Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- 3^(x^2-5x+6)<27
- 2z+5>4z-17
- -x^2+2*x-48>0
- (y-3)(y+4)-(y-5)^2>18
- Graphing y =:
-
abs(cos(x))
- Sum of series:
-
1/2
- Derivative of:
-
1/2
- Integral of d{x}:
-
1/2
-
Identical expressions
- abs(cos(x))< one / two
- abs( co sinus of e of (x)) less than 1 divide by 2
- abs( co sinus of e of (x)) less than one divide by two
- abscosx<1/2
- abs(cos(x))<1 divide by 2
-
Similar expressions
- 2*log(2,(x-1)/(2x+3))+log(2,(2x+3)^2)>=2
- abs(cosx)<1/2
abs(cos(x))<1/2 inequation
The solution
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[src]
|cos(x)| < 1/2
$$\left|{\cos{\left(x \right)}}\right| < \frac{1}{2}$$
Abs(cos(x)) < 1/2
Detail solution
Given the inequality:
$$\left|{\cos{\left(x \right)}}\right| < \frac{1}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{\cos{\left(x \right)}}\right| = \frac{1}{2}$$
Solve:
Given the equation
$$\left|{\cos{\left(x \right)}}\right| = \frac{1}{2}$$
transform
$$\left|{\cos{\left(x \right)}}\right| - \frac{1}{2} = 0$$
$$\left|{\cos{\left(x \right)}}\right| - \frac{1}{2} = 0$$
Do replacement
$$w = \left|{\cos{\left(x \right)}}\right|$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{1}{2}$$
We get the answer: w = 1/2
do backward replacement
$$\left|{\cos{\left(x \right)}}\right| = w$$
substitute w:
$$x_{1} = 85.870199198121$$
$$x_{2} = 74.3510261349584$$
$$x_{3} = -673.348025419412$$
$$x_{4} = -41.8879020478639$$
$$x_{5} = 55.5014702134197$$
$$x_{6} = -68.0678408277789$$
$$x_{7} = -77.4926187885482$$
$$x_{8} = 269.129770657526$$
$$x_{9} = -90.0589894029074$$
$$x_{10} = -71.2094334813686$$
$$x_{11} = -99.4837673636768$$
$$x_{12} = 52.3598775598299$$
$$x_{13} = -42.9350995990605$$
$$x_{14} = -48.1710873550435$$
$$x_{15} = -46.0766922526503$$
$$x_{16} = -2.0943951023932$$
$$x_{17} = -92.1533845053006$$
$$x_{18} = -52.3598775598299$$
$$x_{19} = 70.162235930172$$
$$x_{20} = 4.18879020478639$$
$$x_{21} = -74.3510261349584$$
$$x_{22} = 41.8879020478639$$
$$x_{23} = -70.162235930172$$
$$x_{24} = -13.6135681655558$$
$$x_{25} = 33.5103216382911$$
$$x_{26} = -85.870199198121$$
$$x_{27} = 48.1710873550435$$
$$x_{28} = -17.8023583703422$$
$$x_{29} = 10.471975511966$$
$$x_{30} = -35.6047167406843$$
$$x_{31} = 82.7286065445312$$
$$x_{32} = 3803.42150594604$$
$$x_{33} = -55.5014702134197$$
$$x_{34} = 46.0766922526503$$
$$x_{35} = -83.7758040957278$$
$$x_{36} = 63.8790506229925$$
$$x_{37} = 77.4926187885482$$
$$x_{38} = 39.7935069454707$$
$$x_{39} = -79.5870138909414$$
$$x_{40} = 96.342174710087$$
$$x_{41} = -60.7374579694027$$
$$x_{42} = -30.3687289847013$$
$$x_{43} = -54.4542726622231$$
$$x_{44} = 83.7758040957278$$
$$x_{45} = -19.8967534727354$$
$$x_{46} = 8.37758040957278$$
$$x_{47} = -32.4631240870945$$
$$x_{48} = -33.5103216382911$$
$$x_{49} = -11.5191730631626$$
$$x_{50} = -61.7846555205993$$
$$x_{51} = -93.2005820564972$$
$$x_{52} = -24.0855436775217$$
$$x_{53} = -10.471975511966$$
$$x_{54} = -39.7935069454707$$
$$x_{55} = -5.23598775598299$$
$$x_{56} = 2.0943951023932$$
$$x_{57} = 54.4542726622231$$
$$x_{58} = 17.8023583703422$$
$$x_{59} = -76.4454212373516$$
$$x_{60} = -26.1799387799149$$
$$x_{61} = 98.4365698124802$$
$$x_{62} = 24.0855436775217$$
$$x_{63} = 99.4837673636768$$
$$x_{64} = -27.2271363311115$$
$$x_{65} = 275.412955964705$$
$$x_{66} = 30.3687289847013$$
$$x_{67} = 92.1533845053006$$
$$x_{68} = -98.4365698124802$$
$$x_{69} = 38.7463093942741$$
$$x_{70} = 32.4631240870945$$
$$x_{71} = 61.7846555205993$$
$$x_{72} = -57.5958653158129$$
$$x_{73} = -63.8790506229925$$
$$x_{74} = 11.5191730631626$$
$$x_{75} = -4.18879020478639$$
$$x_{76} = 68.0678408277789$$
$$x_{77} = -49.2182849062401$$
$$x_{78} = 26.1799387799149$$
$$x_{79} = 76.4454212373516$$
$$x_{80} = 90.0589894029074$$
$$x_{81} = 60.7374579694027$$
$$x_{82} = 16.7551608191456$$
$$x_{83} = 19.8967534727354$$
$$x_{84} = -96.342174710087$$
$$x_{1} = 85.870199198121$$
$$x_{2} = 74.3510261349584$$
$$x_{3} = -673.348025419412$$
$$x_{4} = -41.8879020478639$$
$$x_{5} = 55.5014702134197$$
$$x_{6} = -68.0678408277789$$
$$x_{7} = -77.4926187885482$$
$$x_{8} = 269.129770657526$$
$$x_{9} = -90.0589894029074$$
$$x_{10} = -71.2094334813686$$
$$x_{11} = -99.4837673636768$$
$$x_{12} = 52.3598775598299$$
$$x_{13} = -42.9350995990605$$
$$x_{14} = -48.1710873550435$$
$$x_{15} = -46.0766922526503$$
$$x_{16} = -2.0943951023932$$
$$x_{17} = -92.1533845053006$$
$$x_{18} = -52.3598775598299$$
$$x_{19} = 70.162235930172$$
$$x_{20} = 4.18879020478639$$
$$x_{21} = -74.3510261349584$$
$$x_{22} = 41.8879020478639$$
$$x_{23} = -70.162235930172$$
$$x_{24} = -13.6135681655558$$
$$x_{25} = 33.5103216382911$$
$$x_{26} = -85.870199198121$$
$$x_{27} = 48.1710873550435$$
$$x_{28} = -17.8023583703422$$
$$x_{29} = 10.471975511966$$
$$x_{30} = -35.6047167406843$$
$$x_{31} = 82.7286065445312$$
$$x_{32} = 3803.42150594604$$
$$x_{33} = -55.5014702134197$$
$$x_{34} = 46.0766922526503$$
$$x_{35} = -83.7758040957278$$
$$x_{36} = 63.8790506229925$$
$$x_{37} = 77.4926187885482$$
$$x_{38} = 39.7935069454707$$
$$x_{39} = -79.5870138909414$$
$$x_{40} = 96.342174710087$$
$$x_{41} = -60.7374579694027$$
$$x_{42} = -30.3687289847013$$
$$x_{43} = -54.4542726622231$$
$$x_{44} = 83.7758040957278$$
$$x_{45} = -19.8967534727354$$
$$x_{46} = 8.37758040957278$$
$$x_{47} = -32.4631240870945$$
$$x_{48} = -33.5103216382911$$
$$x_{49} = -11.5191730631626$$
$$x_{50} = -61.7846555205993$$
$$x_{51} = -93.2005820564972$$
$$x_{52} = -24.0855436775217$$
$$x_{53} = -10.471975511966$$
$$x_{54} = -39.7935069454707$$
$$x_{55} = -5.23598775598299$$
$$x_{56} = 2.0943951023932$$
$$x_{57} = 54.4542726622231$$
$$x_{58} = 17.8023583703422$$
$$x_{59} = -76.4454212373516$$
$$x_{60} = -26.1799387799149$$
$$x_{61} = 98.4365698124802$$
$$x_{62} = 24.0855436775217$$
$$x_{63} = 99.4837673636768$$
$$x_{64} = -27.2271363311115$$
$$x_{65} = 275.412955964705$$
$$x_{66} = 30.3687289847013$$
$$x_{67} = 92.1533845053006$$
$$x_{68} = -98.4365698124802$$
$$x_{69} = 38.7463093942741$$
$$x_{70} = 32.4631240870945$$
$$x_{71} = 61.7846555205993$$
$$x_{72} = -57.5958653158129$$
$$x_{73} = -63.8790506229925$$
$$x_{74} = 11.5191730631626$$
$$x_{75} = -4.18879020478639$$
$$x_{76} = 68.0678408277789$$
$$x_{77} = -49.2182849062401$$
$$x_{78} = 26.1799387799149$$
$$x_{79} = 76.4454212373516$$
$$x_{80} = 90.0589894029074$$
$$x_{81} = 60.7374579694027$$
$$x_{82} = 16.7551608191456$$
$$x_{83} = 19.8967534727354$$
$$x_{84} = -96.342174710087$$
This roots
$$x_{3} = -673.348025419412$$
$$x_{11} = -99.4837673636768$$
$$x_{68} = -98.4365698124802$$
$$x_{84} = -96.342174710087$$
$$x_{51} = -93.2005820564972$$
$$x_{17} = -92.1533845053006$$
$$x_{9} = -90.0589894029074$$
$$x_{26} = -85.870199198121$$
$$x_{35} = -83.7758040957278$$
$$x_{39} = -79.5870138909414$$
$$x_{7} = -77.4926187885482$$
$$x_{59} = -76.4454212373516$$
$$x_{21} = -74.3510261349584$$
$$x_{10} = -71.2094334813686$$
$$x_{23} = -70.162235930172$$
$$x_{6} = -68.0678408277789$$
$$x_{73} = -63.8790506229925$$
$$x_{50} = -61.7846555205993$$
$$x_{41} = -60.7374579694027$$
$$x_{72} = -57.5958653158129$$
$$x_{33} = -55.5014702134197$$
$$x_{43} = -54.4542726622231$$
$$x_{18} = -52.3598775598299$$
$$x_{77} = -49.2182849062401$$
$$x_{14} = -48.1710873550435$$
$$x_{15} = -46.0766922526503$$
$$x_{13} = -42.9350995990605$$
$$x_{4} = -41.8879020478639$$
$$x_{54} = -39.7935069454707$$
$$x_{30} = -35.6047167406843$$
$$x_{48} = -33.5103216382911$$
$$x_{47} = -32.4631240870945$$
$$x_{42} = -30.3687289847013$$
$$x_{64} = -27.2271363311115$$
$$x_{60} = -26.1799387799149$$
$$x_{52} = -24.0855436775217$$
$$x_{45} = -19.8967534727354$$
$$x_{28} = -17.8023583703422$$
$$x_{24} = -13.6135681655558$$
$$x_{49} = -11.5191730631626$$
$$x_{53} = -10.471975511966$$
$$x_{55} = -5.23598775598299$$
$$x_{75} = -4.18879020478639$$
$$x_{16} = -2.0943951023932$$
$$x_{56} = 2.0943951023932$$
$$x_{20} = 4.18879020478639$$
$$x_{46} = 8.37758040957278$$
$$x_{29} = 10.471975511966$$
$$x_{74} = 11.5191730631626$$
$$x_{82} = 16.7551608191456$$
$$x_{58} = 17.8023583703422$$
$$x_{83} = 19.8967534727354$$
$$x_{62} = 24.0855436775217$$
$$x_{78} = 26.1799387799149$$
$$x_{66} = 30.3687289847013$$
$$x_{70} = 32.4631240870945$$
$$x_{25} = 33.5103216382911$$
$$x_{69} = 38.7463093942741$$
$$x_{38} = 39.7935069454707$$
$$x_{22} = 41.8879020478639$$
$$x_{34} = 46.0766922526503$$
$$x_{27} = 48.1710873550435$$
$$x_{12} = 52.3598775598299$$
$$x_{57} = 54.4542726622231$$
$$x_{5} = 55.5014702134197$$
$$x_{81} = 60.7374579694027$$
$$x_{71} = 61.7846555205993$$
$$x_{36} = 63.8790506229925$$
$$x_{76} = 68.0678408277789$$
$$x_{19} = 70.162235930172$$
$$x_{2} = 74.3510261349584$$
$$x_{79} = 76.4454212373516$$
$$x_{37} = 77.4926187885482$$
$$x_{31} = 82.7286065445312$$
$$x_{44} = 83.7758040957278$$
$$x_{1} = 85.870199198121$$
$$x_{80} = 90.0589894029074$$
$$x_{67} = 92.1533845053006$$
$$x_{40} = 96.342174710087$$
$$x_{61} = 98.4365698124802$$
$$x_{63} = 99.4837673636768$$
$$x_{8} = 269.129770657526$$
$$x_{65} = 275.412955964705$$
$$x_{32} = 3803.42150594604$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{3}$$
For example, let's take the point
$$x_{0} = x_{3} - \frac{1}{10}$$
=
$$-673.348025419412 + - \frac{1}{10}$$
=
$$-673.448025419412$$
substitute to the expression
$$\left|{\cos{\left(x \right)}}\right| < \frac{1}{2}$$
$$\left|{\cos{\left(-673.448025419412 \right)}}\right| < \frac{1}{2}$$
one of the solutions of our inequality is:
$$x < -673.348025419412$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x < -673.348025419412$$
$$x > -99.4837673636768 \wedge x < -98.4365698124802$$
$$x > -96.342174710087 \wedge x < -93.2005820564972$$
$$x > -92.1533845053006 \wedge x < -90.0589894029074$$
$$x > -85.870199198121 \wedge x < -83.7758040957278$$
$$x > -79.5870138909414 \wedge x < -77.4926187885482$$
$$x > -76.4454212373516 \wedge x < -74.3510261349584$$
$$x > -71.2094334813686 \wedge x < -70.162235930172$$
$$x > -68.0678408277789 \wedge x < -63.8790506229925$$
$$x > -61.7846555205993 \wedge x < -60.7374579694027$$
$$x > -57.5958653158129 \wedge x < -55.5014702134197$$
$$x > -54.4542726622231 \wedge x < -52.3598775598299$$
$$x > -49.2182849062401 \wedge x < -48.1710873550435$$
$$x > -46.0766922526503 \wedge x < -42.9350995990605$$
$$x > -41.8879020478639 \wedge x < -39.7935069454707$$
$$x > -35.6047167406843 \wedge x < -33.5103216382911$$
$$x > -32.4631240870945 \wedge x < -30.3687289847013$$
$$x > -27.2271363311115 \wedge x < -26.1799387799149$$
$$x > -24.0855436775217 \wedge x < -19.8967534727354$$
$$x > -17.8023583703422 \wedge x < -13.6135681655558$$
$$x > -11.5191730631626 \wedge x < -10.471975511966$$
$$x > -5.23598775598299 \wedge x < -4.18879020478639$$
$$x > -2.0943951023932 \wedge x < 2.0943951023932$$
$$x > 4.18879020478639 \wedge x < 8.37758040957278$$
$$x > 10.471975511966 \wedge x < 11.5191730631626$$
$$x > 16.7551608191456 \wedge x < 17.8023583703422$$
$$x > 19.8967534727354 \wedge x < 24.0855436775217$$
$$x > 26.1799387799149 \wedge x < 30.3687289847013$$
$$x > 32.4631240870945 \wedge x < 33.5103216382911$$
$$x > 38.7463093942741 \wedge x < 39.7935069454707$$
$$x > 41.8879020478639 \wedge x < 46.0766922526503$$
$$x > 48.1710873550435 \wedge x < 52.3598775598299$$
$$x > 54.4542726622231 \wedge x < 55.5014702134197$$
$$x > 60.7374579694027 \wedge x < 61.7846555205993$$
$$x > 63.8790506229925 \wedge x < 68.0678408277789$$
$$x > 70.162235930172 \wedge x < 74.3510261349584$$
$$x > 76.4454212373516 \wedge x < 77.4926187885482$$
$$x > 82.7286065445312 \wedge x < 83.7758040957278$$
$$x > 85.870199198121 \wedge x < 90.0589894029074$$
$$x > 92.1533845053006 \wedge x < 96.342174710087$$
$$x > 98.4365698124802 \wedge x < 99.4837673636768$$
$$x > 269.129770657526 \wedge x < 275.412955964705$$
$$x > 3803.42150594604$$
$$\left|{\cos{\left(x \right)}}\right| < \frac{1}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{\cos{\left(x \right)}}\right| = \frac{1}{2}$$
Solve:
Given the equation
$$\left|{\cos{\left(x \right)}}\right| = \frac{1}{2}$$
transform
$$\left|{\cos{\left(x \right)}}\right| - \frac{1}{2} = 0$$
$$\left|{\cos{\left(x \right)}}\right| - \frac{1}{2} = 0$$
Do replacement
$$w = \left|{\cos{\left(x \right)}}\right|$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{1}{2}$$
We get the answer: w = 1/2
do backward replacement
$$\left|{\cos{\left(x \right)}}\right| = w$$
substitute w:
$$x_{1} = 85.870199198121$$
$$x_{2} = 74.3510261349584$$
$$x_{3} = -673.348025419412$$
$$x_{4} = -41.8879020478639$$
$$x_{5} = 55.5014702134197$$
$$x_{6} = -68.0678408277789$$
$$x_{7} = -77.4926187885482$$
$$x_{8} = 269.129770657526$$
$$x_{9} = -90.0589894029074$$
$$x_{10} = -71.2094334813686$$
$$x_{11} = -99.4837673636768$$
$$x_{12} = 52.3598775598299$$
$$x_{13} = -42.9350995990605$$
$$x_{14} = -48.1710873550435$$
$$x_{15} = -46.0766922526503$$
$$x_{16} = -2.0943951023932$$
$$x_{17} = -92.1533845053006$$
$$x_{18} = -52.3598775598299$$
$$x_{19} = 70.162235930172$$
$$x_{20} = 4.18879020478639$$
$$x_{21} = -74.3510261349584$$
$$x_{22} = 41.8879020478639$$
$$x_{23} = -70.162235930172$$
$$x_{24} = -13.6135681655558$$
$$x_{25} = 33.5103216382911$$
$$x_{26} = -85.870199198121$$
$$x_{27} = 48.1710873550435$$
$$x_{28} = -17.8023583703422$$
$$x_{29} = 10.471975511966$$
$$x_{30} = -35.6047167406843$$
$$x_{31} = 82.7286065445312$$
$$x_{32} = 3803.42150594604$$
$$x_{33} = -55.5014702134197$$
$$x_{34} = 46.0766922526503$$
$$x_{35} = -83.7758040957278$$
$$x_{36} = 63.8790506229925$$
$$x_{37} = 77.4926187885482$$
$$x_{38} = 39.7935069454707$$
$$x_{39} = -79.5870138909414$$
$$x_{40} = 96.342174710087$$
$$x_{41} = -60.7374579694027$$
$$x_{42} = -30.3687289847013$$
$$x_{43} = -54.4542726622231$$
$$x_{44} = 83.7758040957278$$
$$x_{45} = -19.8967534727354$$
$$x_{46} = 8.37758040957278$$
$$x_{47} = -32.4631240870945$$
$$x_{48} = -33.5103216382911$$
$$x_{49} = -11.5191730631626$$
$$x_{50} = -61.7846555205993$$
$$x_{51} = -93.2005820564972$$
$$x_{52} = -24.0855436775217$$
$$x_{53} = -10.471975511966$$
$$x_{54} = -39.7935069454707$$
$$x_{55} = -5.23598775598299$$
$$x_{56} = 2.0943951023932$$
$$x_{57} = 54.4542726622231$$
$$x_{58} = 17.8023583703422$$
$$x_{59} = -76.4454212373516$$
$$x_{60} = -26.1799387799149$$
$$x_{61} = 98.4365698124802$$
$$x_{62} = 24.0855436775217$$
$$x_{63} = 99.4837673636768$$
$$x_{64} = -27.2271363311115$$
$$x_{65} = 275.412955964705$$
$$x_{66} = 30.3687289847013$$
$$x_{67} = 92.1533845053006$$
$$x_{68} = -98.4365698124802$$
$$x_{69} = 38.7463093942741$$
$$x_{70} = 32.4631240870945$$
$$x_{71} = 61.7846555205993$$
$$x_{72} = -57.5958653158129$$
$$x_{73} = -63.8790506229925$$
$$x_{74} = 11.5191730631626$$
$$x_{75} = -4.18879020478639$$
$$x_{76} = 68.0678408277789$$
$$x_{77} = -49.2182849062401$$
$$x_{78} = 26.1799387799149$$
$$x_{79} = 76.4454212373516$$
$$x_{80} = 90.0589894029074$$
$$x_{81} = 60.7374579694027$$
$$x_{82} = 16.7551608191456$$
$$x_{83} = 19.8967534727354$$
$$x_{84} = -96.342174710087$$
$$x_{1} = 85.870199198121$$
$$x_{2} = 74.3510261349584$$
$$x_{3} = -673.348025419412$$
$$x_{4} = -41.8879020478639$$
$$x_{5} = 55.5014702134197$$
$$x_{6} = -68.0678408277789$$
$$x_{7} = -77.4926187885482$$
$$x_{8} = 269.129770657526$$
$$x_{9} = -90.0589894029074$$
$$x_{10} = -71.2094334813686$$
$$x_{11} = -99.4837673636768$$
$$x_{12} = 52.3598775598299$$
$$x_{13} = -42.9350995990605$$
$$x_{14} = -48.1710873550435$$
$$x_{15} = -46.0766922526503$$
$$x_{16} = -2.0943951023932$$
$$x_{17} = -92.1533845053006$$
$$x_{18} = -52.3598775598299$$
$$x_{19} = 70.162235930172$$
$$x_{20} = 4.18879020478639$$
$$x_{21} = -74.3510261349584$$
$$x_{22} = 41.8879020478639$$
$$x_{23} = -70.162235930172$$
$$x_{24} = -13.6135681655558$$
$$x_{25} = 33.5103216382911$$
$$x_{26} = -85.870199198121$$
$$x_{27} = 48.1710873550435$$
$$x_{28} = -17.8023583703422$$
$$x_{29} = 10.471975511966$$
$$x_{30} = -35.6047167406843$$
$$x_{31} = 82.7286065445312$$
$$x_{32} = 3803.42150594604$$
$$x_{33} = -55.5014702134197$$
$$x_{34} = 46.0766922526503$$
$$x_{35} = -83.7758040957278$$
$$x_{36} = 63.8790506229925$$
$$x_{37} = 77.4926187885482$$
$$x_{38} = 39.7935069454707$$
$$x_{39} = -79.5870138909414$$
$$x_{40} = 96.342174710087$$
$$x_{41} = -60.7374579694027$$
$$x_{42} = -30.3687289847013$$
$$x_{43} = -54.4542726622231$$
$$x_{44} = 83.7758040957278$$
$$x_{45} = -19.8967534727354$$
$$x_{46} = 8.37758040957278$$
$$x_{47} = -32.4631240870945$$
$$x_{48} = -33.5103216382911$$
$$x_{49} = -11.5191730631626$$
$$x_{50} = -61.7846555205993$$
$$x_{51} = -93.2005820564972$$
$$x_{52} = -24.0855436775217$$
$$x_{53} = -10.471975511966$$
$$x_{54} = -39.7935069454707$$
$$x_{55} = -5.23598775598299$$
$$x_{56} = 2.0943951023932$$
$$x_{57} = 54.4542726622231$$
$$x_{58} = 17.8023583703422$$
$$x_{59} = -76.4454212373516$$
$$x_{60} = -26.1799387799149$$
$$x_{61} = 98.4365698124802$$
$$x_{62} = 24.0855436775217$$
$$x_{63} = 99.4837673636768$$
$$x_{64} = -27.2271363311115$$
$$x_{65} = 275.412955964705$$
$$x_{66} = 30.3687289847013$$
$$x_{67} = 92.1533845053006$$
$$x_{68} = -98.4365698124802$$
$$x_{69} = 38.7463093942741$$
$$x_{70} = 32.4631240870945$$
$$x_{71} = 61.7846555205993$$
$$x_{72} = -57.5958653158129$$
$$x_{73} = -63.8790506229925$$
$$x_{74} = 11.5191730631626$$
$$x_{75} = -4.18879020478639$$
$$x_{76} = 68.0678408277789$$
$$x_{77} = -49.2182849062401$$
$$x_{78} = 26.1799387799149$$
$$x_{79} = 76.4454212373516$$
$$x_{80} = 90.0589894029074$$
$$x_{81} = 60.7374579694027$$
$$x_{82} = 16.7551608191456$$
$$x_{83} = 19.8967534727354$$
$$x_{84} = -96.342174710087$$
This roots
$$x_{3} = -673.348025419412$$
$$x_{11} = -99.4837673636768$$
$$x_{68} = -98.4365698124802$$
$$x_{84} = -96.342174710087$$
$$x_{51} = -93.2005820564972$$
$$x_{17} = -92.1533845053006$$
$$x_{9} = -90.0589894029074$$
$$x_{26} = -85.870199198121$$
$$x_{35} = -83.7758040957278$$
$$x_{39} = -79.5870138909414$$
$$x_{7} = -77.4926187885482$$
$$x_{59} = -76.4454212373516$$
$$x_{21} = -74.3510261349584$$
$$x_{10} = -71.2094334813686$$
$$x_{23} = -70.162235930172$$
$$x_{6} = -68.0678408277789$$
$$x_{73} = -63.8790506229925$$
$$x_{50} = -61.7846555205993$$
$$x_{41} = -60.7374579694027$$
$$x_{72} = -57.5958653158129$$
$$x_{33} = -55.5014702134197$$
$$x_{43} = -54.4542726622231$$
$$x_{18} = -52.3598775598299$$
$$x_{77} = -49.2182849062401$$
$$x_{14} = -48.1710873550435$$
$$x_{15} = -46.0766922526503$$
$$x_{13} = -42.9350995990605$$
$$x_{4} = -41.8879020478639$$
$$x_{54} = -39.7935069454707$$
$$x_{30} = -35.6047167406843$$
$$x_{48} = -33.5103216382911$$
$$x_{47} = -32.4631240870945$$
$$x_{42} = -30.3687289847013$$
$$x_{64} = -27.2271363311115$$
$$x_{60} = -26.1799387799149$$
$$x_{52} = -24.0855436775217$$
$$x_{45} = -19.8967534727354$$
$$x_{28} = -17.8023583703422$$
$$x_{24} = -13.6135681655558$$
$$x_{49} = -11.5191730631626$$
$$x_{53} = -10.471975511966$$
$$x_{55} = -5.23598775598299$$
$$x_{75} = -4.18879020478639$$
$$x_{16} = -2.0943951023932$$
$$x_{56} = 2.0943951023932$$
$$x_{20} = 4.18879020478639$$
$$x_{46} = 8.37758040957278$$
$$x_{29} = 10.471975511966$$
$$x_{74} = 11.5191730631626$$
$$x_{82} = 16.7551608191456$$
$$x_{58} = 17.8023583703422$$
$$x_{83} = 19.8967534727354$$
$$x_{62} = 24.0855436775217$$
$$x_{78} = 26.1799387799149$$
$$x_{66} = 30.3687289847013$$
$$x_{70} = 32.4631240870945$$
$$x_{25} = 33.5103216382911$$
$$x_{69} = 38.7463093942741$$
$$x_{38} = 39.7935069454707$$
$$x_{22} = 41.8879020478639$$
$$x_{34} = 46.0766922526503$$
$$x_{27} = 48.1710873550435$$
$$x_{12} = 52.3598775598299$$
$$x_{57} = 54.4542726622231$$
$$x_{5} = 55.5014702134197$$
$$x_{81} = 60.7374579694027$$
$$x_{71} = 61.7846555205993$$
$$x_{36} = 63.8790506229925$$
$$x_{76} = 68.0678408277789$$
$$x_{19} = 70.162235930172$$
$$x_{2} = 74.3510261349584$$
$$x_{79} = 76.4454212373516$$
$$x_{37} = 77.4926187885482$$
$$x_{31} = 82.7286065445312$$
$$x_{44} = 83.7758040957278$$
$$x_{1} = 85.870199198121$$
$$x_{80} = 90.0589894029074$$
$$x_{67} = 92.1533845053006$$
$$x_{40} = 96.342174710087$$
$$x_{61} = 98.4365698124802$$
$$x_{63} = 99.4837673636768$$
$$x_{8} = 269.129770657526$$
$$x_{65} = 275.412955964705$$
$$x_{32} = 3803.42150594604$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{3}$$
For example, let's take the point
$$x_{0} = x_{3} - \frac{1}{10}$$
=
$$-673.348025419412 + - \frac{1}{10}$$
=
$$-673.448025419412$$
substitute to the expression
$$\left|{\cos{\left(x \right)}}\right| < \frac{1}{2}$$
$$\left|{\cos{\left(-673.448025419412 \right)}}\right| < \frac{1}{2}$$
0.411043807676242 < 1/2
one of the solutions of our inequality is:
$$x < -673.348025419412$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
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x3 x11 x68 x84 x51 x17 x9 x26 x35 x39 x7 x59 x21 x10 x23 x6 x73 x50 x41 x72 x33 x43 x18 x77 x14 x15 x13 x4 x54 x30 x48 x47 x42 x64 x60 x52 x45 x28 x24 x49 x53 x55 x75 x16 x56 x20 x46 x29 x74 x82 x58 x83 x62 x78 x66 x70 x25 x69 x38 x22 x34 x27 x12 x57 x5 x81 x71 x36 x76 x19 x2 x79 x37 x31 x44 x1 x80 x67 x40 x61 x63 x8 x65 x32Other solutions will get with the changeover to the next point
etc.
The answer:
$$x < -673.348025419412$$
$$x > -99.4837673636768 \wedge x < -98.4365698124802$$
$$x > -96.342174710087 \wedge x < -93.2005820564972$$
$$x > -92.1533845053006 \wedge x < -90.0589894029074$$
$$x > -85.870199198121 \wedge x < -83.7758040957278$$
$$x > -79.5870138909414 \wedge x < -77.4926187885482$$
$$x > -76.4454212373516 \wedge x < -74.3510261349584$$
$$x > -71.2094334813686 \wedge x < -70.162235930172$$
$$x > -68.0678408277789 \wedge x < -63.8790506229925$$
$$x > -61.7846555205993 \wedge x < -60.7374579694027$$
$$x > -57.5958653158129 \wedge x < -55.5014702134197$$
$$x > -54.4542726622231 \wedge x < -52.3598775598299$$
$$x > -49.2182849062401 \wedge x < -48.1710873550435$$
$$x > -46.0766922526503 \wedge x < -42.9350995990605$$
$$x > -41.8879020478639 \wedge x < -39.7935069454707$$
$$x > -35.6047167406843 \wedge x < -33.5103216382911$$
$$x > -32.4631240870945 \wedge x < -30.3687289847013$$
$$x > -27.2271363311115 \wedge x < -26.1799387799149$$
$$x > -24.0855436775217 \wedge x < -19.8967534727354$$
$$x > -17.8023583703422 \wedge x < -13.6135681655558$$
$$x > -11.5191730631626 \wedge x < -10.471975511966$$
$$x > -5.23598775598299 \wedge x < -4.18879020478639$$
$$x > -2.0943951023932 \wedge x < 2.0943951023932$$
$$x > 4.18879020478639 \wedge x < 8.37758040957278$$
$$x > 10.471975511966 \wedge x < 11.5191730631626$$
$$x > 16.7551608191456 \wedge x < 17.8023583703422$$
$$x > 19.8967534727354 \wedge x < 24.0855436775217$$
$$x > 26.1799387799149 \wedge x < 30.3687289847013$$
$$x > 32.4631240870945 \wedge x < 33.5103216382911$$
$$x > 38.7463093942741 \wedge x < 39.7935069454707$$
$$x > 41.8879020478639 \wedge x < 46.0766922526503$$
$$x > 48.1710873550435 \wedge x < 52.3598775598299$$
$$x > 54.4542726622231 \wedge x < 55.5014702134197$$
$$x > 60.7374579694027 \wedge x < 61.7846555205993$$
$$x > 63.8790506229925 \wedge x < 68.0678408277789$$
$$x > 70.162235930172 \wedge x < 74.3510261349584$$
$$x > 76.4454212373516 \wedge x < 77.4926187885482$$
$$x > 82.7286065445312 \wedge x < 83.7758040957278$$
$$x > 85.870199198121 \wedge x < 90.0589894029074$$
$$x > 92.1533845053006 \wedge x < 96.342174710087$$
$$x > 98.4365698124802 \wedge x < 99.4837673636768$$
$$x > 269.129770657526 \wedge x < 275.412955964705$$
$$x > 3803.42150594604$$
Solving inequality on a graph