do replacement
$$w = \sin{\left(t \right)}$$
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
$$\sin{\left(t \right)} = w$$
substitute w:
$$x_{1} = 94.5876165171479$$
$$x_{2} = 21.6513116656744$$
$$x_{3} = 44.3221340597112$$
$$x_{4} = -56.2088308551622$$
$$x_{5} = -5.94334839772546$$
$$x_{6} = 172.447759037984$$
$$x_{7} = 78.1999794302907$$
$$x_{8} = 100.870801824328$$
$$x_{9} = -43.642460240803$$
$$x_{10} = 69.4548752884296$$
$$x_{11} = -24.7929043192642$$
$$x_{12} = 63.17168998125$$
$$x_{13} = 19.1893928309929$$
$$x_{14} = 53.0672382015724$$
$$x_{15} = 84.4831647374703$$
$$x_{16} = -18.5097190120846$$
$$x_{17} = -53.7469120204806$$
$$x_{18} = -9.7646148702235$$
$$x_{19} = 90.7663500446499$$
$$x_{20} = -112585.595763607$$
$$x_{21} = 75.7380605956092$$
$$x_{22} = 65.6336088159315$$
$$x_{23} = 27.934496972854$$
$$x_{24} = -34.8973560989418$$
$$x_{25} = -12.2265337049051$$
$$x_{26} = -60.0300973276602$$
$$x_{27} = 46.7840528943928$$
$$x_{28} = 59.350423508752$$
$$x_{29} = 40.5008675872132$$
$$x_{30} = -41.1805414061214$$
$$x_{31} = -87.6247573910601$$
$$x_{32} = -47.463726713301$$
$$x_{33} = -72.5964679420194$$
$$x_{34} = -68.7752014695213$$
$$x_{35} = -100.191128005419$$
$$x_{36} = -116.578765092276$$
$$x_{37} = -49.9256455479826$$
$$x_{38} = -78.879653249199$$
$$x_{39} = 97.0495353518295$$
$$x_{40} = 6.62302221663371$$
$$x_{41} = 9.08494105131526$$
$$x_{42} = 38.0389487525316$$
$$x_{43} = -66.3132826348398$$
$$x_{44} = -37.3592749336234$$
$$x_{45} = 34.2176822800336$$
$$x_{46} = 12.9062075238133$$
$$x_{47} = -3.48142956304392$$
$$x_{48} = -75.0583867767009$$
$$x_{49} = -85.1628385563785$$
$$x_{50} = -22.3309854845827$$
$$x_{51} = 2.80175574413567$$
$$x_{52} = -97.7292091707377$$
$$x_{53} = 951.562737128253$$
$$x_{54} = -81.3415720838805$$
$$x_{55} = 25.4725781381725$$
$$x_{56} = -28.6141707917623$$
$$x_{57} = -31.0760896264438$$
$$x_{58} = -93.9079426982397$$
$$x_{59} = 50.6053193668908$$
$$x_{60} = 15.3681263584948$$
$$x_{61} = -91.4460238635581$$
$$x_{62} = 0.339836909454122$$
$$x_{63} = 71.9167941231111$$
$$x_{64} = 88.3044312099683$$
$$x_{65} = 31.7557634453521$$
$$x_{66} = 82.0212459027887$$
$$x_{67} = 56.8885046740704$$
$$x_{68} = -16.0478001774031$$
$$x_{69} = -62.4920161623417$$
$$x_{1} = 94.5876165171479$$
$$x_{2} = 21.6513116656744$$
$$x_{3} = 44.3221340597112$$
$$x_{4} = -56.2088308551622$$
$$x_{5} = -5.94334839772546$$
$$x_{6} = 172.447759037984$$
$$x_{7} = 78.1999794302907$$
$$x_{8} = 100.870801824328$$
$$x_{9} = -43.642460240803$$
$$x_{10} = 69.4548752884296$$
$$x_{11} = -24.7929043192642$$
$$x_{12} = 63.17168998125$$
$$x_{13} = 19.1893928309929$$
$$x_{14} = 53.0672382015724$$
$$x_{15} = 84.4831647374703$$
$$x_{16} = -18.5097190120846$$
$$x_{17} = -53.7469120204806$$
$$x_{18} = -9.7646148702235$$
$$x_{19} = 90.7663500446499$$
$$x_{20} = -112585.595763607$$
$$x_{21} = 75.7380605956092$$
$$x_{22} = 65.6336088159315$$
$$x_{23} = 27.934496972854$$
$$x_{24} = -34.8973560989418$$
$$x_{25} = -12.2265337049051$$
$$x_{26} = -60.0300973276602$$
$$x_{27} = 46.7840528943928$$
$$x_{28} = 59.350423508752$$
$$x_{29} = 40.5008675872132$$
$$x_{30} = -41.1805414061214$$
$$x_{31} = -87.6247573910601$$
$$x_{32} = -47.463726713301$$
$$x_{33} = -72.5964679420194$$
$$x_{34} = -68.7752014695213$$
$$x_{35} = -100.191128005419$$
$$x_{36} = -116.578765092276$$
$$x_{37} = -49.9256455479826$$
$$x_{38} = -78.879653249199$$
$$x_{39} = 97.0495353518295$$
$$x_{40} = 6.62302221663371$$
$$x_{41} = 9.08494105131526$$
$$x_{42} = 38.0389487525316$$
$$x_{43} = -66.3132826348398$$
$$x_{44} = -37.3592749336234$$
$$x_{45} = 34.2176822800336$$
$$x_{46} = 12.9062075238133$$
$$x_{47} = -3.48142956304392$$
$$x_{48} = -75.0583867767009$$
$$x_{49} = -85.1628385563785$$
$$x_{50} = -22.3309854845827$$
$$x_{51} = 2.80175574413567$$
$$x_{52} = -97.7292091707377$$
$$x_{53} = 951.562737128253$$
$$x_{54} = -81.3415720838805$$
$$x_{55} = 25.4725781381725$$
$$x_{56} = -28.6141707917623$$
$$x_{57} = -31.0760896264438$$
$$x_{58} = -93.9079426982397$$
$$x_{59} = 50.6053193668908$$
$$x_{60} = 15.3681263584948$$
$$x_{61} = -91.4460238635581$$
$$x_{62} = 0.339836909454122$$
$$x_{63} = 71.9167941231111$$
$$x_{64} = 88.3044312099683$$
$$x_{65} = 31.7557634453521$$
$$x_{66} = 82.0212459027887$$
$$x_{67} = 56.8885046740704$$
$$x_{68} = -16.0478001774031$$
$$x_{69} = -62.4920161623417$$
This roots
$$x_{20} = -112585.595763607$$
$$x_{36} = -116.578765092276$$
$$x_{35} = -100.191128005419$$
$$x_{52} = -97.7292091707377$$
$$x_{58} = -93.9079426982397$$
$$x_{61} = -91.4460238635581$$
$$x_{31} = -87.6247573910601$$
$$x_{49} = -85.1628385563785$$
$$x_{54} = -81.3415720838805$$
$$x_{38} = -78.879653249199$$
$$x_{48} = -75.0583867767009$$
$$x_{33} = -72.5964679420194$$
$$x_{34} = -68.7752014695213$$
$$x_{43} = -66.3132826348398$$
$$x_{69} = -62.4920161623417$$
$$x_{26} = -60.0300973276602$$
$$x_{4} = -56.2088308551622$$
$$x_{17} = -53.7469120204806$$
$$x_{37} = -49.9256455479826$$
$$x_{32} = -47.463726713301$$
$$x_{9} = -43.642460240803$$
$$x_{30} = -41.1805414061214$$
$$x_{44} = -37.3592749336234$$
$$x_{24} = -34.8973560989418$$
$$x_{57} = -31.0760896264438$$
$$x_{56} = -28.6141707917623$$
$$x_{11} = -24.7929043192642$$
$$x_{50} = -22.3309854845827$$
$$x_{16} = -18.5097190120846$$
$$x_{68} = -16.0478001774031$$
$$x_{25} = -12.2265337049051$$
$$x_{18} = -9.7646148702235$$
$$x_{5} = -5.94334839772546$$
$$x_{47} = -3.48142956304392$$
$$x_{62} = 0.339836909454122$$
$$x_{51} = 2.80175574413567$$
$$x_{40} = 6.62302221663371$$
$$x_{41} = 9.08494105131526$$
$$x_{46} = 12.9062075238133$$
$$x_{60} = 15.3681263584948$$
$$x_{13} = 19.1893928309929$$
$$x_{2} = 21.6513116656744$$
$$x_{55} = 25.4725781381725$$
$$x_{23} = 27.934496972854$$
$$x_{65} = 31.7557634453521$$
$$x_{45} = 34.2176822800336$$
$$x_{42} = 38.0389487525316$$
$$x_{29} = 40.5008675872132$$
$$x_{3} = 44.3221340597112$$
$$x_{27} = 46.7840528943928$$
$$x_{59} = 50.6053193668908$$
$$x_{14} = 53.0672382015724$$
$$x_{67} = 56.8885046740704$$
$$x_{28} = 59.350423508752$$
$$x_{12} = 63.17168998125$$
$$x_{22} = 65.6336088159315$$
$$x_{10} = 69.4548752884296$$
$$x_{63} = 71.9167941231111$$
$$x_{21} = 75.7380605956092$$
$$x_{7} = 78.1999794302907$$
$$x_{66} = 82.0212459027887$$
$$x_{15} = 84.4831647374703$$
$$x_{64} = 88.3044312099683$$
$$x_{19} = 90.7663500446499$$
$$x_{1} = 94.5876165171479$$
$$x_{39} = 97.0495353518295$$
$$x_{8} = 100.870801824328$$
$$x_{6} = 172.447759037984$$
$$x_{53} = 951.562737128253$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{20}$$
For example, let's take the point
$$x_{0} = x_{20} - \frac{1}{10}$$
=
$$-112585.595763607 + - \frac{1}{10}$$
=
$$-112585.695763607$$
substitute to the expression
$$\sin{\left(t \right)} < \frac{1}{3}$$
$$\sin{\left(t \right)} < \frac{1}{3}$$
sin(t) < 1/3
Then
$$x < -112585.595763607$$
no execute
one of the solutions of our inequality is:
$$x > -112585.595763607 \wedge x < -116.578765092276$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------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-------
x20 x36 x35 x52 x58 x61 x31 x49 x54 x38 x48 x33 x34 x43 x69 x26 x4 x17 x37 x32 x9 x30 x44 x24 x57 x56 x11 x50 x16 x68 x25 x18 x5 x47 x62 x51 x40 x41 x46 x60 x13 x2 x55 x23 x65 x45 x42 x29 x3 x27 x59 x14 x67 x28 x12 x22 x10 x63 x21 x7 x66 x15 x64 x19 x1 x39 x8 x6 x53Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -112585.595763607 \wedge x < -116.578765092276$$
$$x > -100.191128005419 \wedge x < -97.7292091707377$$
$$x > -93.9079426982397 \wedge x < -91.4460238635581$$
$$x > -87.6247573910601 \wedge x < -85.1628385563785$$
$$x > -81.3415720838805 \wedge x < -78.879653249199$$
$$x > -75.0583867767009 \wedge x < -72.5964679420194$$
$$x > -68.7752014695213 \wedge x < -66.3132826348398$$
$$x > -62.4920161623417 \wedge x < -60.0300973276602$$
$$x > -56.2088308551622 \wedge x < -53.7469120204806$$
$$x > -49.9256455479826 \wedge x < -47.463726713301$$
$$x > -43.642460240803 \wedge x < -41.1805414061214$$
$$x > -37.3592749336234 \wedge x < -34.8973560989418$$
$$x > -31.0760896264438 \wedge x < -28.6141707917623$$
$$x > -24.7929043192642 \wedge x < -22.3309854845827$$
$$x > -18.5097190120846 \wedge x < -16.0478001774031$$
$$x > -12.2265337049051 \wedge x < -9.7646148702235$$
$$x > -5.94334839772546 \wedge x < -3.48142956304392$$
$$x > 0.339836909454122 \wedge x < 2.80175574413567$$
$$x > 6.62302221663371 \wedge x < 9.08494105131526$$
$$x > 12.9062075238133 \wedge x < 15.3681263584948$$
$$x > 19.1893928309929 \wedge x < 21.6513116656744$$
$$x > 25.4725781381725 \wedge x < 27.934496972854$$
$$x > 31.7557634453521 \wedge x < 34.2176822800336$$
$$x > 38.0389487525316 \wedge x < 40.5008675872132$$
$$x > 44.3221340597112 \wedge x < 46.7840528943928$$
$$x > 50.6053193668908 \wedge x < 53.0672382015724$$
$$x > 56.8885046740704 \wedge x < 59.350423508752$$
$$x > 63.17168998125 \wedge x < 65.6336088159315$$
$$x > 69.4548752884296 \wedge x < 71.9167941231111$$
$$x > 75.7380605956092 \wedge x < 78.1999794302907$$
$$x > 82.0212459027887 \wedge x < 84.4831647374703$$
$$x > 88.3044312099683 \wedge x < 90.7663500446499$$
$$x > 94.5876165171479 \wedge x < 97.0495353518295$$
$$x > 100.870801824328 \wedge x < 172.447759037984$$
$$x > 951.562737128253$$
Rapid solution
[src]
/ / / ___\\ / / ___\ \\ | | |\/ 2 || | |\/ 2 | || Or|And|0 <= t, t < atan|-----||, And|t <= 2*pi, pi - atan|-----| < t|| \ \ \ 4 // \ \ 4 / //
$$\left(0 \leq t \wedge t < \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right) \vee \left(t \leq 2 \pi \wedge \pi - \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)} < t\right)$$
((0 <= t)∧(t < atan(sqrt(2)/4)))∨((t <= 2*pi)∧(pi - atan(sqrt(2)/4) < t))
Rapid solution 2
[src]
/ ___\ / ___\
|\/ 2 | |\/ 2 |
[0, atan|-----|) U (pi - atan|-----|, 2*pi]
\ 4 / \ 4 /
$$x\ in\ \left[0, \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right) \cup \left(\pi - \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}, 2 \pi\right]$$
x in Union(Interval.Ropen(0, atan(sqrt(2)/4)), Interval.Lopen(pi - atan(sqrt(2)/4), 2*pi))