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+9p^2+2x+6y+2>=0
- 3x+1/5-1-2x/2>x
- (x-2)/(x-7)>0
- (x+40)/((x^3-16*x)*((x-4)/(3*x^2+11*x-4)-16/(16-x^2)))≤0
- Derivative of:
-
sin(t)
- Limit of the function:
-
sin(t)
- Integral of d{x}:
-
sin(t)
-
Identical expressions
- sin(t)< one
- sinus of (t) less than 1
- sinus of (t) less than one
- sint<1
-
Similar expressions
- sint>=-1/2
- sint<1\3
sin(t)<1 inequation
The solution
Detail solution
Given the inequality:
$$\sin{\left(t \right)} < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(t \right)} = 1$$
Solve:
Given the equation
$$\sin{\left(t \right)} = 1$$
transform
$$\sin{\left(t \right)} - 1 = 0$$
$$\sin{\left(t \right)} - 1 = 0$$
Do replacement
$$w = \sin{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = 1$$
We get the answer: w = 1
do backward replacement
$$\sin{\left(t \right)} = w$$
substitute w:
$$x_{1} = 39.2699077336963$$
$$x_{2} = -77664.8827844698$$
$$x_{3} = 70.6858358251975$$
$$x_{4} = -98.9601681513438$$
$$x_{5} = -42.4115005850814$$
$$x_{6} = -92.6769837307794$$
$$x_{7} = 51.8362788867584$$
$$x_{8} = 39.2699085343272$$
$$x_{9} = 70.6858344802043$$
$$x_{10} = -42.4115013226904$$
$$x_{11} = -86.3937988139119$$
$$x_{12} = -23.5619450115115$$
$$x_{13} = 14.1371671100222$$
$$x_{14} = 58.1194636580315$$
$$x_{15} = -4.71238862219396$$
$$x_{16} = -61.2610562447228$$
$$x_{17} = -23.5619449492902$$
$$x_{18} = 76.9690196732095$$
$$x_{19} = 26.7035387715281$$
$$x_{20} = 1.57079582971902$$
$$x_{21} = 95.8185760629547$$
$$x_{22} = -67.5442420547782$$
$$x_{23} = -17.2787583315643$$
$$x_{24} = 95.8185764110282$$
$$x_{25} = -29.8451297624452$$
$$x_{26} = 51.8362789031518$$
$$x_{27} = 76.9690204681432$$
$$x_{28} = -42.4115017818136$$
$$x_{29} = -17.2787590920677$$
$$x_{30} = -48.6946865760795$$
$$x_{31} = -67.5442421706656$$
$$x_{32} = -54.9778709962906$$
$$x_{33} = -73.8274269047688$$
$$x_{34} = 83.2522056907544$$
$$x_{35} = 32.9867233134552$$
$$x_{36} = -36.1283160197768$$
$$x_{37} = 70.6858352127237$$
$$x_{38} = -17.2787598356363$$
$$x_{39} = 45.553093730794$$
$$x_{40} = -92.6769829355125$$
$$x_{41} = 45.5530922954328$$
$$x_{42} = 1.57079769954017$$
$$x_{43} = 64.4026493072124$$
$$x_{44} = -36.1283153448593$$
$$x_{45} = 20.420352160156$$
$$x_{46} = -61.2610555612794$$
$$x_{47} = -10.9955746401247$$
$$x_{48} = 3017.49974516717$$
$$x_{49} = 20.4203527610188$$
$$x_{50} = -48.6946857788076$$
$$x_{51} = -86.3937984749131$$
$$x_{52} = -36.1283154173375$$
$$x_{53} = 26.7035380604159$$
$$x_{54} = 51.8362782775539$$
$$x_{55} = 1.57079525114023$$
$$x_{56} = 89.535390888605$$
$$x_{57} = 58.119464520069$$
$$x_{58} = 45.5530929823099$$
$$x_{59} = 95.8185754266891$$
$$x_{60} = 7.85398177249874$$
$$x_{61} = -54.9778717966574$$
$$x_{62} = -4.71238942125338$$
$$x_{63} = 7.85398174307326$$
$$x_{64} = 14.1371673791846$$
$$x_{65} = 1.57079657289894$$
$$x_{66} = -67.5442415371049$$
$$x_{67} = -29.8451306226524$$
$$x_{68} = -29.8451300954883$$
$$x_{69} = 20.4203521477756$$
$$x_{70} = 89.5353901350773$$
$$x_{71} = 58.1194643979608$$
$$x_{72} = 95.8185759975842$$
$$x_{73} = 83.252204888767$$
$$x_{74} = -10.9955738413568$$
$$x_{75} = 26.703537322248$$
$$x_{76} = 14.1371665172699$$
$$x_{77} = 32.9867225164981$$
$$x_{78} = 89.5353893728458$$
$$x_{79} = -86.3937977431483$$
$$x_{80} = -80.1106125781572$$
$$x_{81} = -73.8274277616689$$
$$x_{82} = -98.9601689530982$$
$$x_{83} = -23.5619443878998$$
$$x_{84} = 102.101760799573$$
$$x_{85} = 7.85398112872719$$
$$x_{86} = -61.2610569934486$$
$$x_{87} = 64.4026499096387$$
$$x_{88} = -73.8274272798455$$
$$x_{89} = -80.1106124650157$$
$$x_{90} = -80.1106131679426$$
$$x_{91} = 64.4026492731727$$
$$x_{1} = 39.2699077336963$$
$$x_{2} = -77664.8827844698$$
$$x_{3} = 70.6858358251975$$
$$x_{4} = -98.9601681513438$$
$$x_{5} = -42.4115005850814$$
$$x_{6} = -92.6769837307794$$
$$x_{7} = 51.8362788867584$$
$$x_{8} = 39.2699085343272$$
$$x_{9} = 70.6858344802043$$
$$x_{10} = -42.4115013226904$$
$$x_{11} = -86.3937988139119$$
$$x_{12} = -23.5619450115115$$
$$x_{13} = 14.1371671100222$$
$$x_{14} = 58.1194636580315$$
$$x_{15} = -4.71238862219396$$
$$x_{16} = -61.2610562447228$$
$$x_{17} = -23.5619449492902$$
$$x_{18} = 76.9690196732095$$
$$x_{19} = 26.7035387715281$$
$$x_{20} = 1.57079582971902$$
$$x_{21} = 95.8185760629547$$
$$x_{22} = -67.5442420547782$$
$$x_{23} = -17.2787583315643$$
$$x_{24} = 95.8185764110282$$
$$x_{25} = -29.8451297624452$$
$$x_{26} = 51.8362789031518$$
$$x_{27} = 76.9690204681432$$
$$x_{28} = -42.4115017818136$$
$$x_{29} = -17.2787590920677$$
$$x_{30} = -48.6946865760795$$
$$x_{31} = -67.5442421706656$$
$$x_{32} = -54.9778709962906$$
$$x_{33} = -73.8274269047688$$
$$x_{34} = 83.2522056907544$$
$$x_{35} = 32.9867233134552$$
$$x_{36} = -36.1283160197768$$
$$x_{37} = 70.6858352127237$$
$$x_{38} = -17.2787598356363$$
$$x_{39} = 45.553093730794$$
$$x_{40} = -92.6769829355125$$
$$x_{41} = 45.5530922954328$$
$$x_{42} = 1.57079769954017$$
$$x_{43} = 64.4026493072124$$
$$x_{44} = -36.1283153448593$$
$$x_{45} = 20.420352160156$$
$$x_{46} = -61.2610555612794$$
$$x_{47} = -10.9955746401247$$
$$x_{48} = 3017.49974516717$$
$$x_{49} = 20.4203527610188$$
$$x_{50} = -48.6946857788076$$
$$x_{51} = -86.3937984749131$$
$$x_{52} = -36.1283154173375$$
$$x_{53} = 26.7035380604159$$
$$x_{54} = 51.8362782775539$$
$$x_{55} = 1.57079525114023$$
$$x_{56} = 89.535390888605$$
$$x_{57} = 58.119464520069$$
$$x_{58} = 45.5530929823099$$
$$x_{59} = 95.8185754266891$$
$$x_{60} = 7.85398177249874$$
$$x_{61} = -54.9778717966574$$
$$x_{62} = -4.71238942125338$$
$$x_{63} = 7.85398174307326$$
$$x_{64} = 14.1371673791846$$
$$x_{65} = 1.57079657289894$$
$$x_{66} = -67.5442415371049$$
$$x_{67} = -29.8451306226524$$
$$x_{68} = -29.8451300954883$$
$$x_{69} = 20.4203521477756$$
$$x_{70} = 89.5353901350773$$
$$x_{71} = 58.1194643979608$$
$$x_{72} = 95.8185759975842$$
$$x_{73} = 83.252204888767$$
$$x_{74} = -10.9955738413568$$
$$x_{75} = 26.703537322248$$
$$x_{76} = 14.1371665172699$$
$$x_{77} = 32.9867225164981$$
$$x_{78} = 89.5353893728458$$
$$x_{79} = -86.3937977431483$$
$$x_{80} = -80.1106125781572$$
$$x_{81} = -73.8274277616689$$
$$x_{82} = -98.9601689530982$$
$$x_{83} = -23.5619443878998$$
$$x_{84} = 102.101760799573$$
$$x_{85} = 7.85398112872719$$
$$x_{86} = -61.2610569934486$$
$$x_{87} = 64.4026499096387$$
$$x_{88} = -73.8274272798455$$
$$x_{89} = -80.1106124650157$$
$$x_{90} = -80.1106131679426$$
$$x_{91} = 64.4026492731727$$
This roots
$$x_{2} = -77664.8827844698$$
$$x_{82} = -98.9601689530982$$
$$x_{4} = -98.9601681513438$$
$$x_{6} = -92.6769837307794$$
$$x_{40} = -92.6769829355125$$
$$x_{11} = -86.3937988139119$$
$$x_{51} = -86.3937984749131$$
$$x_{79} = -86.3937977431483$$
$$x_{90} = -80.1106131679426$$
$$x_{80} = -80.1106125781572$$
$$x_{89} = -80.1106124650157$$
$$x_{81} = -73.8274277616689$$
$$x_{88} = -73.8274272798455$$
$$x_{33} = -73.8274269047688$$
$$x_{31} = -67.5442421706656$$
$$x_{22} = -67.5442420547782$$
$$x_{66} = -67.5442415371049$$
$$x_{86} = -61.2610569934486$$
$$x_{16} = -61.2610562447228$$
$$x_{46} = -61.2610555612794$$
$$x_{61} = -54.9778717966574$$
$$x_{32} = -54.9778709962906$$
$$x_{30} = -48.6946865760795$$
$$x_{50} = -48.6946857788076$$
$$x_{28} = -42.4115017818136$$
$$x_{10} = -42.4115013226904$$
$$x_{5} = -42.4115005850814$$
$$x_{36} = -36.1283160197768$$
$$x_{52} = -36.1283154173375$$
$$x_{44} = -36.1283153448593$$
$$x_{67} = -29.8451306226524$$
$$x_{68} = -29.8451300954883$$
$$x_{25} = -29.8451297624452$$
$$x_{12} = -23.5619450115115$$
$$x_{17} = -23.5619449492902$$
$$x_{83} = -23.5619443878998$$
$$x_{38} = -17.2787598356363$$
$$x_{29} = -17.2787590920677$$
$$x_{23} = -17.2787583315643$$
$$x_{47} = -10.9955746401247$$
$$x_{74} = -10.9955738413568$$
$$x_{62} = -4.71238942125338$$
$$x_{15} = -4.71238862219396$$
$$x_{55} = 1.57079525114023$$
$$x_{20} = 1.57079582971902$$
$$x_{65} = 1.57079657289894$$
$$x_{42} = 1.57079769954017$$
$$x_{85} = 7.85398112872719$$
$$x_{63} = 7.85398174307326$$
$$x_{60} = 7.85398177249874$$
$$x_{76} = 14.1371665172699$$
$$x_{13} = 14.1371671100222$$
$$x_{64} = 14.1371673791846$$
$$x_{69} = 20.4203521477756$$
$$x_{45} = 20.420352160156$$
$$x_{49} = 20.4203527610188$$
$$x_{75} = 26.703537322248$$
$$x_{53} = 26.7035380604159$$
$$x_{19} = 26.7035387715281$$
$$x_{77} = 32.9867225164981$$
$$x_{35} = 32.9867233134552$$
$$x_{1} = 39.2699077336963$$
$$x_{8} = 39.2699085343272$$
$$x_{41} = 45.5530922954328$$
$$x_{58} = 45.5530929823099$$
$$x_{39} = 45.553093730794$$
$$x_{54} = 51.8362782775539$$
$$x_{7} = 51.8362788867584$$
$$x_{26} = 51.8362789031518$$
$$x_{14} = 58.1194636580315$$
$$x_{71} = 58.1194643979608$$
$$x_{57} = 58.119464520069$$
$$x_{91} = 64.4026492731727$$
$$x_{43} = 64.4026493072124$$
$$x_{87} = 64.4026499096387$$
$$x_{9} = 70.6858344802043$$
$$x_{37} = 70.6858352127237$$
$$x_{3} = 70.6858358251975$$
$$x_{18} = 76.9690196732095$$
$$x_{27} = 76.9690204681432$$
$$x_{73} = 83.252204888767$$
$$x_{34} = 83.2522056907544$$
$$x_{78} = 89.5353893728458$$
$$x_{70} = 89.5353901350773$$
$$x_{56} = 89.535390888605$$
$$x_{59} = 95.8185754266891$$
$$x_{72} = 95.8185759975842$$
$$x_{21} = 95.8185760629547$$
$$x_{24} = 95.8185764110282$$
$$x_{84} = 102.101760799573$$
$$x_{48} = 3017.49974516717$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{2}$$
For example, let's take the point
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$-77664.8827844698 + - \frac{1}{10}$$
=
$$-77664.9827844698$$
substitute to the expression
$$\sin{\left(t \right)} < 1$$
$$\sin{\left(t \right)} < 1$$
Then
$$x < -77664.8827844698$$
no execute
one of the solutions of our inequality is:
$$x > -77664.8827844698 \wedge x < -98.9601689530982$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -77664.8827844698 \wedge x < -98.9601689530982$$
$$x > -98.9601681513438 \wedge x < -92.6769837307794$$
$$x > -92.6769829355125 \wedge x < -86.3937988139119$$
$$x > -86.3937984749131 \wedge x < -86.3937977431483$$
$$x > -80.1106131679426 \wedge x < -80.1106125781572$$
$$x > -80.1106124650157 \wedge x < -73.8274277616689$$
$$x > -73.8274272798455 \wedge x < -73.8274269047688$$
$$x > -67.5442421706656 \wedge x < -67.5442420547782$$
$$x > -67.5442415371049 \wedge x < -61.2610569934486$$
$$x > -61.2610562447228 \wedge x < -61.2610555612794$$
$$x > -54.9778717966574 \wedge x < -54.9778709962906$$
$$x > -48.6946865760795 \wedge x < -48.6946857788076$$
$$x > -42.4115017818136 \wedge x < -42.4115013226904$$
$$x > -42.4115005850814 \wedge x < -36.1283160197768$$
$$x > -36.1283154173375 \wedge x < -36.1283153448593$$
$$x > -29.8451306226524 \wedge x < -29.8451300954883$$
$$x > -29.8451297624452 \wedge x < -23.5619450115115$$
$$x > -23.5619449492902 \wedge x < -23.5619443878998$$
$$x > -17.2787598356363 \wedge x < -17.2787590920677$$
$$x > -17.2787583315643 \wedge x < -10.9955746401247$$
$$x > -10.9955738413568 \wedge x < -4.71238942125338$$
$$x > -4.71238862219396 \wedge x < 1.57079525114023$$
$$x > 1.57079582971902 \wedge x < 1.57079657289894$$
$$x > 1.57079769954017 \wedge x < 7.85398112872719$$
$$x > 7.85398174307326 \wedge x < 7.85398177249874$$
$$x > 14.1371665172699 \wedge x < 14.1371671100222$$
$$x > 14.1371673791846 \wedge x < 20.4203521477756$$
$$x > 20.420352160156 \wedge x < 20.4203527610188$$
$$x > 26.703537322248 \wedge x < 26.7035380604159$$
$$x > 26.7035387715281 \wedge x < 32.9867225164981$$
$$x > 32.9867233134552 \wedge x < 39.2699077336963$$
$$x > 39.2699085343272 \wedge x < 45.5530922954328$$
$$x > 45.5530929823099 \wedge x < 45.553093730794$$
$$x > 51.8362782775539 \wedge x < 51.8362788867584$$
$$x > 51.8362789031518 \wedge x < 58.1194636580315$$
$$x > 58.1194643979608 \wedge x < 58.119464520069$$
$$x > 64.4026492731727 \wedge x < 64.4026493072124$$
$$x > 64.4026499096387 \wedge x < 70.6858344802043$$
$$x > 70.6858352127237 \wedge x < 70.6858358251975$$
$$x > 76.9690196732095 \wedge x < 76.9690204681432$$
$$x > 83.252204888767 \wedge x < 83.2522056907544$$
$$x > 89.5353893728458 \wedge x < 89.5353901350773$$
$$x > 89.535390888605 \wedge x < 95.8185754266891$$
$$x > 95.8185759975842 \wedge x < 95.8185760629547$$
$$x > 95.8185764110282 \wedge x < 102.101760799573$$
$$x > 3017.49974516717$$
$$\sin{\left(t \right)} < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(t \right)} = 1$$
Solve:
Given the equation
$$\sin{\left(t \right)} = 1$$
transform
$$\sin{\left(t \right)} - 1 = 0$$
$$\sin{\left(t \right)} - 1 = 0$$
Do replacement
$$w = \sin{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = 1$$
We get the answer: w = 1
do backward replacement
$$\sin{\left(t \right)} = w$$
substitute w:
$$x_{1} = 39.2699077336963$$
$$x_{2} = -77664.8827844698$$
$$x_{3} = 70.6858358251975$$
$$x_{4} = -98.9601681513438$$
$$x_{5} = -42.4115005850814$$
$$x_{6} = -92.6769837307794$$
$$x_{7} = 51.8362788867584$$
$$x_{8} = 39.2699085343272$$
$$x_{9} = 70.6858344802043$$
$$x_{10} = -42.4115013226904$$
$$x_{11} = -86.3937988139119$$
$$x_{12} = -23.5619450115115$$
$$x_{13} = 14.1371671100222$$
$$x_{14} = 58.1194636580315$$
$$x_{15} = -4.71238862219396$$
$$x_{16} = -61.2610562447228$$
$$x_{17} = -23.5619449492902$$
$$x_{18} = 76.9690196732095$$
$$x_{19} = 26.7035387715281$$
$$x_{20} = 1.57079582971902$$
$$x_{21} = 95.8185760629547$$
$$x_{22} = -67.5442420547782$$
$$x_{23} = -17.2787583315643$$
$$x_{24} = 95.8185764110282$$
$$x_{25} = -29.8451297624452$$
$$x_{26} = 51.8362789031518$$
$$x_{27} = 76.9690204681432$$
$$x_{28} = -42.4115017818136$$
$$x_{29} = -17.2787590920677$$
$$x_{30} = -48.6946865760795$$
$$x_{31} = -67.5442421706656$$
$$x_{32} = -54.9778709962906$$
$$x_{33} = -73.8274269047688$$
$$x_{34} = 83.2522056907544$$
$$x_{35} = 32.9867233134552$$
$$x_{36} = -36.1283160197768$$
$$x_{37} = 70.6858352127237$$
$$x_{38} = -17.2787598356363$$
$$x_{39} = 45.553093730794$$
$$x_{40} = -92.6769829355125$$
$$x_{41} = 45.5530922954328$$
$$x_{42} = 1.57079769954017$$
$$x_{43} = 64.4026493072124$$
$$x_{44} = -36.1283153448593$$
$$x_{45} = 20.420352160156$$
$$x_{46} = -61.2610555612794$$
$$x_{47} = -10.9955746401247$$
$$x_{48} = 3017.49974516717$$
$$x_{49} = 20.4203527610188$$
$$x_{50} = -48.6946857788076$$
$$x_{51} = -86.3937984749131$$
$$x_{52} = -36.1283154173375$$
$$x_{53} = 26.7035380604159$$
$$x_{54} = 51.8362782775539$$
$$x_{55} = 1.57079525114023$$
$$x_{56} = 89.535390888605$$
$$x_{57} = 58.119464520069$$
$$x_{58} = 45.5530929823099$$
$$x_{59} = 95.8185754266891$$
$$x_{60} = 7.85398177249874$$
$$x_{61} = -54.9778717966574$$
$$x_{62} = -4.71238942125338$$
$$x_{63} = 7.85398174307326$$
$$x_{64} = 14.1371673791846$$
$$x_{65} = 1.57079657289894$$
$$x_{66} = -67.5442415371049$$
$$x_{67} = -29.8451306226524$$
$$x_{68} = -29.8451300954883$$
$$x_{69} = 20.4203521477756$$
$$x_{70} = 89.5353901350773$$
$$x_{71} = 58.1194643979608$$
$$x_{72} = 95.8185759975842$$
$$x_{73} = 83.252204888767$$
$$x_{74} = -10.9955738413568$$
$$x_{75} = 26.703537322248$$
$$x_{76} = 14.1371665172699$$
$$x_{77} = 32.9867225164981$$
$$x_{78} = 89.5353893728458$$
$$x_{79} = -86.3937977431483$$
$$x_{80} = -80.1106125781572$$
$$x_{81} = -73.8274277616689$$
$$x_{82} = -98.9601689530982$$
$$x_{83} = -23.5619443878998$$
$$x_{84} = 102.101760799573$$
$$x_{85} = 7.85398112872719$$
$$x_{86} = -61.2610569934486$$
$$x_{87} = 64.4026499096387$$
$$x_{88} = -73.8274272798455$$
$$x_{89} = -80.1106124650157$$
$$x_{90} = -80.1106131679426$$
$$x_{91} = 64.4026492731727$$
$$x_{1} = 39.2699077336963$$
$$x_{2} = -77664.8827844698$$
$$x_{3} = 70.6858358251975$$
$$x_{4} = -98.9601681513438$$
$$x_{5} = -42.4115005850814$$
$$x_{6} = -92.6769837307794$$
$$x_{7} = 51.8362788867584$$
$$x_{8} = 39.2699085343272$$
$$x_{9} = 70.6858344802043$$
$$x_{10} = -42.4115013226904$$
$$x_{11} = -86.3937988139119$$
$$x_{12} = -23.5619450115115$$
$$x_{13} = 14.1371671100222$$
$$x_{14} = 58.1194636580315$$
$$x_{15} = -4.71238862219396$$
$$x_{16} = -61.2610562447228$$
$$x_{17} = -23.5619449492902$$
$$x_{18} = 76.9690196732095$$
$$x_{19} = 26.7035387715281$$
$$x_{20} = 1.57079582971902$$
$$x_{21} = 95.8185760629547$$
$$x_{22} = -67.5442420547782$$
$$x_{23} = -17.2787583315643$$
$$x_{24} = 95.8185764110282$$
$$x_{25} = -29.8451297624452$$
$$x_{26} = 51.8362789031518$$
$$x_{27} = 76.9690204681432$$
$$x_{28} = -42.4115017818136$$
$$x_{29} = -17.2787590920677$$
$$x_{30} = -48.6946865760795$$
$$x_{31} = -67.5442421706656$$
$$x_{32} = -54.9778709962906$$
$$x_{33} = -73.8274269047688$$
$$x_{34} = 83.2522056907544$$
$$x_{35} = 32.9867233134552$$
$$x_{36} = -36.1283160197768$$
$$x_{37} = 70.6858352127237$$
$$x_{38} = -17.2787598356363$$
$$x_{39} = 45.553093730794$$
$$x_{40} = -92.6769829355125$$
$$x_{41} = 45.5530922954328$$
$$x_{42} = 1.57079769954017$$
$$x_{43} = 64.4026493072124$$
$$x_{44} = -36.1283153448593$$
$$x_{45} = 20.420352160156$$
$$x_{46} = -61.2610555612794$$
$$x_{47} = -10.9955746401247$$
$$x_{48} = 3017.49974516717$$
$$x_{49} = 20.4203527610188$$
$$x_{50} = -48.6946857788076$$
$$x_{51} = -86.3937984749131$$
$$x_{52} = -36.1283154173375$$
$$x_{53} = 26.7035380604159$$
$$x_{54} = 51.8362782775539$$
$$x_{55} = 1.57079525114023$$
$$x_{56} = 89.535390888605$$
$$x_{57} = 58.119464520069$$
$$x_{58} = 45.5530929823099$$
$$x_{59} = 95.8185754266891$$
$$x_{60} = 7.85398177249874$$
$$x_{61} = -54.9778717966574$$
$$x_{62} = -4.71238942125338$$
$$x_{63} = 7.85398174307326$$
$$x_{64} = 14.1371673791846$$
$$x_{65} = 1.57079657289894$$
$$x_{66} = -67.5442415371049$$
$$x_{67} = -29.8451306226524$$
$$x_{68} = -29.8451300954883$$
$$x_{69} = 20.4203521477756$$
$$x_{70} = 89.5353901350773$$
$$x_{71} = 58.1194643979608$$
$$x_{72} = 95.8185759975842$$
$$x_{73} = 83.252204888767$$
$$x_{74} = -10.9955738413568$$
$$x_{75} = 26.703537322248$$
$$x_{76} = 14.1371665172699$$
$$x_{77} = 32.9867225164981$$
$$x_{78} = 89.5353893728458$$
$$x_{79} = -86.3937977431483$$
$$x_{80} = -80.1106125781572$$
$$x_{81} = -73.8274277616689$$
$$x_{82} = -98.9601689530982$$
$$x_{83} = -23.5619443878998$$
$$x_{84} = 102.101760799573$$
$$x_{85} = 7.85398112872719$$
$$x_{86} = -61.2610569934486$$
$$x_{87} = 64.4026499096387$$
$$x_{88} = -73.8274272798455$$
$$x_{89} = -80.1106124650157$$
$$x_{90} = -80.1106131679426$$
$$x_{91} = 64.4026492731727$$
This roots
$$x_{2} = -77664.8827844698$$
$$x_{82} = -98.9601689530982$$
$$x_{4} = -98.9601681513438$$
$$x_{6} = -92.6769837307794$$
$$x_{40} = -92.6769829355125$$
$$x_{11} = -86.3937988139119$$
$$x_{51} = -86.3937984749131$$
$$x_{79} = -86.3937977431483$$
$$x_{90} = -80.1106131679426$$
$$x_{80} = -80.1106125781572$$
$$x_{89} = -80.1106124650157$$
$$x_{81} = -73.8274277616689$$
$$x_{88} = -73.8274272798455$$
$$x_{33} = -73.8274269047688$$
$$x_{31} = -67.5442421706656$$
$$x_{22} = -67.5442420547782$$
$$x_{66} = -67.5442415371049$$
$$x_{86} = -61.2610569934486$$
$$x_{16} = -61.2610562447228$$
$$x_{46} = -61.2610555612794$$
$$x_{61} = -54.9778717966574$$
$$x_{32} = -54.9778709962906$$
$$x_{30} = -48.6946865760795$$
$$x_{50} = -48.6946857788076$$
$$x_{28} = -42.4115017818136$$
$$x_{10} = -42.4115013226904$$
$$x_{5} = -42.4115005850814$$
$$x_{36} = -36.1283160197768$$
$$x_{52} = -36.1283154173375$$
$$x_{44} = -36.1283153448593$$
$$x_{67} = -29.8451306226524$$
$$x_{68} = -29.8451300954883$$
$$x_{25} = -29.8451297624452$$
$$x_{12} = -23.5619450115115$$
$$x_{17} = -23.5619449492902$$
$$x_{83} = -23.5619443878998$$
$$x_{38} = -17.2787598356363$$
$$x_{29} = -17.2787590920677$$
$$x_{23} = -17.2787583315643$$
$$x_{47} = -10.9955746401247$$
$$x_{74} = -10.9955738413568$$
$$x_{62} = -4.71238942125338$$
$$x_{15} = -4.71238862219396$$
$$x_{55} = 1.57079525114023$$
$$x_{20} = 1.57079582971902$$
$$x_{65} = 1.57079657289894$$
$$x_{42} = 1.57079769954017$$
$$x_{85} = 7.85398112872719$$
$$x_{63} = 7.85398174307326$$
$$x_{60} = 7.85398177249874$$
$$x_{76} = 14.1371665172699$$
$$x_{13} = 14.1371671100222$$
$$x_{64} = 14.1371673791846$$
$$x_{69} = 20.4203521477756$$
$$x_{45} = 20.420352160156$$
$$x_{49} = 20.4203527610188$$
$$x_{75} = 26.703537322248$$
$$x_{53} = 26.7035380604159$$
$$x_{19} = 26.7035387715281$$
$$x_{77} = 32.9867225164981$$
$$x_{35} = 32.9867233134552$$
$$x_{1} = 39.2699077336963$$
$$x_{8} = 39.2699085343272$$
$$x_{41} = 45.5530922954328$$
$$x_{58} = 45.5530929823099$$
$$x_{39} = 45.553093730794$$
$$x_{54} = 51.8362782775539$$
$$x_{7} = 51.8362788867584$$
$$x_{26} = 51.8362789031518$$
$$x_{14} = 58.1194636580315$$
$$x_{71} = 58.1194643979608$$
$$x_{57} = 58.119464520069$$
$$x_{91} = 64.4026492731727$$
$$x_{43} = 64.4026493072124$$
$$x_{87} = 64.4026499096387$$
$$x_{9} = 70.6858344802043$$
$$x_{37} = 70.6858352127237$$
$$x_{3} = 70.6858358251975$$
$$x_{18} = 76.9690196732095$$
$$x_{27} = 76.9690204681432$$
$$x_{73} = 83.252204888767$$
$$x_{34} = 83.2522056907544$$
$$x_{78} = 89.5353893728458$$
$$x_{70} = 89.5353901350773$$
$$x_{56} = 89.535390888605$$
$$x_{59} = 95.8185754266891$$
$$x_{72} = 95.8185759975842$$
$$x_{21} = 95.8185760629547$$
$$x_{24} = 95.8185764110282$$
$$x_{84} = 102.101760799573$$
$$x_{48} = 3017.49974516717$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{2}$$
For example, let's take the point
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$-77664.8827844698 + - \frac{1}{10}$$
=
$$-77664.9827844698$$
substitute to the expression
$$\sin{\left(t \right)} < 1$$
$$\sin{\left(t \right)} < 1$$
sin(t) < 1
Then
$$x < -77664.8827844698$$
no execute
one of the solutions of our inequality is:
$$x > -77664.8827844698 \wedge x < -98.9601689530982$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------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-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------
x2 x82 x4 x6 x40 x11 x51 x79 x90 x80 x89 x81 x88 x33 x31 x22 x66 x86 x16 x46 x61 x32 x30 x50 x28 x10 x5 x36 x52 x44 x67 x68 x25 x12 x17 x83 x38 x29 x23 x47 x74 x62 x15 x55 x20 x65 x42 x85 x63 x60 x76 x13 x64 x69 x45 x49 x75 x53 x19 x77 x35 x1 x8 x41 x58 x39 x54 x7 x26 x14 x71 x57 x91 x43 x87 x9 x37 x3 x18 x27 x73 x34 x78 x70 x56 x59 x72 x21 x24 x84 x48Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -77664.8827844698 \wedge x < -98.9601689530982$$
$$x > -98.9601681513438 \wedge x < -92.6769837307794$$
$$x > -92.6769829355125 \wedge x < -86.3937988139119$$
$$x > -86.3937984749131 \wedge x < -86.3937977431483$$
$$x > -80.1106131679426 \wedge x < -80.1106125781572$$
$$x > -80.1106124650157 \wedge x < -73.8274277616689$$
$$x > -73.8274272798455 \wedge x < -73.8274269047688$$
$$x > -67.5442421706656 \wedge x < -67.5442420547782$$
$$x > -67.5442415371049 \wedge x < -61.2610569934486$$
$$x > -61.2610562447228 \wedge x < -61.2610555612794$$
$$x > -54.9778717966574 \wedge x < -54.9778709962906$$
$$x > -48.6946865760795 \wedge x < -48.6946857788076$$
$$x > -42.4115017818136 \wedge x < -42.4115013226904$$
$$x > -42.4115005850814 \wedge x < -36.1283160197768$$
$$x > -36.1283154173375 \wedge x < -36.1283153448593$$
$$x > -29.8451306226524 \wedge x < -29.8451300954883$$
$$x > -29.8451297624452 \wedge x < -23.5619450115115$$
$$x > -23.5619449492902 \wedge x < -23.5619443878998$$
$$x > -17.2787598356363 \wedge x < -17.2787590920677$$
$$x > -17.2787583315643 \wedge x < -10.9955746401247$$
$$x > -10.9955738413568 \wedge x < -4.71238942125338$$
$$x > -4.71238862219396 \wedge x < 1.57079525114023$$
$$x > 1.57079582971902 \wedge x < 1.57079657289894$$
$$x > 1.57079769954017 \wedge x < 7.85398112872719$$
$$x > 7.85398174307326 \wedge x < 7.85398177249874$$
$$x > 14.1371665172699 \wedge x < 14.1371671100222$$
$$x > 14.1371673791846 \wedge x < 20.4203521477756$$
$$x > 20.420352160156 \wedge x < 20.4203527610188$$
$$x > 26.703537322248 \wedge x < 26.7035380604159$$
$$x > 26.7035387715281 \wedge x < 32.9867225164981$$
$$x > 32.9867233134552 \wedge x < 39.2699077336963$$
$$x > 39.2699085343272 \wedge x < 45.5530922954328$$
$$x > 45.5530929823099 \wedge x < 45.553093730794$$
$$x > 51.8362782775539 \wedge x < 51.8362788867584$$
$$x > 51.8362789031518 \wedge x < 58.1194636580315$$
$$x > 58.1194643979608 \wedge x < 58.119464520069$$
$$x > 64.4026492731727 \wedge x < 64.4026493072124$$
$$x > 64.4026499096387 \wedge x < 70.6858344802043$$
$$x > 70.6858352127237 \wedge x < 70.6858358251975$$
$$x > 76.9690196732095 \wedge x < 76.9690204681432$$
$$x > 83.252204888767 \wedge x < 83.2522056907544$$
$$x > 89.5353893728458 \wedge x < 89.5353901350773$$
$$x > 89.535390888605 \wedge x < 95.8185754266891$$
$$x > 95.8185759975842 \wedge x < 95.8185760629547$$
$$x > 95.8185764110282 \wedge x < 102.101760799573$$
$$x > 3017.49974516717$$
Rapid solution 2
[src]
pi pi
[0, --) U (--, 2*pi]
2 2
$$x\ in\ \left[0, \frac{\pi}{2}\right) \cup \left(\frac{\pi}{2}, 2 \pi\right]$$
x in Union(Interval.Ropen(0, pi/2), Interval.Lopen(pi/2, 2*pi))
Rapid solution
[src]
/ / pi\ / pi \\ Or|And|0 <= t, t < --|, And|t <= 2*pi, -- < t|| \ \ 2 / \ 2 //
$$\left(0 \leq t \wedge t < \frac{\pi}{2}\right) \vee \left(t \leq 2 \pi \wedge \frac{\pi}{2} < t\right)$$
((0 <= t)∧(t < pi/2))∨((t <= 2*pi)∧(pi/2 < t))