76:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000 Trigonometría analítica:@0.073089:0.043661:0.282466:0.043661:0.282466:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Entonces, concluimos que::@0.293660:0.136836:0.487833:0.136836:0.487833:0.120402:0.293660:0.120402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.293660:0.164614:0.302643:0.164614:0.302643:0.148180:0.293660:0.148180:0.000000 senx:@0.302569:0.164614:0.333457:0.164614:0.333457:0.148208:0.302569:0.148208:0.000000:0.000000:0.000000:0.000000 + 1 = 0:@0.333420:0.164614:0.388936:0.164614:0.388936:0.148180:0.333420:0.148180:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 senx:@0.293679:0.187982:0.324566:0.187982:0.324566:0.171576:0.293679:0.171576:0.000000:0.000000:0.000000:0.000000 = :@0.324529:0.187982:0.343415:0.187982:0.343415:0.171548:0.324529:0.171548:0.000000:0.000000:0.000000 1:@0.358176:0.181364:0.367159:0.181364:0.367159:0.164931:0.358176:0.164931:0.000000 2:@0.358176:0.197133:0.367159:0.197133:0.367159:0.180699:0.358176:0.180699:0.000000 –:@0.343284:0.189089:0.352488:0.189089:0.352488:0.171435:0.343284:0.171435:0.000000 x:@0.293658:0.218517:0.301113:0.218517:0.301113:0.202111:0.293658:0.202111:0.000000 = :@0.301040:0.218517:0.319926:0.218517:0.319926:0.202084:0.301040:0.202084:0.000000:0.000000:0.000000 sen:@0.319834:0.218517:0.343340:0.218517:0.343340:0.202111:0.319834:0.202111:0.000000:0.000000:0.000000 –:@0.343294:0.212780:0.348660:0.212780:0.348660:0.202488:0.343294:0.202488:0.000000 1:@0.348606:0.212441:0.353843:0.212441:0.353843:0.202860:0.348606:0.202860:0.000000 1:@0.372473:0.211882:0.381456:0.211882:0.381456:0.195448:0.372473:0.195448:0.000000 2:@0.372473:0.227650:0.381456:0.227650:0.381456:0.211216:0.372473:0.211216:0.000000 –:@0.357590:0.219599:0.366794:0.219599:0.366794:0.201945:0.357590:0.201945:0.000000 x:@0.293660:0.249276:0.301115:0.249276:0.301115:0.232870:0.293660:0.232870:0.000000 = :@0.301005:0.249276:0.319338:0.249276:0.319338:0.232842:0.301005:0.232842:0.000000:0.000000:0.000000 5:@0.319425:0.242401:0.328408:0.242401:0.328408:0.225967:0.319425:0.225967:0.000000 p:@0.328334:0.241846:0.340612:0.241846:0.340612:0.228131:0.328334:0.228131:0.000000 6:@0.325536:0.256533:0.334519:0.256533:0.334519:0.240099:0.325536:0.240099:0.000000 + 2:@0.341698:0.249280:0.368462:0.249280:0.368462:0.232846:0.341698:0.232846:0.000000:0.000000:0.000000:0.000000 p:@0.368333:0.248725:0.380611:0.248725:0.380611:0.235009:0.368333:0.235009:0.000000 k:@0.380445:0.249280:0.388011:0.249280:0.388011:0.232873:0.380445:0.232873:0.000000 , donde :@0.387900:0.249280:0.446343:0.249280:0.446343:0.232846:0.387900:0.232846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k Z:@0.445828:0.249280:0.477728:0.249280:0.477728:0.232873:0.445828:0.232873:0.000000:0.000000:0.000000 ∈:@0.453283:0.249862:0.468616:0.249862:0.468616:0.232208:0.453283:0.232208:0.000000 x:@0.293674:0.280053:0.301128:0.280053:0.301128:0.263647:0.293674:0.263647:0.000000 = :@0.301018:0.280053:0.319352:0.280053:0.319352:0.263619:0.301018:0.263619:0.000000:0.000000:0.000000 7:@0.319425:0.273172:0.328408:0.273172:0.328408:0.256738:0.319425:0.256738:0.000000 p:@0.328334:0.272617:0.340612:0.272617:0.340612:0.258902:0.328334:0.258902:0.000000 6 :@0.325536:0.287304:0.357933:0.287432:0.357933:0.270998:0.325536:0.270870:0.000000:0.000000:0.000000:0.000000 + 2:@0.341698:0.280051:0.368462:0.280051:0.368462:0.263617:0.341698:0.263617:0.000000:0.000000:0.000000:0.000000 p:@0.368333:0.279496:0.380611:0.279496:0.380611:0.265780:0.368333:0.265780:0.000000 k:@0.380445:0.280051:0.388011:0.280051:0.388011:0.263644:0.380445:0.263644:0.000000 , donde :@0.387900:0.280051:0.446343:0.280051:0.446343:0.263617:0.387900:0.263617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k Z:@0.445828:0.280051:0.477728:0.280051:0.477728:0.263644:0.445828:0.263644:0.000000:0.000000:0.000000 ∈:@0.453283:0.280633:0.468616:0.280633:0.468616:0.262979:0.453283:0.262979:0.000000 o :@0.477654:0.232705:0.610131:0.232705:0.610131:0.216271:0.477654:0.216271:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.609837:0.163932:0.618819:0.163932:0.618819:0.147498:0.609837:0.147498:0.000000 senx:@0.618746:0.163932:0.649633:0.163932:0.649633:0.147526:0.618746:0.147526:0.000000:0.000000:0.000000:0.000000 3 = 0:@0.649596:0.163932:0.703327:0.163932:0.703327:0.147498:0.649596:0.147498:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –:@0.653554:0.164515:0.662757:0.164515:0.662757:0.146860:0.653554:0.146860:0.000000 senx:@0.609855:0.196176:0.640742:0.196176:0.640742:0.179770:0.609855:0.179770:0.000000:0.000000:0.000000:0.000000 = :@0.640705:0.196176:0.659591:0.196176:0.659591:0.179742:0.640705:0.179742:0.000000:0.000000:0.000000 3:@0.666168:0.187832:0.675150:0.187832:0.675150:0.171398:0.666168:0.171398:0.000000 2 :@0.666168:0.201964:0.679182:0.201964:0.679182:0.185530:0.666168:0.185530:0.000000:0.000000 x sen:@0.609805:0.228272:0.658786:0.228272:0.658786:0.211866:0.609805:0.211866:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = :@0.620444:0.228272:0.635372:0.228272:0.635372:0.211838:0.620444:0.211838:0.000000:0.000000 –:@0.658736:0.222554:0.664102:0.222554:0.664102:0.212261:0.658736:0.212261:0.000000 1:@0.664048:0.222214:0.669285:0.222214:0.669285:0.212633:0.664048:0.212633:0.000000 :@0.669238:0.228278:0.673270:0.228278:0.673270:0.211844:0.669238:0.211844:0.000000 3:@0.682379:0.220081:0.691362:0.220081:0.691362:0.203647:0.682379:0.203647:0.000000 2:@0.682379:0.235849:0.691362:0.235849:0.691362:0.219415:0.682379:0.219415:0.000000 Solución :@0.609805:0.255641:0.685967:0.255641:0.685967:0.239207:0.609805:0.239207:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.293660:0.260070:0.297691:0.260070:0.297691:0.243636:0.293660:0.243636:0.000000 :@0.353907:0.260070:0.591747:0.260070:0.591747:0.243636:0.353907:0.243636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.293660:0.287432:0.297691:0.287432:0.297691:0.270998:0.293660:0.270998:0.000000 :@0.414136:0.287432:0.627917:0.287432:0.627917:0.270998:0.414136:0.270998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La solución final es la unión de las soluciones encontradas, que en este caso es::@0.293660:0.325517:0.865117:0.325517:0.865117:0.309083:0.293660:0.309083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = :@0.293660:0.353614:0.359429:0.353614:0.359429:0.337180:0.293660:0.337180:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.333162:0.353614:0.340617:0.353614:0.340617:0.337208:0.333162:0.337208:0.000000 5:@0.359976:0.345840:0.368959:0.345840:0.368959:0.329406:0.359976:0.329406:0.000000 p:@0.368886:0.345285:0.381163:0.345285:0.381163:0.331570:0.368886:0.331570:0.000000 6 :@0.366088:0.359972:0.379102:0.359972:0.379102:0.343538:0.366088:0.343538:0.000000:0.000000 + 2:@0.382323:0.353606:0.410118:0.353606:0.410118:0.337172:0.382323:0.337172:0.000000:0.000000:0.000000:0.000000 p:@0.410007:0.353051:0.422285:0.353051:0.422285:0.339336:0.410007:0.339336:0.000000 k:@0.422193:0.353606:0.429758:0.353606:0.429758:0.337200:0.422193:0.337200:0.000000 , donde Z = :@0.429685:0.353606:0.622814:0.353606:0.622814:0.337172:0.429685:0.337172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.488919:0.353606:0.496485:0.353606:0.496485:0.337200:0.488919:0.337200:0.000000 ∈:@0.500369:0.354189:0.515702:0.354189:0.515702:0.336534:0.500369:0.336534:0.000000 x:@0.600504:0.353606:0.607959:0.353606:0.607959:0.337200:0.600504:0.337200:0.000000 7:@0.623664:0.345840:0.632646:0.345840:0.632646:0.329406:0.623664:0.329406:0.000000 p:@0.632573:0.345285:0.644850:0.345285:0.644850:0.331570:0.632573:0.331570:0.000000 6 :@0.629775:0.359972:0.642789:0.359972:0.642789:0.343538:0.629775:0.343538:0.000000:0.000000 + 2:@0.645697:0.353606:0.673492:0.353606:0.673492:0.337172:0.645697:0.337172:0.000000:0.000000:0.000000:0.000000 p:@0.673382:0.353051:0.685659:0.353051:0.685659:0.339336:0.673382:0.339336:0.000000 k:@0.685567:0.353606:0.693133:0.353606:0.693133:0.337200:0.685567:0.337200:0.000000 , donde Z:@0.693059:0.353606:0.792863:0.353606:0.792863:0.337172:0.693059:0.337172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.752294:0.353606:0.759859:0.353606:0.759859:0.337200:0.752294:0.337200:0.000000 ∈:@0.763743:0.354189:0.779076:0.354189:0.779076:0.336534:0.763743:0.336534:0.000000 Ejemplo 4:@0.293658:0.388110:0.369441:0.388110:0.369441:0.371441:0.293658:0.371441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Resuelve la ecuación 4:@0.293658:0.415472:0.457321:0.415472:0.457321:0.399038:0.293658:0.399038:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tan x :@0.457115:0.415472:0.500884:0.415482:0.500884:0.399076:0.457115:0.399066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.481043:0.409418:0.486279:0.409418:0.486279:0.399837:0.481043:0.399837:0.000000 = 5:@0.486232:0.415482:0.524666:0.415482:0.524666:0.399048:0.486232:0.399048:0.000000:0.000000:0.000000:0.000000:0.000000 tanx:@0.524574:0.415482:0.555940:0.415482:0.555940:0.399076:0.524574:0.399076:0.000000:0.000000:0.000000:0.000000 En este caso, iniciamos igualando a cero y luego aplicamos la factorización como en el :@0.293674:0.435702:0.931327:0.435702:0.931327:0.419268:0.293674:0.419268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ejemplo anterior.:@0.293674:0.452344:0.416963:0.452344:0.416963:0.435910:0.293674:0.435910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tanx tan x:@0.540294:0.468986:0.621875:0.468982:0.621875:0.452576:0.540294:0.452580:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (4:@0.571623:0.468986:0.585410:0.468986:0.585410:0.452552:0.571623:0.452552:0.000000:0.000000 2:@0.609231:0.462918:0.614468:0.462918:0.614468:0.453337:0.609231:0.453337:0.000000 5) = 0:@0.621801:0.468982:0.680336:0.468982:0.680336:0.452548:0.621801:0.452548:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –:@0.625759:0.469564:0.634962:0.469564:0.634962:0.451910:0.625759:0.451910:0.000000 tanx tanx :@0.494865:0.489202:0.574495:0.489202:0.574495:0.472796:0.494865:0.472796:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (2:@0.526194:0.489202:0.539981:0.489202:0.539981:0.472768:0.526194:0.472768:0.000000:0.000000 –:@0.574458:0.489784:0.583661:0.489784:0.583661:0.472130:0.574458:0.472130:0.000000 √5)(2:@0.583569:0.489202:0.624986:0.489202:0.624986:0.472768:0.583569:0.472768:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tanx :@0.624875:0.489202:0.659481:0.489202:0.659481:0.472796:0.624875:0.472796:0.000000:0.000000:0.000000:0.000000:0.000000 + √5) = 0:@0.659444:0.489202:0.725765:0.489202:0.725765:0.472768:0.659444:0.472768:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 De modo que::@0.293674:0.516564:0.398422:0.516564:0.398422:0.500130:0.293674:0.500130:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 i. :@0.293660:0.536776:0.300913:0.536776:0.300913:0.520342:0.293660:0.520342:0.000000:0.000000:0.000000 :@0.325702:0.536776:0.329733:0.536776:0.329733:0.520342:0.325702:0.520342:0.000000 tanx :@0.326082:0.536776:0.360688:0.536776:0.360688:0.520370:0.326082:0.520370:0.000000:0.000000:0.000000:0.000000:0.000000 = 0, entonces = :@0.360651:0.536776:0.488379:0.536776:0.488379:0.520342:0.360651:0.520342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x tan:@0.462811:0.536776:0.512271:0.536776:0.512271:0.520370:0.462811:0.520370:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –:@0.512214:0.531052:0.517580:0.531052:0.517580:0.520759:0.512214:0.520759:0.000000 1:@0.517526:0.530712:0.522763:0.530712:0.522763:0.521131:0.517526:0.521131:0.000000 0:@0.522717:0.536776:0.535657:0.536776:0.535657:0.520342:0.522717:0.520342:0.000000:0.000000 x :@0.323789:0.553418:0.334484:0.553418:0.334484:0.537012:0.323789:0.537012:0.000000:0.000000 = 0:@0.334429:0.553418:0.358266:0.553418:0.358266:0.536984:0.334429:0.536984:0.000000:0.000000:0.000000 x:@0.323789:0.570060:0.331244:0.570060:0.331244:0.553654:0.323789:0.553654:0.000000 = :@0.331171:0.570060:0.350057:0.570060:0.350057:0.553626:0.331171:0.553626:0.000000:0.000000:0.000000 p:@0.349965:0.569505:0.362242:0.569505:0.362242:0.555789:0.349965:0.555789:0.000000 En general = :@0.323789:0.590280:0.431104:0.590280:0.431104:0.573846:0.323789:0.573846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.404837:0.590280:0.412292:0.590280:0.412292:0.573873:0.404837:0.573873:0.000000 k:@0.431012:0.590280:0.438577:0.590280:0.438577:0.573873:0.431012:0.573873:0.000000 p:@0.438503:0.589725:0.450781:0.589725:0.450781:0.576009:0.438503:0.576009:0.000000 , donde Z:@0.450689:0.590280:0.550493:0.590280:0.550493:0.573846:0.450689:0.573846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.509924:0.590280:0.517489:0.590280:0.517489:0.573873:0.509924:0.573873:0.000000 ∈:@0.521373:0.590862:0.536706:0.590862:0.536706:0.573208:0.521373:0.573208:0.000000 +:@0.550406:0.584212:0.556802:0.584212:0.556802:0.574631:0.550406:0.574631:0.000000 ii. 2:@0.293660:0.619270:0.332844:0.619270:0.332844:0.602837:0.293660:0.602837:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tanx :@0.332771:0.619270:0.367376:0.619270:0.367376:0.602864:0.332771:0.602864:0.000000:0.000000:0.000000:0.000000:0.000000 –:@0.367339:0.619853:0.376543:0.619853:0.376543:0.602199:0.367339:0.602199:0.000000 5 = 0 despejando :@0.376451:0.619270:0.528714:0.619270:0.528714:0.602837:0.376451:0.602837:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tanx:@0.528530:0.619270:0.559896:0.619270:0.559896:0.602864:0.528530:0.602864:0.000000:0.000000:0.000000:0.000000 tenemos: :@0.559859:0.619270:0.635487:0.619270:0.635487:0.602837:0.559859:0.602837:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tanx:@0.635347:0.619270:0.666713:0.619270:0.666713:0.602864:0.635347:0.602864:0.000000:0.000000:0.000000:0.000000 = :@0.666676:0.619270:0.685562:0.619270:0.685562:0.602837:0.666676:0.602837:0.000000:0.000000:0.000000 5:@0.695728:0.608453:0.704711:0.608453:0.704711:0.592019:0.695728:0.592019:0.000000 2 :@0.692186:0.625050:0.705199:0.625050:0.705199:0.608616:0.692186:0.608616:0.000000:0.000000 , entonces, = :@0.712176:0.619267:0.819766:0.619267:0.819766:0.602833:0.712176:0.602833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.793499:0.619267:0.800954:0.619267:0.800954:0.602861:0.793499:0.602861:0.000000 tan:@0.819674:0.619267:0.843659:0.619267:0.843659:0.602861:0.819674:0.602861:0.000000:0.000000:0.000000 –:@0.843614:0.613546:0.848979:0.613546:0.848979:0.603254:0.843614:0.603254:0.000000 1:@0.848926:0.613206:0.854163:0.613206:0.854163:0.603626:0.848926:0.603626:0.000000 :@0.854116:0.619270:0.862105:0.619270:0.862105:0.602837:0.854116:0.602837:0.000000:0.000000 5:@0.872289:0.608453:0.881272:0.608453:0.881272:0.592019:0.872289:0.592019:0.000000 2 :@0.868746:0.625050:0.881760:0.625050:0.881760:0.608616:0.868746:0.608616:0.000000:0.000000 , :@0.888737:0.619267:0.895971:0.619267:0.895971:0.602833:0.888737:0.602833:0.000000:0.000000 Las soluciones están en el primer y tercer cuadrante.:@0.323781:0.639486:0.701730:0.639486:0.701730:0.623053:0.323781:0.623053:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.525635:0.659706:0.533090:0.659706:0.533090:0.643300:0.525635:0.643300:0.000000 = 1007 + :@0.533016:0.659706:0.606351:0.659706:0.606351:0.643272:0.533016:0.643272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.606204:0.659706:0.613769:0.659706:0.613769:0.643300:0.606204:0.643300:0.000000 p:@0.613695:0.659152:0.625973:0.659152:0.625973:0.645436:0.613695:0.645436:0.000000 , donde :@0.625881:0.659706:0.715837:0.659706:0.715837:0.643272:0.625881:0.643272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.685115:0.659706:0.692681:0.659706:0.692681:0.643300:0.685115:0.643300:0.000000 ∈:@0.696565:0.660289:0.711898:0.660289:0.711898:0.642635:0.696565:0.642635:0.000000 Z:@0.715764:0.659706:0.725041:0.659706:0.725041:0.643300:0.715764:0.643300:0.000000 iii. 2:@0.293660:0.698526:0.332794:0.698526:0.332794:0.682092:0.293660:0.682092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tanx:@0.332684:0.698526:0.364049:0.698526:0.364049:0.682120:0.332684:0.682120:0.000000:0.000000:0.000000:0.000000 + 5 = 0, :@0.364013:0.698526:0.440204:0.698526:0.440204:0.682092:0.364013:0.682092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tanx :@0.440093:0.698526:0.474699:0.698526:0.474699:0.682120:0.440093:0.682120:0.000000:0.000000:0.000000:0.000000:0.000000 = :@0.474662:0.698526:0.502641:0.698526:0.502641:0.682092:0.474662:0.682092:0.000000:0.000000:0.000000:0.000000 –:@0.489498:0.699108:0.498702:0.699108:0.498702:0.681454:0.489498:0.681454:0.000000 5:@0.512839:0.688601:0.521821:0.688601:0.521821:0.672167:0.512839:0.672167:0.000000 2 :@0.509294:0.705198:0.522308:0.705198:0.522308:0.688764:0.509294:0.688764:0.000000:0.000000 , entonces, = :@0.529285:0.698527:0.636875:0.698527:0.636875:0.682093:0.529285:0.682093:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.610608:0.698527:0.618063:0.698527:0.618063:0.682121:0.610608:0.682121:0.000000 tan:@0.636783:0.698527:0.660768:0.698527:0.660768:0.682121:0.636783:0.682121:0.000000:0.000000:0.000000 –:@0.660724:0.692802:0.666090:0.692802:0.666090:0.682509:0.660724:0.682509:0.000000 1 :@0.666036:0.692462:0.675888:0.692462:0.675888:0.682881:0.666036:0.682881:0.000000:0.000000:0.000000 5:@0.702780:0.691303:0.711762:0.691303:0.711762:0.674869:0.702780:0.674869:0.000000 2:@0.699237:0.709528:0.708220:0.709528:0.708220:0.693095:0.699237:0.693095:0.000000 –:@0.679627:0.697590:0.688830:0.697590:0.688830:0.679936:0.679627:0.679936:0.000000 Las soluciones están en el segundo y cuarto cuadrante. Se debe tener en cuenta que :@0.323781:0.725889:0.930549:0.725889:0.930549:0.709455:0.323781:0.709455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la calculadora posiblemente da como respuesta un arco negativo, es decir, medido :@0.323781:0.742531:0.931406:0.742531:0.931406:0.726097:0.323781:0.726097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en el sentido de las manecillas del reloj, como se explicó en la unidad anterior, por lo :@0.323781:0.759173:0.930615:0.759173:0.930615:0.742739:0.323781:0.742739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que debemos generar su equivalente positivo, tomándolo en el sentido contrario al :@0.323781:0.775815:0.931395:0.775815:0.931395:0.759381:0.323781:0.759381:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 movimiento de las manecillas del reloj.:@0.323781:0.792456:0.604151:0.792456:0.604151:0.776023:0.323781:0.776023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.323781:0.819818:0.334476:0.819818:0.334476:0.803412:0.323781:0.803412:0.000000:0.000000 = 1007 + 2 = 5276 (cuarto cuadrante):@0.334420:0.819818:0.626829:0.819818:0.626829:0.803385:0.334420:0.803385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –:@0.349257:0.820401:0.358460:0.820401:0.358460:0.802747:0.349257:0.802747:0.000000 p:@0.421671:0.819264:0.433948:0.819264:0.433948:0.805548:0.421671:0.805548:0.000000 x :@0.323781:0.836460:0.334476:0.836460:0.334476:0.820054:0.323781:0.820054:0.000000:0.000000 = 5276 :@0.334420:0.836460:0.388943:0.836460:0.388943:0.820026:0.334420:0.820026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – :@0.388814:0.837043:0.402527:0.837043:0.402527:0.819388:0.388814:0.819388:0.000000:0.000000 p:@0.402527:0.835905:0.414805:0.835905:0.414805:0.822190:0.402527:0.822190:0.000000 = 2135 (segundo cuadrante):@0.414621:0.836460:0.625250:0.836460:0.625250:0.820026:0.414621:0.820026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En general = 2135+ :@0.323781:0.860244:0.480887:0.860244:0.480887:0.843810:0.323781:0.843810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.404828:0.860244:0.415523:0.860244:0.415523:0.843838:0.404828:0.843838:0.000000:0.000000 k:@0.480758:0.860244:0.488324:0.860244:0.488324:0.843838:0.480758:0.843838:0.000000 p:@0.488250:0.859689:0.500528:0.859689:0.500528:0.845974:0.488250:0.845974:0.000000 , donde k Z:@0.500435:0.860244:0.600442:0.860244:0.600442:0.843810:0.500435:0.843810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∈:@0.571322:0.860827:0.586655:0.860827:0.586655:0.843172:0.571322:0.843172:0.000000 Las soluciones de la ecuación 4:@0.323781:0.884028:0.550209:0.884028:0.550209:0.867594:0.323781:0.867594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tan x :@0.549914:0.884028:0.592970:0.884039:0.592970:0.867633:0.549914:0.867622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.573847:0.877976:0.579084:0.877976:0.579084:0.868395:0.573847:0.868395:0.000000 = 5:@0.592915:0.884039:0.616753:0.884039:0.616753:0.867606:0.592915:0.867606:0.000000:0.000000:0.000000 tanx:@0.616661:0.884039:0.648027:0.884039:0.648027:0.867633:0.616661:0.867633:0.000000:0.000000:0.000000:0.000000 son::@0.647990:0.884039:0.681454:0.884039:0.681454:0.867606:0.647990:0.867606:0.000000:0.000000:0.000000:0.000000:0.000000 x k:@0.323783:0.904259:0.356824:0.904259:0.356824:0.887853:0.323783:0.887853:0.000000:0.000000:0.000000:0.000000 = :@0.334422:0.904259:0.349350:0.904259:0.349350:0.887825:0.334422:0.887825:0.000000:0.000000 p:@0.356750:0.903705:0.369028:0.903705:0.369028:0.889989:0.356750:0.889989:0.000000 , donde :@0.368936:0.904259:0.428299:0.904259:0.428299:0.887825:0.368936:0.887825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k :@0.428170:0.904259:0.438975:0.904259:0.438975:0.887853:0.428170:0.887853:0.000000:0.000000 ∈ :@0.438920:0.904842:0.458763:0.904842:0.458763:0.887188:0.438920:0.887188:0.000000:0.000000 Z:@0.458763:0.904259:0.468685:0.904259:0.468685:0.887825:0.458763:0.887825:0.000000 x :@0.323783:0.920901:0.334477:0.920901:0.334477:0.904495:0.323783:0.904495:0.000000:0.000000 = 1007 + :@0.334422:0.920901:0.403799:0.920901:0.403799:0.904467:0.334422:0.904467:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.403670:0.920901:0.411236:0.920901:0.411236:0.904495:0.403670:0.904495:0.000000 p:@0.411162:0.920346:0.423440:0.920346:0.423440:0.906631:0.411162:0.906631:0.000000 , donde :@0.423348:0.920901:0.482711:0.920901:0.482711:0.904467:0.423348:0.904467:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k :@0.482582:0.920901:0.493387:0.920901:0.493387:0.904495:0.482582:0.904495:0.000000:0.000000 ∈ :@0.493332:0.921484:0.513175:0.921484:0.513175:0.903829:0.493332:0.903829:0.000000:0.000000 Z:@0.513175:0.920901:0.523097:0.920901:0.523097:0.904467:0.513175:0.904467:0.000000 x :@0.323783:0.937543:0.334477:0.937543:0.334477:0.921137:0.323783:0.921137:0.000000:0.000000 = 2135 + :@0.334422:0.937543:0.403799:0.937543:0.403799:0.921109:0.334422:0.921109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.403670:0.937543:0.411236:0.937543:0.411236:0.921137:0.403670:0.921137:0.000000 p:@0.411162:0.936988:0.423440:0.936988:0.423440:0.923273:0.411162:0.923273:0.000000 , donde :@0.423348:0.937543:0.482711:0.937543:0.482711:0.921109:0.423348:0.921109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k :@0.482582:0.937543:0.493387:0.937543:0.493387:0.921137:0.482582:0.921137:0.000000:0.000000 ∈ :@0.493332:0.938125:0.513175:0.938125:0.513175:0.920471:0.493332:0.920471:0.000000:0.000000 Z:@0.513175:0.937543:0.522452:0.937543:0.522452:0.921137:0.513175:0.921137:0.000000 En la programación y :@0.078581:0.207917:0.221759:0.207917:0.221759:0.192977:0.078581:0.192977:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 control de robots, como :@0.078581:0.223046:0.241584:0.223046:0.241584:0.208106:0.078581:0.208106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 los brazos robóticos que :@0.078581:0.238175:0.243046:0.238175:0.243046:0.223235:0.078581:0.223235:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ves en fábricas o cadenas :@0.078581:0.253304:0.249236:0.253304:0.249236:0.238364:0.078581:0.238364:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de montaje, se necesita :@0.078581:0.268433:0.237295:0.268433:0.237295:0.253493:0.078581:0.253493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 calcular con precisión los :@0.078581:0.283562:0.247302:0.283562:0.247302:0.268622:0.078581:0.268622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 movimientos para que :@0.078581:0.298691:0.231816:0.298691:0.231816:0.283751:0.078581:0.283751:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el robot realice tareas :@0.078581:0.313820:0.222944:0.313820:0.222944:0.298880:0.078581:0.298880:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de manera eficiente y :@0.078581:0.328949:0.224627:0.328949:0.224627:0.314009:0.078581:0.314009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 repetitiva. :@0.078581:0.344077:0.147200:0.344077:0.147200:0.329138:0.078581:0.329138:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Un brazo robótico tiene :@0.078581:0.360997:0.239181:0.360997:0.239181:0.346057:0.078581:0.346057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 varias articulaciones que :@0.078581:0.376126:0.243896:0.376126:0.243896:0.361186:0.078581:0.361186:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 se doblan y giran, como el :@0.078581:0.391255:0.255485:0.391255:0.255485:0.376315:0.078581:0.376315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 codo y la muñeca de un :@0.078581:0.406384:0.241853:0.406384:0.241853:0.391444:0.078581:0.391444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 brazo humano. Cada vez :@0.078581:0.421512:0.244810:0.421512:0.244810:0.406573:0.078581:0.406573:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que el robot se mueve, :@0.078581:0.436641:0.233612:0.436641:0.233612:0.421702:0.078581:0.421702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cambian los :@0.078581:0.451770:0.161932:0.451770:0.161932:0.436830:0.078581:0.436830:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ángulos:@0.161782:0.451770:0.212920:0.451770:0.212920:0.436856:0.161782:0.436856:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de :@0.212904:0.451770:0.237318:0.451770:0.237318:0.436830:0.212904:0.436830:0.000000:0.000000:0.000000:0.000000 esas articulaciones. :@0.078581:0.466899:0.207872:0.466899:0.207872:0.451959:0.078581:0.451959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Las ecuaciones :@0.078581:0.483818:0.181628:0.483818:0.181628:0.468879:0.078581:0.468879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 trigonométricas (como :@0.078581:0.498947:0.234336:0.498947:0.234336:0.484008:0.078581:0.484008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las de seno, coseno o :@0.078581:0.514076:0.222502:0.514076:0.222502:0.499137:0.078581:0.499137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tangente) nos ayudan a :@0.078581:0.529205:0.238495:0.529205:0.238495:0.514265:0.078581:0.514265:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 calcular: ¿:@0.078581:0.544334:0.142196:0.544334:0.142196:0.529394:0.078581:0.529394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Cuánto debe :@0.142069:0.544334:0.234848:0.544334:0.234848:0.529180:0.142069:0.529180:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 girar:@0.078581:0.559463:0.110400:0.559463:0.110400:0.544309:0.078581:0.544309:0.000000:0.000000:0.000000:0.000000:0.000000 cada articulación :@0.110325:0.559463:0.229899:0.559463:0.229899:0.544523:0.110325:0.544523:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 para llegar a un punto :@0.078581:0.574592:0.228225:0.574592:0.228225:0.559652:0.078581:0.559652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 específico? y ¿:@0.078581:0.589721:0.172006:0.589721:0.172006:0.574781:0.078581:0.574781:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 qué :@0.171839:0.589721:0.202278:0.589721:0.202278:0.574567:0.171839:0.574567:0.000000:0.000000:0.000000:0.000000 distancia:@0.078581:0.604850:0.140396:0.604850:0.140396:0.589696:0.078581:0.589696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 debe recorrer :@0.140295:0.604850:0.237062:0.604850:0.237062:0.589910:0.140295:0.589910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el extremo del brazo, :@0.078581:0.619979:0.220357:0.619979:0.220357:0.605039:0.078581:0.605039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y calcular trayectorias :@0.078581:0.635108:0.223444:0.635108:0.223444:0.620168:0.078581:0.620168:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 precisas?:@0.078581:0.650237:0.137561:0.650237:0.137561:0.635297:0.078581:0.635297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Interdisciplinariedad :@0.078581:0.145093:0.244955:0.145093:0.244955:0.128146:0.078581:0.128146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Matemática :@0.078581:0.161735:0.172624:0.161735:0.172624:0.145301:0.078581:0.145301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y robótica:@0.078581:0.178377:0.151117:0.178377:0.151117:0.161943:0.078581:0.161943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Las soluciones de una :@0.078581:0.721673:0.226676:0.721673:0.226676:0.706733:0.078581:0.706733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ecuación trigonométrica, :@0.078581:0.736802:0.248366:0.736802:0.248366:0.721862:0.078581:0.721862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 como 5 :@0.078581:0.751931:0.132648:0.751931:0.132648:0.736991:0.078581:0.736991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tan:@0.132531:0.751931:0.154335:0.751931:0.154335:0.737016:0.132531:0.737016:0.000000:0.000000:0.000000 (x)−6=0 :@0.154285:0.751931:0.209875:0.751931:0.209875:0.736991:0.154285:0.736991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 demuestran que hay :@0.078581:0.767060:0.219172:0.767060:0.219172:0.752120:0.078581:0.752120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 múltiples ángulos que :@0.078581:0.782189:0.229504:0.782189:0.229504:0.767249:0.078581:0.767249:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 satisfacen la misma :@0.078581:0.797318:0.209540:0.797318:0.209540:0.782378:0.078581:0.782378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 relación entre las funciones :@0.078581:0.812447:0.262207:0.812447:0.262207:0.797507:0.078581:0.797507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 trigonométricas. Esto :@0.078581:0.827576:0.221729:0.827576:0.221729:0.812636:0.078581:0.812636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ocurre debido a la :@0.078581:0.842705:0.201965:0.842705:0.201965:0.827765:0.078581:0.827765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 naturaleza periódica de las :@0.078581:0.857834:0.257727:0.857834:0.257727:0.842894:0.078581:0.842894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 funciones trigonométricas, :@0.078581:0.872963:0.258818:0.872963:0.258818:0.858023:0.078581:0.858023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 como la tangente, que :@0.078581:0.888091:0.231933:0.888091:0.231933:0.873152:0.078581:0.873152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 repite sus valores en :@0.078581:0.903220:0.215847:0.903220:0.215847:0.888281:0.078581:0.888281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 intervalos regulares de π :@0.078581:0.918349:0.243702:0.918349:0.243702:0.903410:0.078581:0.903410:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 radianes.:@0.078581:0.933478:0.136825:0.933478:0.136825:0.918538:0.078581:0.918538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.078581:0.682753:0.187141:0.682753:0.187141:0.665806:0.078581:0.665806:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.078581:0.699395:0.176057:0.699395:0.176057:0.682448:0.078581:0.682448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000