ctgt<=-√3 desigualdades

Se da la desigualdad:
$$\cot{\left(t \right)} \leq - \sqrt{3}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\cot{\left(t \right)} = - \sqrt{3}$$
Resolvemos:
$$x_{1} = 62.3082542961976$$
$$x_{2} = 24.60914245312$$
$$x_{3} = -60.2138591938044$$
$$x_{4} = 27.7507351067098$$
$$x_{5} = -47.6474885794452$$
$$x_{6} = 93.7241808320955$$
$$x_{7} = 43.4586983746588$$
$$x_{8} = 84.2994028713261$$
$$x_{9} = 74.8746249105567$$
$$x_{10} = 56.025068989018$$
$$x_{11} = -31.9395253114962$$
$$x_{12} = -3.66519142918809$$
$$x_{13} = 46.6002910282486$$
$$x_{14} = 34.0339204138894$$
$$x_{15} = -63.3554518473942$$
$$x_{16} = 90.5825881785057$$
$$x_{17} = -82.2050077689329$$
$$x_{18} = 71.733032256967$$
$$x_{19} = -41.3643032722656$$
$$x_{20} = -9.94837673636768$$
$$x_{21} = -69.6386371545737$$
$$x_{22} = -97.9129710368819$$
$$x_{23} = -94.7713783832921$$
$$x_{24} = 87.4409955249159$$
$$x_{25} = 52.8834763354282$$
$$x_{26} = -72.7802298081635$$
$$x_{27} = -19.3731546971371$$
$$x_{28} = -53.9306738866248$$
$$x_{29} = 68.5914396033772$$
$$x_{30} = 40.317105721069$$
$$x_{31} = 96.8657734856853$$
$$x_{32} = 65.4498469497874$$
$$x_{33} = 78.0162175641465$$
$$x_{34} = -16.2315620435473$$
$$x_{35} = -38.2227106186758$$
$$x_{36} = -75.9218224617533$$
$$x_{37} = -13.0899693899575$$
$$x_{38} = -25.6563400043166$$
$$x_{39} = 81.1578102177363$$
$$x_{40} = -85.3466004225227$$
$$x_{41} = 37.1755130674792$$
$$x_{42} = 100.007366139275$$
$$x_{43} = -22.5147473507269$$
$$x_{44} = 8.90117918517108$$
$$x_{45} = 49.7418836818384$$
$$x_{46} = -28.7979326579064$$
$$x_{47} = 18.3259571459405$$
$$x_{48} = 5.75958653158129$$
$$x_{49} = 15.1843644923507$$
$$x_{50} = -0.523598775598299$$
$$x_{51} = 21.4675497995303$$
$$x_{52} = 59.1666616426078$$
$$x_{53} = -6.80678408277789$$
$$x_{54} = -91.6297857297023$$
$$x_{55} = -79.0634151153431$$
$$x_{56} = -57.0722665402146$$
$$x_{57} = -88.4881930761125$$
$$x_{58} = 2.61799387799149$$
$$x_{59} = 30.8923277602996$$
$$x_{60} = -50.789081233035$$
$$x_{61} = -66.497044500984$$
$$x_{62} = 12.0427718387609$$
$$x_{63} = -44.5058959258554$$
$$x_{1} = 62.3082542961976$$
$$x_{2} = 24.60914245312$$
$$x_{3} = -60.2138591938044$$
$$x_{4} = 27.7507351067098$$
$$x_{5} = -47.6474885794452$$
$$x_{6} = 93.7241808320955$$
$$x_{7} = 43.4586983746588$$
$$x_{8} = 84.2994028713261$$
$$x_{9} = 74.8746249105567$$
$$x_{10} = 56.025068989018$$
$$x_{11} = -31.9395253114962$$
$$x_{12} = -3.66519142918809$$
$$x_{13} = 46.6002910282486$$
$$x_{14} = 34.0339204138894$$
$$x_{15} = -63.3554518473942$$
$$x_{16} = 90.5825881785057$$
$$x_{17} = -82.2050077689329$$
$$x_{18} = 71.733032256967$$
$$x_{19} = -41.3643032722656$$
$$x_{20} = -9.94837673636768$$
$$x_{21} = -69.6386371545737$$
$$x_{22} = -97.9129710368819$$
$$x_{23} = -94.7713783832921$$
$$x_{24} = 87.4409955249159$$
$$x_{25} = 52.8834763354282$$
$$x_{26} = -72.7802298081635$$
$$x_{27} = -19.3731546971371$$
$$x_{28} = -53.9306738866248$$
$$x_{29} = 68.5914396033772$$
$$x_{30} = 40.317105721069$$
$$x_{31} = 96.8657734856853$$
$$x_{32} = 65.4498469497874$$
$$x_{33} = 78.0162175641465$$
$$x_{34} = -16.2315620435473$$
$$x_{35} = -38.2227106186758$$
$$x_{36} = -75.9218224617533$$
$$x_{37} = -13.0899693899575$$
$$x_{38} = -25.6563400043166$$
$$x_{39} = 81.1578102177363$$
$$x_{40} = -85.3466004225227$$
$$x_{41} = 37.1755130674792$$
$$x_{42} = 100.007366139275$$
$$x_{43} = -22.5147473507269$$
$$x_{44} = 8.90117918517108$$
$$x_{45} = 49.7418836818384$$
$$x_{46} = -28.7979326579064$$
$$x_{47} = 18.3259571459405$$
$$x_{48} = 5.75958653158129$$
$$x_{49} = 15.1843644923507$$
$$x_{50} = -0.523598775598299$$
$$x_{51} = 21.4675497995303$$
$$x_{52} = 59.1666616426078$$
$$x_{53} = -6.80678408277789$$
$$x_{54} = -91.6297857297023$$
$$x_{55} = -79.0634151153431$$
$$x_{56} = -57.0722665402146$$
$$x_{57} = -88.4881930761125$$
$$x_{58} = 2.61799387799149$$
$$x_{59} = 30.8923277602996$$
$$x_{60} = -50.789081233035$$
$$x_{61} = -66.497044500984$$
$$x_{62} = 12.0427718387609$$
$$x_{63} = -44.5058959258554$$
Las raíces dadas
$$x_{22} = -97.9129710368819$$
$$x_{23} = -94.7713783832921$$
$$x_{54} = -91.6297857297023$$
$$x_{57} = -88.4881930761125$$
$$x_{40} = -85.3466004225227$$
$$x_{17} = -82.2050077689329$$
$$x_{55} = -79.0634151153431$$
$$x_{36} = -75.9218224617533$$
$$x_{26} = -72.7802298081635$$
$$x_{21} = -69.6386371545737$$
$$x_{61} = -66.497044500984$$
$$x_{15} = -63.3554518473942$$
$$x_{3} = -60.2138591938044$$
$$x_{56} = -57.0722665402146$$
$$x_{28} = -53.9306738866248$$
$$x_{60} = -50.789081233035$$
$$x_{5} = -47.6474885794452$$
$$x_{63} = -44.5058959258554$$
$$x_{19} = -41.3643032722656$$
$$x_{35} = -38.2227106186758$$
$$x_{11} = -31.9395253114962$$
$$x_{46} = -28.7979326579064$$
$$x_{38} = -25.6563400043166$$
$$x_{43} = -22.5147473507269$$
$$x_{27} = -19.3731546971371$$
$$x_{34} = -16.2315620435473$$
$$x_{37} = -13.0899693899575$$
$$x_{20} = -9.94837673636768$$
$$x_{53} = -6.80678408277789$$
$$x_{12} = -3.66519142918809$$
$$x_{50} = -0.523598775598299$$
$$x_{58} = 2.61799387799149$$
$$x_{48} = 5.75958653158129$$
$$x_{44} = 8.90117918517108$$
$$x_{62} = 12.0427718387609$$
$$x_{49} = 15.1843644923507$$
$$x_{47} = 18.3259571459405$$
$$x_{51} = 21.4675497995303$$
$$x_{2} = 24.60914245312$$
$$x_{4} = 27.7507351067098$$
$$x_{59} = 30.8923277602996$$
$$x_{14} = 34.0339204138894$$
$$x_{41} = 37.1755130674792$$
$$x_{30} = 40.317105721069$$
$$x_{7} = 43.4586983746588$$
$$x_{13} = 46.6002910282486$$
$$x_{45} = 49.7418836818384$$
$$x_{25} = 52.8834763354282$$
$$x_{10} = 56.025068989018$$
$$x_{52} = 59.1666616426078$$
$$x_{1} = 62.3082542961976$$
$$x_{32} = 65.4498469497874$$
$$x_{29} = 68.5914396033772$$
$$x_{18} = 71.733032256967$$
$$x_{9} = 74.8746249105567$$
$$x_{33} = 78.0162175641465$$
$$x_{39} = 81.1578102177363$$
$$x_{8} = 84.2994028713261$$
$$x_{24} = 87.4409955249159$$
$$x_{16} = 90.5825881785057$$
$$x_{6} = 93.7241808320955$$
$$x_{31} = 96.8657734856853$$
$$x_{42} = 100.007366139275$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{22}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{22} - \frac{1}{10}$$
=
$$-97.9129710368819 + - \frac{1}{10}$$
=
$$-98.0129710368819$$
lo sustituimos en la expresión
$$\cot{\left(t \right)} \leq - \sqrt{3}$$
$$\cot{\left(t \right)} \leq - \sqrt{3}$$

             ___
cot(t) <= -\/ 3 
          

Entonces
$$x \leq -97.9129710368819$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -97.9129710368819 \wedge x \leq -94.7713783832921$$

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Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -97.9129710368819 \wedge x \leq -94.7713783832921$$
$$x \geq -91.6297857297023 \wedge x \leq -88.4881930761125$$
$$x \geq -85.3466004225227 \wedge x \leq -82.2050077689329$$
$$x \geq -79.0634151153431 \wedge x \leq -75.9218224617533$$
$$x \geq -72.7802298081635 \wedge x \leq -69.6386371545737$$
$$x \geq -66.497044500984 \wedge x \leq -63.3554518473942$$
$$x \geq -60.2138591938044 \wedge x \leq -57.0722665402146$$
$$x \geq -53.9306738866248 \wedge x \leq -50.789081233035$$
$$x \geq -47.6474885794452 \wedge x \leq -44.5058959258554$$
$$x \geq -41.3643032722656 \wedge x \leq -38.2227106186758$$
$$x \geq -31.9395253114962 \wedge x \leq -28.7979326579064$$
$$x \geq -25.6563400043166 \wedge x \leq -22.5147473507269$$
$$x \geq -19.3731546971371 \wedge x \leq -16.2315620435473$$
$$x \geq -13.0899693899575 \wedge x \leq -9.94837673636768$$
$$x \geq -6.80678408277789 \wedge x \leq -3.66519142918809$$
$$x \geq -0.523598775598299 \wedge x \leq 2.61799387799149$$
$$x \geq 5.75958653158129 \wedge x \leq 8.90117918517108$$
$$x \geq 12.0427718387609 \wedge x \leq 15.1843644923507$$
$$x \geq 18.3259571459405 \wedge x \leq 21.4675497995303$$
$$x \geq 24.60914245312 \wedge x \leq 27.7507351067098$$
$$x \geq 30.8923277602996 \wedge x \leq 34.0339204138894$$
$$x \geq 37.1755130674792 \wedge x \leq 40.317105721069$$
$$x \geq 43.4586983746588 \wedge x \leq 46.6002910282486$$
$$x \geq 49.7418836818384 \wedge x \leq 52.8834763354282$$
$$x \geq 56.025068989018 \wedge x \leq 59.1666616426078$$
$$x \geq 62.3082542961976 \wedge x \leq 65.4498469497874$$
$$x \geq 68.5914396033772 \wedge x \leq 71.733032256967$$
$$x \geq 74.8746249105567 \wedge x \leq 78.0162175641465$$
$$x \geq 81.1578102177363 \wedge x \leq 84.2994028713261$$
$$x \geq 87.4409955249159 \wedge x \leq 90.5825881785057$$
$$x \geq 93.7241808320955 \wedge x \leq 96.8657734856853$$
$$x \geq 100.007366139275$$