Given the inequality:
sin ( t ) < ( − 1 ) 3 2 \sin{\left(t \right)} < \frac{\left(-1\right) \sqrt{3}}{2} sin ( t ) < 2 ( − 1 ) 3 To solve this inequality, we must first solve the corresponding equation:
sin ( t ) = ( − 1 ) 3 2 \sin{\left(t \right)} = \frac{\left(-1\right) \sqrt{3}}{2} sin ( t ) = 2 ( − 1 ) 3 Solve:
x 1 = − 19.8967534727354 x_{1} = -19.8967534727354 x 1 = − 19.8967534727354 x 2 = 24.0855436775217 x_{2} = 24.0855436775217 x 2 = 24.0855436775217 x 3 = − 101.57816246607 x_{3} = -101.57816246607 x 3 = − 101.57816246607 x 4 = − 95.2949771588904 x_{4} = -95.2949771588904 x 4 = − 95.2949771588904 x 5 = − 89.0117918517108 x_{5} = -89.0117918517108 x 5 = − 89.0117918517108 x 6 = − 2.0943951023932 x_{6} = -2.0943951023932 x 6 = − 2.0943951023932 x 7 = 49.2182849062401 x_{7} = 49.2182849062401 x 7 = 49.2182849062401 x 8 = − 14.6607657167524 x_{8} = -14.6607657167524 x 8 = − 14.6607657167524 x 9 = 86.9173967493176 x_{9} = 86.9173967493176 x 9 = 86.9173967493176 x 10 = − 45.0294947014537 x_{10} = -45.0294947014537 x 10 = − 45.0294947014537 x 11 = 54.4542726622231 x_{11} = 54.4542726622231 x 11 = 54.4542726622231 x 12 = − 46.0766922526503 x_{12} = -46.0766922526503 x 12 = − 46.0766922526503 x 13 = − 63.8790506229925 x_{13} = -63.8790506229925 x 13 = − 63.8790506229925 x 14 = − 8.37758040957278 x_{14} = -8.37758040957278 x 14 = − 8.37758040957278 x 15 = − 32.4631240870945 x_{15} = -32.4631240870945 x 15 = − 32.4631240870945 x 16 = − 114.144533080429 x_{16} = -114.144533080429 x 16 = − 114.144533080429 x 17 = 5.23598775598299 x_{17} = 5.23598775598299 x 17 = 5.23598775598299 x 18 = − 83.7758040957278 x_{18} = -83.7758040957278 x 18 = − 83.7758040957278 x 19 = 60.7374579694027 x_{19} = 60.7374579694027 x 19 = 60.7374579694027 x 20 = − 71.2094334813686 x_{20} = -71.2094334813686 x 20 = − 71.2094334813686 x 21 = − 76.4454212373516 x_{21} = -76.4454212373516 x 21 = − 76.4454212373516 x 22 = 23.0383461263252 x_{22} = 23.0383461263252 x 22 = 23.0383461263252 x 23 = 74.3510261349584 x_{23} = 74.3510261349584 x 23 = 74.3510261349584 x 24 = 16.7551608191456 x_{24} = 16.7551608191456 x 24 = 16.7551608191456 x 25 = 10.471975511966 x_{25} = 10.471975511966 x 25 = 10.471975511966 x 26 = − 38.7463093942741 x_{26} = -38.7463093942741 x 26 = − 38.7463093942741 x 27 = 42.9350995990605 x_{27} = 42.9350995990605 x 27 = 42.9350995990605 x 28 = − 70.162235930172 x_{28} = -70.162235930172 x 28 = − 70.162235930172 x 29 = − 7.33038285837618 x_{29} = -7.33038285837618 x 29 = − 7.33038285837618 x 30 = 68.0678408277789 x_{30} = 68.0678408277789 x 30 = 68.0678408277789 x 31 = − 64.9262481741891 x_{31} = -64.9262481741891 x 31 = − 64.9262481741891 x 32 = − 51.3126800086333 x_{32} = -51.3126800086333 x 32 = − 51.3126800086333 x 33 = − 58.6430628670095 x_{33} = -58.6430628670095 x 33 = − 58.6430628670095 x 34 = 29.3215314335047 x_{34} = 29.3215314335047 x 34 = 29.3215314335047 x 35 = 55.5014702134197 x_{35} = 55.5014702134197 x 35 = 55.5014702134197 x 36 = − 27.2271363311115 x_{36} = -27.2271363311115 x 36 = − 27.2271363311115 x 37 = 93.2005820564972 x_{37} = 93.2005820564972 x 37 = 93.2005820564972 x 38 = − 33.5103216382911 x_{38} = -33.5103216382911 x 38 = − 33.5103216382911 x 39 = 30.3687289847013 x_{39} = 30.3687289847013 x 39 = 30.3687289847013 x 40 = − 151.843644923507 x_{40} = -151.843644923507 x 40 = − 151.843644923507 x 41 = 11.5191730631626 x_{41} = 11.5191730631626 x 41 = 11.5191730631626 x 42 = 4.18879020478639 x_{42} = 4.18879020478639 x 42 = 4.18879020478639 x 43 = − 90.0589894029074 x_{43} = -90.0589894029074 x 43 = − 90.0589894029074 x 44 = − 13.6135681655558 x_{44} = -13.6135681655558 x 44 = − 13.6135681655558 x 45 = − 20.943951023932 x_{45} = -20.943951023932 x 45 = − 20.943951023932 x 46 = 36.6519142918809 x_{46} = 36.6519142918809 x 46 = 36.6519142918809 x 47 = − 11851.1346868919 x_{47} = -11851.1346868919 x 47 = − 11851.1346868919 x 48 = − 1559.27715373173 x_{48} = -1559.27715373173 x 48 = − 1559.27715373173 x 49 = 79.5870138909414 x_{49} = 79.5870138909414 x 49 = 79.5870138909414 x 50 = 61.7846555205993 x_{50} = 61.7846555205993 x 50 = 61.7846555205993 x 51 = 73.3038285837618 x_{51} = 73.3038285837618 x 51 = 73.3038285837618 x 52 = − 26.1799387799149 x_{52} = -26.1799387799149 x 52 = − 26.1799387799149 x 53 = 85.870199198121 x_{53} = 85.870199198121 x 53 = 85.870199198121 x 54 = − 82.7286065445312 x_{54} = -82.7286065445312 x 54 = − 82.7286065445312 x 55 = 98.4365698124802 x_{55} = 98.4365698124802 x 55 = 98.4365698124802 x 56 = − 5606.69568910658 x_{56} = -5606.69568910658 x 56 = − 5606.69568910658 x 57 = − 77.4926187885482 x_{57} = -77.4926187885482 x 57 = − 77.4926187885482 x 58 = 48.1710873550435 x_{58} = 48.1710873550435 x 58 = 48.1710873550435 x 59 = 41.8879020478639 x_{59} = 41.8879020478639 x 59 = 41.8879020478639 x 60 = − 57.5958653158129 x_{60} = -57.5958653158129 x 60 = − 57.5958653158129 x 61 = 393.746279249921 x_{61} = 393.746279249921 x 61 = 393.746279249921 x 62 = 35.6047167406843 x_{62} = 35.6047167406843 x 62 = 35.6047167406843 x 63 = 17.8023583703422 x_{63} = 17.8023583703422 x 63 = 17.8023583703422 x 64 = − 1.0471975511966 x_{64} = -1.0471975511966 x 64 = − 1.0471975511966 x 65 = 99.4837673636768 x_{65} = 99.4837673636768 x 65 = 99.4837673636768 x 66 = − 96.342174710087 x_{66} = -96.342174710087 x 66 = − 96.342174710087 x 67 = 92.1533845053006 x_{67} = 92.1533845053006 x 67 = 92.1533845053006 x 68 = 67.0206432765823 x_{68} = 67.0206432765823 x 68 = 67.0206432765823 x 69 = 80.634211442138 x_{69} = 80.634211442138 x 69 = 80.634211442138 x 70 = − 52.3598775598299 x_{70} = -52.3598775598299 x 70 = − 52.3598775598299 x 71 = − 39.7935069454707 x_{71} = -39.7935069454707 x 71 = − 39.7935069454707 x 1 = − 19.8967534727354 x_{1} = -19.8967534727354 x 1 = − 19.8967534727354 x 2 = 24.0855436775217 x_{2} = 24.0855436775217 x 2 = 24.0855436775217 x 3 = − 101.57816246607 x_{3} = -101.57816246607 x 3 = − 101.57816246607 x 4 = − 95.2949771588904 x_{4} = -95.2949771588904 x 4 = − 95.2949771588904 x 5 = − 89.0117918517108 x_{5} = -89.0117918517108 x 5 = − 89.0117918517108 x 6 = − 2.0943951023932 x_{6} = -2.0943951023932 x 6 = − 2.0943951023932 x 7 = 49.2182849062401 x_{7} = 49.2182849062401 x 7 = 49.2182849062401 x 8 = − 14.6607657167524 x_{8} = -14.6607657167524 x 8 = − 14.6607657167524 x 9 = 86.9173967493176 x_{9} = 86.9173967493176 x 9 = 86.9173967493176 x 10 = − 45.0294947014537 x_{10} = -45.0294947014537 x 10 = − 45.0294947014537 x 11 = 54.4542726622231 x_{11} = 54.4542726622231 x 11 = 54.4542726622231 x 12 = − 46.0766922526503 x_{12} = -46.0766922526503 x 12 = − 46.0766922526503 x 13 = − 63.8790506229925 x_{13} = -63.8790506229925 x 13 = − 63.8790506229925 x 14 = − 8.37758040957278 x_{14} = -8.37758040957278 x 14 = − 8.37758040957278 x 15 = − 32.4631240870945 x_{15} = -32.4631240870945 x 15 = − 32.4631240870945 x 16 = − 114.144533080429 x_{16} = -114.144533080429 x 16 = − 114.144533080429 x 17 = 5.23598775598299 x_{17} = 5.23598775598299 x 17 = 5.23598775598299 x 18 = − 83.7758040957278 x_{18} = -83.7758040957278 x 18 = − 83.7758040957278 x 19 = 60.7374579694027 x_{19} = 60.7374579694027 x 19 = 60.7374579694027 x 20 = − 71.2094334813686 x_{20} = -71.2094334813686 x 20 = − 71.2094334813686 x 21 = − 76.4454212373516 x_{21} = -76.4454212373516 x 21 = − 76.4454212373516 x 22 = 23.0383461263252 x_{22} = 23.0383461263252 x 22 = 23.0383461263252 x 23 = 74.3510261349584 x_{23} = 74.3510261349584 x 23 = 74.3510261349584 x 24 = 16.7551608191456 x_{24} = 16.7551608191456 x 24 = 16.7551608191456 x 25 = 10.471975511966 x_{25} = 10.471975511966 x 25 = 10.471975511966 x 26 = − 38.7463093942741 x_{26} = -38.7463093942741 x 26 = − 38.7463093942741 x 27 = 42.9350995990605 x_{27} = 42.9350995990605 x 27 = 42.9350995990605 x 28 = − 70.162235930172 x_{28} = -70.162235930172 x 28 = − 70.162235930172 x 29 = − 7.33038285837618 x_{29} = -7.33038285837618 x 29 = − 7.33038285837618 x 30 = 68.0678408277789 x_{30} = 68.0678408277789 x 30 = 68.0678408277789 x 31 = − 64.9262481741891 x_{31} = -64.9262481741891 x 31 = − 64.9262481741891 x 32 = − 51.3126800086333 x_{32} = -51.3126800086333 x 32 = − 51.3126800086333 x 33 = − 58.6430628670095 x_{33} = -58.6430628670095 x 33 = − 58.6430628670095 x 34 = 29.3215314335047 x_{34} = 29.3215314335047 x 34 = 29.3215314335047 x 35 = 55.5014702134197 x_{35} = 55.5014702134197 x 35 = 55.5014702134197 x 36 = − 27.2271363311115 x_{36} = -27.2271363311115 x 36 = − 27.2271363311115 x 37 = 93.2005820564972 x_{37} = 93.2005820564972 x 37 = 93.2005820564972 x 38 = − 33.5103216382911 x_{38} = -33.5103216382911 x 38 = − 33.5103216382911 x 39 = 30.3687289847013 x_{39} = 30.3687289847013 x 39 = 30.3687289847013 x 40 = − 151.843644923507 x_{40} = -151.843644923507 x 40 = − 151.843644923507 x 41 = 11.5191730631626 x_{41} = 11.5191730631626 x 41 = 11.5191730631626 x 42 = 4.18879020478639 x_{42} = 4.18879020478639 x 42 = 4.18879020478639 x 43 = − 90.0589894029074 x_{43} = -90.0589894029074 x 43 = − 90.0589894029074 x 44 = − 13.6135681655558 x_{44} = -13.6135681655558 x 44 = − 13.6135681655558 x 45 = − 20.943951023932 x_{45} = -20.943951023932 x 45 = − 20.943951023932 x 46 = 36.6519142918809 x_{46} = 36.6519142918809 x 46 = 36.6519142918809 x 47 = − 11851.1346868919 x_{47} = -11851.1346868919 x 47 = − 11851.1346868919 x 48 = − 1559.27715373173 x_{48} = -1559.27715373173 x 48 = − 1559.27715373173 x 49 = 79.5870138909414 x_{49} = 79.5870138909414 x 49 = 79.5870138909414 x 50 = 61.7846555205993 x_{50} = 61.7846555205993 x 50 = 61.7846555205993 x 51 = 73.3038285837618 x_{51} = 73.3038285837618 x 51 = 73.3038285837618 x 52 = − 26.1799387799149 x_{52} = -26.1799387799149 x 52 = − 26.1799387799149 x 53 = 85.870199198121 x_{53} = 85.870199198121 x 53 = 85.870199198121 x 54 = − 82.7286065445312 x_{54} = -82.7286065445312 x 54 = − 82.7286065445312 x 55 = 98.4365698124802 x_{55} = 98.4365698124802 x 55 = 98.4365698124802 x 56 = − 5606.69568910658 x_{56} = -5606.69568910658 x 56 = − 5606.69568910658 x 57 = − 77.4926187885482 x_{57} = -77.4926187885482 x 57 = − 77.4926187885482 x 58 = 48.1710873550435 x_{58} = 48.1710873550435 x 58 = 48.1710873550435 x 59 = 41.8879020478639 x_{59} = 41.8879020478639 x 59 = 41.8879020478639 x 60 = − 57.5958653158129 x_{60} = -57.5958653158129 x 60 = − 57.5958653158129 x 61 = 393.746279249921 x_{61} = 393.746279249921 x 61 = 393.746279249921 x 62 = 35.6047167406843 x_{62} = 35.6047167406843 x 62 = 35.6047167406843 x 63 = 17.8023583703422 x_{63} = 17.8023583703422 x 63 = 17.8023583703422 x 64 = − 1.0471975511966 x_{64} = -1.0471975511966 x 64 = − 1.0471975511966 x 65 = 99.4837673636768 x_{65} = 99.4837673636768 x 65 = 99.4837673636768 x 66 = − 96.342174710087 x_{66} = -96.342174710087 x 66 = − 96.342174710087 x 67 = 92.1533845053006 x_{67} = 92.1533845053006 x 67 = 92.1533845053006 x 68 = 67.0206432765823 x_{68} = 67.0206432765823 x 68 = 67.0206432765823 x 69 = 80.634211442138 x_{69} = 80.634211442138 x 69 = 80.634211442138 x 70 = − 52.3598775598299 x_{70} = -52.3598775598299 x 70 = − 52.3598775598299 x 71 = − 39.7935069454707 x_{71} = -39.7935069454707 x 71 = − 39.7935069454707 This roots
x 47 = − 11851.1346868919 x_{47} = -11851.1346868919 x 47 = − 11851.1346868919 x 56 = − 5606.69568910658 x_{56} = -5606.69568910658 x 56 = − 5606.69568910658 x 48 = − 1559.27715373173 x_{48} = -1559.27715373173 x 48 = − 1559.27715373173 x 40 = − 151.843644923507 x_{40} = -151.843644923507 x 40 = − 151.843644923507 x 16 = − 114.144533080429 x_{16} = -114.144533080429 x 16 = − 114.144533080429 x 3 = − 101.57816246607 x_{3} = -101.57816246607 x 3 = − 101.57816246607 x 66 = − 96.342174710087 x_{66} = -96.342174710087 x 66 = − 96.342174710087 x 4 = − 95.2949771588904 x_{4} = -95.2949771588904 x 4 = − 95.2949771588904 x 43 = − 90.0589894029074 x_{43} = -90.0589894029074 x 43 = − 90.0589894029074 x 5 = − 89.0117918517108 x_{5} = -89.0117918517108 x 5 = − 89.0117918517108 x 18 = − 83.7758040957278 x_{18} = -83.7758040957278 x 18 = − 83.7758040957278 x 54 = − 82.7286065445312 x_{54} = -82.7286065445312 x 54 = − 82.7286065445312 x 57 = − 77.4926187885482 x_{57} = -77.4926187885482 x 57 = − 77.4926187885482 x 21 = − 76.4454212373516 x_{21} = -76.4454212373516 x 21 = − 76.4454212373516 x 20 = − 71.2094334813686 x_{20} = -71.2094334813686 x 20 = − 71.2094334813686 x 28 = − 70.162235930172 x_{28} = -70.162235930172 x 28 = − 70.162235930172 x 31 = − 64.9262481741891 x_{31} = -64.9262481741891 x 31 = − 64.9262481741891 x 13 = − 63.8790506229925 x_{13} = -63.8790506229925 x 13 = − 63.8790506229925 x 33 = − 58.6430628670095 x_{33} = -58.6430628670095 x 33 = − 58.6430628670095 x 60 = − 57.5958653158129 x_{60} = -57.5958653158129 x 60 = − 57.5958653158129 x 70 = − 52.3598775598299 x_{70} = -52.3598775598299 x 70 = − 52.3598775598299 x 32 = − 51.3126800086333 x_{32} = -51.3126800086333 x 32 = − 51.3126800086333 x 12 = − 46.0766922526503 x_{12} = -46.0766922526503 x 12 = − 46.0766922526503 x 10 = − 45.0294947014537 x_{10} = -45.0294947014537 x 10 = − 45.0294947014537 x 71 = − 39.7935069454707 x_{71} = -39.7935069454707 x 71 = − 39.7935069454707 x 26 = − 38.7463093942741 x_{26} = -38.7463093942741 x 26 = − 38.7463093942741 x 38 = − 33.5103216382911 x_{38} = -33.5103216382911 x 38 = − 33.5103216382911 x 15 = − 32.4631240870945 x_{15} = -32.4631240870945 x 15 = − 32.4631240870945 x 36 = − 27.2271363311115 x_{36} = -27.2271363311115 x 36 = − 27.2271363311115 x 52 = − 26.1799387799149 x_{52} = -26.1799387799149 x 52 = − 26.1799387799149 x 45 = − 20.943951023932 x_{45} = -20.943951023932 x 45 = − 20.943951023932 x 1 = − 19.8967534727354 x_{1} = -19.8967534727354 x 1 = − 19.8967534727354 x 8 = − 14.6607657167524 x_{8} = -14.6607657167524 x 8 = − 14.6607657167524 x 44 = − 13.6135681655558 x_{44} = -13.6135681655558 x 44 = − 13.6135681655558 x 14 = − 8.37758040957278 x_{14} = -8.37758040957278 x 14 = − 8.37758040957278 x 29 = − 7.33038285837618 x_{29} = -7.33038285837618 x 29 = − 7.33038285837618 x 6 = − 2.0943951023932 x_{6} = -2.0943951023932 x 6 = − 2.0943951023932 x 64 = − 1.0471975511966 x_{64} = -1.0471975511966 x 64 = − 1.0471975511966 x 42 = 4.18879020478639 x_{42} = 4.18879020478639 x 42 = 4.18879020478639 x 17 = 5.23598775598299 x_{17} = 5.23598775598299 x 17 = 5.23598775598299 x 25 = 10.471975511966 x_{25} = 10.471975511966 x 25 = 10.471975511966 x 41 = 11.5191730631626 x_{41} = 11.5191730631626 x 41 = 11.5191730631626 x 24 = 16.7551608191456 x_{24} = 16.7551608191456 x 24 = 16.7551608191456 x 63 = 17.8023583703422 x_{63} = 17.8023583703422 x 63 = 17.8023583703422 x 22 = 23.0383461263252 x_{22} = 23.0383461263252 x 22 = 23.0383461263252 x 2 = 24.0855436775217 x_{2} = 24.0855436775217 x 2 = 24.0855436775217 x 34 = 29.3215314335047 x_{34} = 29.3215314335047 x 34 = 29.3215314335047 x 39 = 30.3687289847013 x_{39} = 30.3687289847013 x 39 = 30.3687289847013 x 62 = 35.6047167406843 x_{62} = 35.6047167406843 x 62 = 35.6047167406843 x 46 = 36.6519142918809 x_{46} = 36.6519142918809 x 46 = 36.6519142918809 x 59 = 41.8879020478639 x_{59} = 41.8879020478639 x 59 = 41.8879020478639 x 27 = 42.9350995990605 x_{27} = 42.9350995990605 x 27 = 42.9350995990605 x 58 = 48.1710873550435 x_{58} = 48.1710873550435 x 58 = 48.1710873550435 x 7 = 49.2182849062401 x_{7} = 49.2182849062401 x 7 = 49.2182849062401 x 11 = 54.4542726622231 x_{11} = 54.4542726622231 x 11 = 54.4542726622231 x 35 = 55.5014702134197 x_{35} = 55.5014702134197 x 35 = 55.5014702134197 x 19 = 60.7374579694027 x_{19} = 60.7374579694027 x 19 = 60.7374579694027 x 50 = 61.7846555205993 x_{50} = 61.7846555205993 x 50 = 61.7846555205993 x 68 = 67.0206432765823 x_{68} = 67.0206432765823 x 68 = 67.0206432765823 x 30 = 68.0678408277789 x_{30} = 68.0678408277789 x 30 = 68.0678408277789 x 51 = 73.3038285837618 x_{51} = 73.3038285837618 x 51 = 73.3038285837618 x 23 = 74.3510261349584 x_{23} = 74.3510261349584 x 23 = 74.3510261349584 x 49 = 79.5870138909414 x_{49} = 79.5870138909414 x 49 = 79.5870138909414 x 69 = 80.634211442138 x_{69} = 80.634211442138 x 69 = 80.634211442138 x 53 = 85.870199198121 x_{53} = 85.870199198121 x 53 = 85.870199198121 x 9 = 86.9173967493176 x_{9} = 86.9173967493176 x 9 = 86.9173967493176 x 67 = 92.1533845053006 x_{67} = 92.1533845053006 x 67 = 92.1533845053006 x 37 = 93.2005820564972 x_{37} = 93.2005820564972 x 37 = 93.2005820564972 x 55 = 98.4365698124802 x_{55} = 98.4365698124802 x 55 = 98.4365698124802 x 65 = 99.4837673636768 x_{65} = 99.4837673636768 x 65 = 99.4837673636768 x 61 = 393.746279249921 x_{61} = 393.746279249921 x 61 = 393.746279249921 is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
x 0 < x 47 x_{0} < x_{47} x 0 < x 47 For example, let's take the point
x 0 = x 47 − 1 10 x_{0} = x_{47} - \frac{1}{10} x 0 = x 47 − 10 1 =
− 11851.1346868919 − 1 10 -11851.1346868919 - \frac{1}{10} − 11851.1346868919 − 10 1 =
− 11851.2346868919 -11851.2346868919 − 11851.2346868919 substitute to the expression
sin ( t ) < ( − 1 ) 3 2 \sin{\left(t \right)} < \frac{\left(-1\right) \sqrt{3}}{2} sin ( t ) < 2 ( − 1 ) 3 sin ( t ) < ( − 1 ) 3 2 \sin{\left(t \right)} < \frac{\left(-1\right) \sqrt{3}}{2} sin ( t ) < 2 ( − 1 ) 3 ___
-\/ 3
sin(t) < -------
2
Then
x < − 11851.1346868919 x < -11851.1346868919 x < − 11851.1346868919 no execute
one of the solutions of our inequality is:
x > − 11851.1346868919 ∧ x < − 5606.69568910658 x > -11851.1346868919 \wedge x < -5606.69568910658 x > − 11851.1346868919 ∧ x < − 5606.69568910658 _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------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-------
x_47 x_56 x_48 x_40 x_16 x_3 x_66 x_4 x_43 x_5 x_18 x_54 x_57 x_21 x_20 x_28 x_31 x_13 x_33 x_60 x_70 x_32 x_12 x_10 x_71 x_26 x_38 x_15 x_36 x_52 x_45 x_1 x_8 x_44 x_14 x_29 x_6 x_64 x_42 x_17 x_25 x_41 x_24 x_63 x_22 x_2 x_34 x_39 x_62 x_46 x_59 x_27 x_58 x_7 x_11 x_35 x_19 x_50 x_68 x_30 x_51 x_23 x_49 x_69 x_53 x_9 x_67 x_37 x_55 x_65 x_61 Other solutions will get with the changeover to the next point
etc.
The answer:
x > − 11851.1346868919 ∧ x < − 5606.69568910658 x > -11851.1346868919 \wedge x < -5606.69568910658 x > − 11851.1346868919 ∧ x < − 5606.69568910658 x > − 1559.27715373173 ∧ x < − 151.843644923507 x > -1559.27715373173 \wedge x < -151.843644923507 x > − 1559.27715373173 ∧ x < − 151.843644923507 x > − 114.144533080429 ∧ x < − 101.57816246607 x > -114.144533080429 \wedge x < -101.57816246607 x > − 114.144533080429 ∧ x < − 101.57816246607 x > − 96.342174710087 ∧ x < − 95.2949771588904 x > -96.342174710087 \wedge x < -95.2949771588904 x > − 96.342174710087 ∧ x < − 95.2949771588904 x > − 90.0589894029074 ∧ x < − 89.0117918517108 x > -90.0589894029074 \wedge x < -89.0117918517108 x > − 90.0589894029074 ∧ x < − 89.0117918517108 x > − 83.7758040957278 ∧ x < − 82.7286065445312 x > -83.7758040957278 \wedge x < -82.7286065445312 x > − 83.7758040957278 ∧ x < − 82.7286065445312 x > − 77.4926187885482 ∧ x < − 76.4454212373516 x > -77.4926187885482 \wedge x < -76.4454212373516 x > − 77.4926187885482 ∧ x < − 76.4454212373516 x > − 71.2094334813686 ∧ x < − 70.162235930172 x > -71.2094334813686 \wedge x < -70.162235930172 x > − 71.2094334813686 ∧ x < − 70.162235930172 x > − 64.9262481741891 ∧ x < − 63.8790506229925 x > -64.9262481741891 \wedge x < -63.8790506229925 x > − 64.9262481741891 ∧ x < − 63.8790506229925 x > − 58.6430628670095 ∧ x < − 57.5958653158129 x > -58.6430628670095 \wedge x < -57.5958653158129 x > − 58.6430628670095 ∧ x < − 57.5958653158129 x > − 52.3598775598299 ∧ x < − 51.3126800086333 x > -52.3598775598299 \wedge x < -51.3126800086333 x > − 52.3598775598299 ∧ x < − 51.3126800086333 x > − 46.0766922526503 ∧ x < − 45.0294947014537 x > -46.0766922526503 \wedge x < -45.0294947014537 x > − 46.0766922526503 ∧ x < − 45.0294947014537 x > − 39.7935069454707 ∧ x < − 38.7463093942741 x > -39.7935069454707 \wedge x < -38.7463093942741 x > − 39.7935069454707 ∧ x < − 38.7463093942741 x > − 33.5103216382911 ∧ x < − 32.4631240870945 x > -33.5103216382911 \wedge x < -32.4631240870945 x > − 33.5103216382911 ∧ x < − 32.4631240870945 x > − 27.2271363311115 ∧ x < − 26.1799387799149 x > -27.2271363311115 \wedge x < -26.1799387799149 x > − 27.2271363311115 ∧ x < − 26.1799387799149 x > − 20.943951023932 ∧ x < − 19.8967534727354 x > -20.943951023932 \wedge x < -19.8967534727354 x > − 20.943951023932 ∧ x < − 19.8967534727354 x > − 14.6607657167524 ∧ x < − 13.6135681655558 x > -14.6607657167524 \wedge x < -13.6135681655558 x > − 14.6607657167524 ∧ x < − 13.6135681655558 x > − 8.37758040957278 ∧ x < − 7.33038285837618 x > -8.37758040957278 \wedge x < -7.33038285837618 x > − 8.37758040957278 ∧ x < − 7.33038285837618 x > − 2.0943951023932 ∧ x < − 1.0471975511966 x > -2.0943951023932 \wedge x < -1.0471975511966 x > − 2.0943951023932 ∧ x < − 1.0471975511966 x > 4.18879020478639 ∧ x < 5.23598775598299 x > 4.18879020478639 \wedge x < 5.23598775598299 x > 4.18879020478639 ∧ x < 5.23598775598299 x > 10.471975511966 ∧ x < 11.5191730631626 x > 10.471975511966 \wedge x < 11.5191730631626 x > 10.471975511966 ∧ x < 11.5191730631626 x > 16.7551608191456 ∧ x < 17.8023583703422 x > 16.7551608191456 \wedge x < 17.8023583703422 x > 16.7551608191456 ∧ x < 17.8023583703422 x > 23.0383461263252 ∧ x < 24.0855436775217 x > 23.0383461263252 \wedge x < 24.0855436775217 x > 23.0383461263252 ∧ x < 24.0855436775217 x > 29.3215314335047 ∧ x < 30.3687289847013 x > 29.3215314335047 \wedge x < 30.3687289847013 x > 29.3215314335047 ∧ x < 30.3687289847013 x > 35.6047167406843 ∧ x < 36.6519142918809 x > 35.6047167406843 \wedge x < 36.6519142918809 x > 35.6047167406843 ∧ x < 36.6519142918809 x > 41.8879020478639 ∧ x < 42.9350995990605 x > 41.8879020478639 \wedge x < 42.9350995990605 x > 41.8879020478639 ∧ x < 42.9350995990605 x > 48.1710873550435 ∧ x < 49.2182849062401 x > 48.1710873550435 \wedge x < 49.2182849062401 x > 48.1710873550435 ∧ x < 49.2182849062401 x > 54.4542726622231 ∧ x < 55.5014702134197 x > 54.4542726622231 \wedge x < 55.5014702134197 x > 54.4542726622231 ∧ x < 55.5014702134197 x > 60.7374579694027 ∧ x < 61.7846555205993 x > 60.7374579694027 \wedge x < 61.7846555205993 x > 60.7374579694027 ∧ x < 61.7846555205993 x > 67.0206432765823 ∧ x < 68.0678408277789 x > 67.0206432765823 \wedge x < 68.0678408277789 x > 67.0206432765823 ∧ x < 68.0678408277789 x > 73.3038285837618 ∧ x < 74.3510261349584 x > 73.3038285837618 \wedge x < 74.3510261349584 x > 73.3038285837618 ∧ x < 74.3510261349584 x > 79.5870138909414 ∧ x < 80.634211442138 x > 79.5870138909414 \wedge x < 80.634211442138 x > 79.5870138909414 ∧ x < 80.634211442138 x > 85.870199198121 ∧ x < 86.9173967493176 x > 85.870199198121 \wedge x < 86.9173967493176 x > 85.870199198121 ∧ x < 86.9173967493176 x > 92.1533845053006 ∧ x < 93.2005820564972 x > 92.1533845053006 \wedge x < 93.2005820564972 x > 92.1533845053006 ∧ x < 93.2005820564972 x > 98.4365698124802 ∧ x < 99.4837673636768 x > 98.4365698124802 \wedge x < 99.4837673636768 x > 98.4365698124802 ∧ x < 99.4837673636768 x > 393.746279249921 x > 393.746279249921 x > 393.746279249921 
sint
sint