Mister Exam
ctgt=<-sqrt3/3 inequation
The solution
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-\/ 3
cot(t) <= -------
3
$$\cot{\left(t \right)} \leq \frac{\left(-1\right) \sqrt{3}}{3}$$
cot(t) <= (-sqrt(3))/3
Detail solution
Given the inequality:
$$\cot{\left(t \right)} \leq \frac{\left(-1\right) \sqrt{3}}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(t \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
Solve:
$$x_{1} = 39.7935069454707$$
$$x_{2} = 11.5191730631626$$
$$x_{3} = 71.2094334813686$$
$$x_{4} = -98.4365698124802$$
$$x_{5} = -85.870199198121$$
$$x_{6} = -51.3126800086333$$
$$x_{7} = 36.6519142918809$$
$$x_{8} = 14.6607657167524$$
$$x_{9} = -70.162235930172$$
$$x_{10} = 93.2005820564972$$
$$x_{11} = -95.2949771588904$$
$$x_{12} = 49.2182849062401$$
$$x_{13} = 30.3687289847013$$
$$x_{14} = -29.3215314335047$$
$$x_{15} = 17.8023583703422$$
$$x_{16} = -41.8879020478639$$
$$x_{17} = -32.4631240870945$$
$$x_{18} = -92.1533845053006$$
$$x_{19} = 42.9350995990605$$
$$x_{20} = 77.4926187885482$$
$$x_{21} = 46.0766922526503$$
$$x_{22} = -54.4542726622231$$
$$x_{23} = 96.342174710087$$
$$x_{24} = -26.1799387799149$$
$$x_{25} = 8.37758040957278$$
$$x_{26} = -76.4454212373516$$
$$x_{27} = -79.5870138909414$$
$$x_{28} = -16.7551608191456$$
$$x_{29} = -1.0471975511966$$
$$x_{30} = 52.3598775598299$$
$$x_{31} = 20.943951023932$$
$$x_{32} = -10.471975511966$$
$$x_{33} = 55.5014702134197$$
$$x_{34} = 33.5103216382911$$
$$x_{35} = 27.2271363311115$$
$$x_{36} = 83.7758040957278$$
$$x_{37} = 68.0678408277789$$
$$x_{38} = -23.0383461263252$$
$$x_{39} = -60.7374579694027$$
$$x_{40} = -19.8967534727354$$
$$x_{41} = -82.7286065445312$$
$$x_{42} = 74.3510261349584$$
$$x_{43} = -35.6047167406843$$
$$x_{44} = -38.7463093942741$$
$$x_{45} = 80.634211442138$$
$$x_{46} = 99.4837673636768$$
$$x_{47} = -45.0294947014537$$
$$x_{48} = -48.1710873550435$$
$$x_{49} = -73.3038285837618$$
$$x_{50} = 64.9262481741891$$
$$x_{51} = -57.5958653158129$$
$$x_{52} = -4.18879020478639$$
$$x_{53} = -63.8790506229925$$
$$x_{54} = 5.23598775598299$$
$$x_{55} = -89.0117918517108$$
$$x_{56} = 2.0943951023932$$
$$x_{57} = -13.6135681655558$$
$$x_{58} = 58.6430628670095$$
$$x_{59} = 86.9173967493176$$
$$x_{60} = 90.0589894029074$$
$$x_{61} = 24.0855436775217$$
$$x_{62} = 61.7846555205993$$
$$x_{63} = -67.0206432765823$$
$$x_{64} = -7.33038285837618$$
$$x_{1} = 39.7935069454707$$
$$x_{2} = 11.5191730631626$$
$$x_{3} = 71.2094334813686$$
$$x_{4} = -98.4365698124802$$
$$x_{5} = -85.870199198121$$
$$x_{6} = -51.3126800086333$$
$$x_{7} = 36.6519142918809$$
$$x_{8} = 14.6607657167524$$
$$x_{9} = -70.162235930172$$
$$x_{10} = 93.2005820564972$$
$$x_{11} = -95.2949771588904$$
$$x_{12} = 49.2182849062401$$
$$x_{13} = 30.3687289847013$$
$$x_{14} = -29.3215314335047$$
$$x_{15} = 17.8023583703422$$
$$x_{16} = -41.8879020478639$$
$$x_{17} = -32.4631240870945$$
$$x_{18} = -92.1533845053006$$
$$x_{19} = 42.9350995990605$$
$$x_{20} = 77.4926187885482$$
$$x_{21} = 46.0766922526503$$
$$x_{22} = -54.4542726622231$$
$$x_{23} = 96.342174710087$$
$$x_{24} = -26.1799387799149$$
$$x_{25} = 8.37758040957278$$
$$x_{26} = -76.4454212373516$$
$$x_{27} = -79.5870138909414$$
$$x_{28} = -16.7551608191456$$
$$x_{29} = -1.0471975511966$$
$$x_{30} = 52.3598775598299$$
$$x_{31} = 20.943951023932$$
$$x_{32} = -10.471975511966$$
$$x_{33} = 55.5014702134197$$
$$x_{34} = 33.5103216382911$$
$$x_{35} = 27.2271363311115$$
$$x_{36} = 83.7758040957278$$
$$x_{37} = 68.0678408277789$$
$$x_{38} = -23.0383461263252$$
$$x_{39} = -60.7374579694027$$
$$x_{40} = -19.8967534727354$$
$$x_{41} = -82.7286065445312$$
$$x_{42} = 74.3510261349584$$
$$x_{43} = -35.6047167406843$$
$$x_{44} = -38.7463093942741$$
$$x_{45} = 80.634211442138$$
$$x_{46} = 99.4837673636768$$
$$x_{47} = -45.0294947014537$$
$$x_{48} = -48.1710873550435$$
$$x_{49} = -73.3038285837618$$
$$x_{50} = 64.9262481741891$$
$$x_{51} = -57.5958653158129$$
$$x_{52} = -4.18879020478639$$
$$x_{53} = -63.8790506229925$$
$$x_{54} = 5.23598775598299$$
$$x_{55} = -89.0117918517108$$
$$x_{56} = 2.0943951023932$$
$$x_{57} = -13.6135681655558$$
$$x_{58} = 58.6430628670095$$
$$x_{59} = 86.9173967493176$$
$$x_{60} = 90.0589894029074$$
$$x_{61} = 24.0855436775217$$
$$x_{62} = 61.7846555205993$$
$$x_{63} = -67.0206432765823$$
$$x_{64} = -7.33038285837618$$
This roots
$$x_{4} = -98.4365698124802$$
$$x_{11} = -95.2949771588904$$
$$x_{18} = -92.1533845053006$$
$$x_{55} = -89.0117918517108$$
$$x_{5} = -85.870199198121$$
$$x_{41} = -82.7286065445312$$
$$x_{27} = -79.5870138909414$$
$$x_{26} = -76.4454212373516$$
$$x_{49} = -73.3038285837618$$
$$x_{9} = -70.162235930172$$
$$x_{63} = -67.0206432765823$$
$$x_{53} = -63.8790506229925$$
$$x_{39} = -60.7374579694027$$
$$x_{51} = -57.5958653158129$$
$$x_{22} = -54.4542726622231$$
$$x_{6} = -51.3126800086333$$
$$x_{48} = -48.1710873550435$$
$$x_{47} = -45.0294947014537$$
$$x_{16} = -41.8879020478639$$
$$x_{44} = -38.7463093942741$$
$$x_{43} = -35.6047167406843$$
$$x_{17} = -32.4631240870945$$
$$x_{14} = -29.3215314335047$$
$$x_{24} = -26.1799387799149$$
$$x_{38} = -23.0383461263252$$
$$x_{40} = -19.8967534727354$$
$$x_{28} = -16.7551608191456$$
$$x_{57} = -13.6135681655558$$
$$x_{32} = -10.471975511966$$
$$x_{64} = -7.33038285837618$$
$$x_{52} = -4.18879020478639$$
$$x_{29} = -1.0471975511966$$
$$x_{56} = 2.0943951023932$$
$$x_{54} = 5.23598775598299$$
$$x_{25} = 8.37758040957278$$
$$x_{2} = 11.5191730631626$$
$$x_{8} = 14.6607657167524$$
$$x_{15} = 17.8023583703422$$
$$x_{31} = 20.943951023932$$
$$x_{61} = 24.0855436775217$$
$$x_{35} = 27.2271363311115$$
$$x_{13} = 30.3687289847013$$
$$x_{34} = 33.5103216382911$$
$$x_{7} = 36.6519142918809$$
$$x_{1} = 39.7935069454707$$
$$x_{19} = 42.9350995990605$$
$$x_{21} = 46.0766922526503$$
$$x_{12} = 49.2182849062401$$
$$x_{30} = 52.3598775598299$$
$$x_{33} = 55.5014702134197$$
$$x_{58} = 58.6430628670095$$
$$x_{62} = 61.7846555205993$$
$$x_{50} = 64.9262481741891$$
$$x_{37} = 68.0678408277789$$
$$x_{3} = 71.2094334813686$$
$$x_{42} = 74.3510261349584$$
$$x_{20} = 77.4926187885482$$
$$x_{45} = 80.634211442138$$
$$x_{36} = 83.7758040957278$$
$$x_{59} = 86.9173967493176$$
$$x_{60} = 90.0589894029074$$
$$x_{10} = 93.2005820564972$$
$$x_{23} = 96.342174710087$$
$$x_{46} = 99.4837673636768$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{4}$$
For example, let's take the point
$$x_{0} = x_{4} - \frac{1}{10}$$
=
$$-98.4365698124802 + - \frac{1}{10}$$
=
$$-98.5365698124802$$
substitute to the expression
$$\cot{\left(t \right)} \leq \frac{\left(-1\right) \sqrt{3}}{3}$$
$$\cot{\left(t \right)} \leq \frac{\left(-1\right) \sqrt{3}}{3}$$
Then
$$x \leq -98.4365698124802$$
no execute
one of the solutions of our inequality is:
$$x \geq -98.4365698124802 \wedge x \leq -95.2949771588904$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \geq -98.4365698124802 \wedge x \leq -95.2949771588904$$
$$x \geq -92.1533845053006 \wedge x \leq -89.0117918517108$$
$$x \geq -85.870199198121 \wedge x \leq -82.7286065445312$$
$$x \geq -79.5870138909414 \wedge x \leq -76.4454212373516$$
$$x \geq -73.3038285837618 \wedge x \leq -70.162235930172$$
$$x \geq -67.0206432765823 \wedge x \leq -63.8790506229925$$
$$x \geq -60.7374579694027 \wedge x \leq -57.5958653158129$$
$$x \geq -54.4542726622231 \wedge x \leq -51.3126800086333$$
$$x \geq -48.1710873550435 \wedge x \leq -45.0294947014537$$
$$x \geq -41.8879020478639 \wedge x \leq -38.7463093942741$$
$$x \geq -35.6047167406843 \wedge x \leq -32.4631240870945$$
$$x \geq -29.3215314335047 \wedge x \leq -26.1799387799149$$
$$x \geq -23.0383461263252 \wedge x \leq -19.8967534727354$$
$$x \geq -16.7551608191456 \wedge x \leq -13.6135681655558$$
$$x \geq -10.471975511966 \wedge x \leq -7.33038285837618$$
$$x \geq -4.18879020478639 \wedge x \leq -1.0471975511966$$
$$x \geq 2.0943951023932 \wedge x \leq 5.23598775598299$$
$$x \geq 8.37758040957278 \wedge x \leq 11.5191730631626$$
$$x \geq 14.6607657167524 \wedge x \leq 17.8023583703422$$
$$x \geq 20.943951023932 \wedge x \leq 24.0855436775217$$
$$x \geq 27.2271363311115 \wedge x \leq 30.3687289847013$$
$$x \geq 33.5103216382911 \wedge x \leq 36.6519142918809$$
$$x \geq 39.7935069454707 \wedge x \leq 42.9350995990605$$
$$x \geq 46.0766922526503 \wedge x \leq 49.2182849062401$$
$$x \geq 52.3598775598299 \wedge x \leq 55.5014702134197$$
$$x \geq 58.6430628670095 \wedge x \leq 61.7846555205993$$
$$x \geq 64.9262481741891 \wedge x \leq 68.0678408277789$$
$$x \geq 71.2094334813686 \wedge x \leq 74.3510261349584$$
$$x \geq 77.4926187885482 \wedge x \leq 80.634211442138$$
$$x \geq 83.7758040957278 \wedge x \leq 86.9173967493176$$
$$x \geq 90.0589894029074 \wedge x \leq 93.2005820564972$$
$$x \geq 96.342174710087 \wedge x \leq 99.4837673636768$$
$$\cot{\left(t \right)} \leq \frac{\left(-1\right) \sqrt{3}}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(t \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
Solve:
$$x_{1} = 39.7935069454707$$
$$x_{2} = 11.5191730631626$$
$$x_{3} = 71.2094334813686$$
$$x_{4} = -98.4365698124802$$
$$x_{5} = -85.870199198121$$
$$x_{6} = -51.3126800086333$$
$$x_{7} = 36.6519142918809$$
$$x_{8} = 14.6607657167524$$
$$x_{9} = -70.162235930172$$
$$x_{10} = 93.2005820564972$$
$$x_{11} = -95.2949771588904$$
$$x_{12} = 49.2182849062401$$
$$x_{13} = 30.3687289847013$$
$$x_{14} = -29.3215314335047$$
$$x_{15} = 17.8023583703422$$
$$x_{16} = -41.8879020478639$$
$$x_{17} = -32.4631240870945$$
$$x_{18} = -92.1533845053006$$
$$x_{19} = 42.9350995990605$$
$$x_{20} = 77.4926187885482$$
$$x_{21} = 46.0766922526503$$
$$x_{22} = -54.4542726622231$$
$$x_{23} = 96.342174710087$$
$$x_{24} = -26.1799387799149$$
$$x_{25} = 8.37758040957278$$
$$x_{26} = -76.4454212373516$$
$$x_{27} = -79.5870138909414$$
$$x_{28} = -16.7551608191456$$
$$x_{29} = -1.0471975511966$$
$$x_{30} = 52.3598775598299$$
$$x_{31} = 20.943951023932$$
$$x_{32} = -10.471975511966$$
$$x_{33} = 55.5014702134197$$
$$x_{34} = 33.5103216382911$$
$$x_{35} = 27.2271363311115$$
$$x_{36} = 83.7758040957278$$
$$x_{37} = 68.0678408277789$$
$$x_{38} = -23.0383461263252$$
$$x_{39} = -60.7374579694027$$
$$x_{40} = -19.8967534727354$$
$$x_{41} = -82.7286065445312$$
$$x_{42} = 74.3510261349584$$
$$x_{43} = -35.6047167406843$$
$$x_{44} = -38.7463093942741$$
$$x_{45} = 80.634211442138$$
$$x_{46} = 99.4837673636768$$
$$x_{47} = -45.0294947014537$$
$$x_{48} = -48.1710873550435$$
$$x_{49} = -73.3038285837618$$
$$x_{50} = 64.9262481741891$$
$$x_{51} = -57.5958653158129$$
$$x_{52} = -4.18879020478639$$
$$x_{53} = -63.8790506229925$$
$$x_{54} = 5.23598775598299$$
$$x_{55} = -89.0117918517108$$
$$x_{56} = 2.0943951023932$$
$$x_{57} = -13.6135681655558$$
$$x_{58} = 58.6430628670095$$
$$x_{59} = 86.9173967493176$$
$$x_{60} = 90.0589894029074$$
$$x_{61} = 24.0855436775217$$
$$x_{62} = 61.7846555205993$$
$$x_{63} = -67.0206432765823$$
$$x_{64} = -7.33038285837618$$
$$x_{1} = 39.7935069454707$$
$$x_{2} = 11.5191730631626$$
$$x_{3} = 71.2094334813686$$
$$x_{4} = -98.4365698124802$$
$$x_{5} = -85.870199198121$$
$$x_{6} = -51.3126800086333$$
$$x_{7} = 36.6519142918809$$
$$x_{8} = 14.6607657167524$$
$$x_{9} = -70.162235930172$$
$$x_{10} = 93.2005820564972$$
$$x_{11} = -95.2949771588904$$
$$x_{12} = 49.2182849062401$$
$$x_{13} = 30.3687289847013$$
$$x_{14} = -29.3215314335047$$
$$x_{15} = 17.8023583703422$$
$$x_{16} = -41.8879020478639$$
$$x_{17} = -32.4631240870945$$
$$x_{18} = -92.1533845053006$$
$$x_{19} = 42.9350995990605$$
$$x_{20} = 77.4926187885482$$
$$x_{21} = 46.0766922526503$$
$$x_{22} = -54.4542726622231$$
$$x_{23} = 96.342174710087$$
$$x_{24} = -26.1799387799149$$
$$x_{25} = 8.37758040957278$$
$$x_{26} = -76.4454212373516$$
$$x_{27} = -79.5870138909414$$
$$x_{28} = -16.7551608191456$$
$$x_{29} = -1.0471975511966$$
$$x_{30} = 52.3598775598299$$
$$x_{31} = 20.943951023932$$
$$x_{32} = -10.471975511966$$
$$x_{33} = 55.5014702134197$$
$$x_{34} = 33.5103216382911$$
$$x_{35} = 27.2271363311115$$
$$x_{36} = 83.7758040957278$$
$$x_{37} = 68.0678408277789$$
$$x_{38} = -23.0383461263252$$
$$x_{39} = -60.7374579694027$$
$$x_{40} = -19.8967534727354$$
$$x_{41} = -82.7286065445312$$
$$x_{42} = 74.3510261349584$$
$$x_{43} = -35.6047167406843$$
$$x_{44} = -38.7463093942741$$
$$x_{45} = 80.634211442138$$
$$x_{46} = 99.4837673636768$$
$$x_{47} = -45.0294947014537$$
$$x_{48} = -48.1710873550435$$
$$x_{49} = -73.3038285837618$$
$$x_{50} = 64.9262481741891$$
$$x_{51} = -57.5958653158129$$
$$x_{52} = -4.18879020478639$$
$$x_{53} = -63.8790506229925$$
$$x_{54} = 5.23598775598299$$
$$x_{55} = -89.0117918517108$$
$$x_{56} = 2.0943951023932$$
$$x_{57} = -13.6135681655558$$
$$x_{58} = 58.6430628670095$$
$$x_{59} = 86.9173967493176$$
$$x_{60} = 90.0589894029074$$
$$x_{61} = 24.0855436775217$$
$$x_{62} = 61.7846555205993$$
$$x_{63} = -67.0206432765823$$
$$x_{64} = -7.33038285837618$$
This roots
$$x_{4} = -98.4365698124802$$
$$x_{11} = -95.2949771588904$$
$$x_{18} = -92.1533845053006$$
$$x_{55} = -89.0117918517108$$
$$x_{5} = -85.870199198121$$
$$x_{41} = -82.7286065445312$$
$$x_{27} = -79.5870138909414$$
$$x_{26} = -76.4454212373516$$
$$x_{49} = -73.3038285837618$$
$$x_{9} = -70.162235930172$$
$$x_{63} = -67.0206432765823$$
$$x_{53} = -63.8790506229925$$
$$x_{39} = -60.7374579694027$$
$$x_{51} = -57.5958653158129$$
$$x_{22} = -54.4542726622231$$
$$x_{6} = -51.3126800086333$$
$$x_{48} = -48.1710873550435$$
$$x_{47} = -45.0294947014537$$
$$x_{16} = -41.8879020478639$$
$$x_{44} = -38.7463093942741$$
$$x_{43} = -35.6047167406843$$
$$x_{17} = -32.4631240870945$$
$$x_{14} = -29.3215314335047$$
$$x_{24} = -26.1799387799149$$
$$x_{38} = -23.0383461263252$$
$$x_{40} = -19.8967534727354$$
$$x_{28} = -16.7551608191456$$
$$x_{57} = -13.6135681655558$$
$$x_{32} = -10.471975511966$$
$$x_{64} = -7.33038285837618$$
$$x_{52} = -4.18879020478639$$
$$x_{29} = -1.0471975511966$$
$$x_{56} = 2.0943951023932$$
$$x_{54} = 5.23598775598299$$
$$x_{25} = 8.37758040957278$$
$$x_{2} = 11.5191730631626$$
$$x_{8} = 14.6607657167524$$
$$x_{15} = 17.8023583703422$$
$$x_{31} = 20.943951023932$$
$$x_{61} = 24.0855436775217$$
$$x_{35} = 27.2271363311115$$
$$x_{13} = 30.3687289847013$$
$$x_{34} = 33.5103216382911$$
$$x_{7} = 36.6519142918809$$
$$x_{1} = 39.7935069454707$$
$$x_{19} = 42.9350995990605$$
$$x_{21} = 46.0766922526503$$
$$x_{12} = 49.2182849062401$$
$$x_{30} = 52.3598775598299$$
$$x_{33} = 55.5014702134197$$
$$x_{58} = 58.6430628670095$$
$$x_{62} = 61.7846555205993$$
$$x_{50} = 64.9262481741891$$
$$x_{37} = 68.0678408277789$$
$$x_{3} = 71.2094334813686$$
$$x_{42} = 74.3510261349584$$
$$x_{20} = 77.4926187885482$$
$$x_{45} = 80.634211442138$$
$$x_{36} = 83.7758040957278$$
$$x_{59} = 86.9173967493176$$
$$x_{60} = 90.0589894029074$$
$$x_{10} = 93.2005820564972$$
$$x_{23} = 96.342174710087$$
$$x_{46} = 99.4837673636768$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{4}$$
For example, let's take the point
$$x_{0} = x_{4} - \frac{1}{10}$$
=
$$-98.4365698124802 + - \frac{1}{10}$$
=
$$-98.5365698124802$$
substitute to the expression
$$\cot{\left(t \right)} \leq \frac{\left(-1\right) \sqrt{3}}{3}$$
$$\cot{\left(t \right)} \leq \frac{\left(-1\right) \sqrt{3}}{3}$$
___
-\/ 3
cot(t) <= -------
3
Then
$$x \leq -98.4365698124802$$
no execute
one of the solutions of our inequality is:
$$x \geq -98.4365698124802 \wedge x \leq -95.2949771588904$$
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x4 x11 x18 x55 x5 x41 x27 x26 x49 x9 x63 x53 x39 x51 x22 x6 x48 x47 x16 x44 x43 x17 x14 x24 x38 x40 x28 x57 x32 x64 x52 x29 x56 x54 x25 x2 x8 x15 x31 x61 x35 x13 x34 x7 x1 x19 x21 x12 x30 x33 x58 x62 x50 x37 x3 x42 x20 x45 x36 x59 x60 x10 x23 x46Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \geq -98.4365698124802 \wedge x \leq -95.2949771588904$$
$$x \geq -92.1533845053006 \wedge x \leq -89.0117918517108$$
$$x \geq -85.870199198121 \wedge x \leq -82.7286065445312$$
$$x \geq -79.5870138909414 \wedge x \leq -76.4454212373516$$
$$x \geq -73.3038285837618 \wedge x \leq -70.162235930172$$
$$x \geq -67.0206432765823 \wedge x \leq -63.8790506229925$$
$$x \geq -60.7374579694027 \wedge x \leq -57.5958653158129$$
$$x \geq -54.4542726622231 \wedge x \leq -51.3126800086333$$
$$x \geq -48.1710873550435 \wedge x \leq -45.0294947014537$$
$$x \geq -41.8879020478639 \wedge x \leq -38.7463093942741$$
$$x \geq -35.6047167406843 \wedge x \leq -32.4631240870945$$
$$x \geq -29.3215314335047 \wedge x \leq -26.1799387799149$$
$$x \geq -23.0383461263252 \wedge x \leq -19.8967534727354$$
$$x \geq -16.7551608191456 \wedge x \leq -13.6135681655558$$
$$x \geq -10.471975511966 \wedge x \leq -7.33038285837618$$
$$x \geq -4.18879020478639 \wedge x \leq -1.0471975511966$$
$$x \geq 2.0943951023932 \wedge x \leq 5.23598775598299$$
$$x \geq 8.37758040957278 \wedge x \leq 11.5191730631626$$
$$x \geq 14.6607657167524 \wedge x \leq 17.8023583703422$$
$$x \geq 20.943951023932 \wedge x \leq 24.0855436775217$$
$$x \geq 27.2271363311115 \wedge x \leq 30.3687289847013$$
$$x \geq 33.5103216382911 \wedge x \leq 36.6519142918809$$
$$x \geq 39.7935069454707 \wedge x \leq 42.9350995990605$$
$$x \geq 46.0766922526503 \wedge x \leq 49.2182849062401$$
$$x \geq 52.3598775598299 \wedge x \leq 55.5014702134197$$
$$x \geq 58.6430628670095 \wedge x \leq 61.7846555205993$$
$$x \geq 64.9262481741891 \wedge x \leq 68.0678408277789$$
$$x \geq 71.2094334813686 \wedge x \leq 74.3510261349584$$
$$x \geq 77.4926187885482 \wedge x \leq 80.634211442138$$
$$x \geq 83.7758040957278 \wedge x \leq 86.9173967493176$$
$$x \geq 90.0589894029074 \wedge x \leq 93.2005820564972$$
$$x \geq 96.342174710087 \wedge x \leq 99.4837673636768$$
Rapid solution
[src]
/2*pi \ And|---- <= x, x < pi| \ 3 /
$$\frac{2 \pi}{3} \leq x \wedge x < \pi$$
(x < pi)∧(2*pi/3 <= x)
Rapid solution 2
[src]
2*pi [----, pi) 3
$$x\ in\ \left[\frac{2 \pi}{3}, \pi\right)$$
x in Interval.Ropen(2*pi/3, pi)