65:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000 Pensamiento espacial, métrico, numérico y variacional:@0.444548:0.043661:0.926841:0.043661:0.926841:0.024916:0.444548:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Identidades de ángulo doble:@0.073089:0.136836:0.291669:0.136836:0.291669:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sen x:@0.321440:0.160620:0.361254:0.160620:0.361254:0.144214:0.321440:0.144214:0.000000:0.000000:0.000000:0.000000:0.000000 2 = 2 :@0.344890:0.160620:0.392933:0.160620:0.392933:0.144186:0.344890:0.144186:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 senx cosx:@0.392823:0.160620:0.457999:0.160620:0.457999:0.144214:0.392823:0.144214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.423673:0.160620:0.427705:0.160620:0.427705:0.144186:0.423673:0.144186:0.000000 cos x:@0.228980:0.184404:0.268206:0.184404:0.268206:0.167998:0.228980:0.167998:0.000000:0.000000:0.000000:0.000000:0.000000 2 = :@0.251842:0.184404:0.287018:0.184404:0.287018:0.167970:0.251842:0.167970:0.000000:0.000000:0.000000:0.000000:0.000000 cos x sen x:@0.286926:0.184404:0.371759:0.184415:0.371759:0.168009:0.286926:0.167998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.309777:0.178352:0.315013:0.178352:0.315013:0.168771:0.309777:0.168771:0.000000 - :@0.322349:0.184415:0.335749:0.184415:0.335749:0.167982:0.322349:0.167982:0.000000:0.000000:0.000000 2:@0.359115:0.178352:0.364352:0.178352:0.364352:0.168771:0.359115:0.168771:0.000000 = 1 2:@0.371685:0.184415:0.425379:0.184415:0.425379:0.167982:0.371685:0.167982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –:@0.403327:0.184998:0.412531:0.184998:0.412531:0.167344:0.403327:0.167344:0.000000 sen x:@0.425287:0.184415:0.461399:0.184415:0.461399:0.168009:0.425287:0.168009:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.448755:0.178352:0.453991:0.178352:0.453991:0.168771:0.448755:0.168771:0.000000 = 2:@0.461325:0.184415:0.489120:0.184415:0.489120:0.167982:0.461325:0.167982:0.000000:0.000000:0.000000:0.000000 cos x:@0.489010:0.184415:0.524536:0.184415:0.524536:0.168009:0.489010:0.168009:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.511892:0.178352:0.517128:0.178352:0.517128:0.168771:0.511892:0.168771:0.000000 1:@0.524462:0.184415:0.550471:0.184415:0.550471:0.167982:0.524462:0.167982:0.000000:0.000000:0.000000:0.000000 –:@0.528420:0.184998:0.537623:0.184998:0.537623:0.167344:0.528420:0.167344:0.000000 tan2x:@0.322461:0.215952:0.362257:0.215952:0.362257:0.199546:0.322461:0.199546:0.000000:0.000000:0.000000:0.000000:0.000000 = :@0.362220:0.215952:0.381106:0.215952:0.381106:0.199518:0.362220:0.199518:0.000000:0.000000:0.000000 2:@0.397897:0.208312:0.406880:0.208312:0.406880:0.191878:0.397897:0.191878:0.000000 tanx:@0.406806:0.208312:0.438172:0.208312:0.438172:0.191906:0.406806:0.191906:0.000000:0.000000:0.000000:0.000000 1 :@0.386797:0.225647:0.412789:0.225647:0.412789:0.209213:0.386797:0.209213:0.000000:0.000000:0.000000:0.000000 –:@0.399646:0.226229:0.408849:0.226229:0.408849:0.208575:0.399646:0.208575:0.000000 tan x :@0.412715:0.225647:0.452600:0.225647:0.452600:0.209241:0.412715:0.209241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.436643:0.219583:0.441880:0.219583:0.441880:0.210002:0.436643:0.210002:0.000000 Identidades de mitad de ángulo:@0.073079:0.259957:0.315424:0.259957:0.315424:0.243287:0.073079:0.243287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sen:@0.209713:0.301689:0.233366:0.301689:0.233366:0.285283:0.209713:0.285283:0.000000:0.000000:0.000000 = + _:@0.256983:0.301689:0.285320:0.301009:0.285320:0.284603:0.256983:0.285283:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.241097:0.293520:0.248552:0.293520:0.248552:0.277114:0.241097:0.277114:0.000000 2:@0.240306:0.312312:0.249289:0.312312:0.249289:0.295878:0.240306:0.295878:0.000000 2:@0.324353:0.312312:0.333336:0.312312:0.333336:0.295878:0.324353:0.295878:0.000000 1:@0.301804:0.295345:0.310787:0.295345:0.310787:0.278911:0.301804:0.278911:0.000000 cosx:@0.310787:0.295345:0.357192:0.295345:0.357192:0.278939:0.310787:0.278939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 _ :@0.314101:0.290297:0.326617:0.290297:0.326617:0.273891:0.314101:0.273891:0.000000:0.000000 cos:@0.413495:0.301689:0.436559:0.301689:0.436559:0.285283:0.413495:0.285283:0.000000:0.000000:0.000000 = + _:@0.460765:0.301689:0.489100:0.301009:0.489100:0.284603:0.460765:0.285283:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.444879:0.293520:0.452334:0.293520:0.452334:0.277114:0.444879:0.277114:0.000000 2:@0.444088:0.312312:0.453070:0.312312:0.453070:0.295878:0.444088:0.295878:0.000000 2:@0.528135:0.312312:0.537118:0.312312:0.537118:0.295878:0.528135:0.295878:0.000000 1:@0.504701:0.295345:0.513684:0.295345:0.513684:0.278911:0.504701:0.278911:0.000000 + cosx:@0.513684:0.295345:0.561855:0.295345:0.561855:0.278939:0.513684:0.278939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.527968:0.290297:0.531281:0.290297:0.531281:0.273891:0.527968:0.273891:0.000000 El signo + o – depende del cuadrante donde esté el ángulo.:@0.073089:0.345607:0.506340:0.345607:0.506340:0.329173:0.073089:0.329173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tan:@0.279765:0.378932:0.303750:0.378932:0.303750:0.362526:0.279765:0.362526:0.000000:0.000000:0.000000 :@0.303695:0.378932:0.307726:0.378932:0.307726:0.362498:0.303695:0.362498:0.000000 x:@0.312399:0.372183:0.319854:0.372183:0.319854:0.355777:0.312399:0.355777:0.000000 2:@0.311626:0.389727:0.320608:0.389727:0.320608:0.373293:0.311626:0.373293:0.000000 :@0.320608:0.389727:0.323922:0.389727:0.323922:0.373320:0.320608:0.373320:0.000000 = :@0.330990:0.378923:0.345918:0.378923:0.345918:0.362489:0.330990:0.362489:0.000000:0.000000 1 :@0.346799:0.372706:0.372790:0.372706:0.372790:0.356273:0.346799:0.356273:0.000000:0.000000:0.000000:0.000000 –:@0.359647:0.373289:0.368850:0.373289:0.368850:0.355635:0.359647:0.355635:0.000000 cosx:@0.372716:0.372706:0.403084:0.372706:0.403084:0.356300:0.372716:0.356300:0.000000:0.000000:0.000000:0.000000 senx:@0.359500:0.386838:0.390387:0.386838:0.390387:0.370432:0.359500:0.370432:0.000000:0.000000:0.000000:0.000000 :@0.390405:0.386838:0.394436:0.386838:0.394436:0.370404:0.390405:0.370404:0.000000 = :@0.404929:0.378919:0.423814:0.378919:0.423814:0.362486:0.404929:0.362486:0.000000:0.000000:0.000000 senx:@0.442603:0.372173:0.473491:0.372173:0.473491:0.355767:0.442603:0.355767:0.000000:0.000000:0.000000:0.000000 1 :@0.426571:0.389508:0.439511:0.389508:0.439511:0.373075:0.426571:0.373075:0.000000:0.000000 + :@0.439419:0.390091:0.459262:0.390091:0.459262:0.372437:0.439419:0.372437:0.000000:0.000000 cosx :@0.459262:0.389508:0.492943:0.389508:0.492943:0.373102:0.459262:0.373102:0.000000:0.000000:0.000000:0.000000:0.000000 Identidades de transformaciones: sumas y productos:@0.073078:0.422931:0.472813:0.422931:0.472813:0.406261:0.073078:0.406261:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a. Identidades de producto a suma:@0.073089:0.450295:0.349080:0.450295:0.349080:0.433626:0.073089:0.433626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 senx cosy :@0.253197:0.479529:0.321569:0.479529:0.321569:0.463123:0.253197:0.463123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.284047:0.479529:0.288078:0.479529:0.288078:0.463096:0.284047:0.463096:0.000000 = :@0.321524:0.479529:0.340410:0.479529:0.340410:0.463096:0.321524:0.463096:0.000000:0.000000:0.000000 1:@0.344980:0.471689:0.353962:0.471689:0.353962:0.455255:0.344980:0.455255:0.000000 2:@0.344980:0.487457:0.353962:0.487457:0.353962:0.471023:0.344980:0.471023:0.000000 :@0.353962:0.487457:0.357276:0.487457:0.357276:0.471051:0.353962:0.471051:0.000000 [:@0.363737:0.479538:0.372572:0.479538:0.372572:0.463104:0.363737:0.463104:0.000000:0.000000 sen x y:@0.372480:0.479538:0.433684:0.479538:0.433684:0.463132:0.372480:0.463132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( + ) + :@0.395931:0.479538:0.457301:0.479538:0.457301:0.463104:0.395931:0.463104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sen x y:@0.457190:0.479538:0.516627:0.479538:0.516627:0.463132:0.457190:0.463132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.480641:0.479538:0.485519:0.479538:0.485519:0.463104:0.480641:0.463104:0.000000 –:@0.496085:0.480121:0.505288:0.480121:0.505288:0.462466:0.496085:0.462466:0.000000 )]:@0.505196:0.479538:0.526236:0.479538:0.526236:0.463104:0.505196:0.463104:0.000000:0.000000:0.000000:0.000000 cosx cosy:@0.257361:0.514847:0.321219:0.514847:0.321219:0.498441:0.257361:0.498441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = :@0.321197:0.514847:0.340083:0.514847:0.340083:0.498413:0.321197:0.498413:0.000000:0.000000:0.000000 1:@0.345259:0.506999:0.354242:0.506999:0.354242:0.490565:0.345259:0.490565:0.000000 2:@0.345259:0.522767:0.354242:0.522767:0.354242:0.506333:0.345259:0.506333:0.000000 :@0.354242:0.522767:0.357555:0.522767:0.357555:0.506361:0.354242:0.506361:0.000000 [:@0.363427:0.514848:0.372262:0.514848:0.372262:0.498414:0.363427:0.498414:0.000000:0.000000 cos x y:@0.372170:0.514848:0.429527:0.514848:0.429527:0.498442:0.372170:0.498442:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( + ) + :@0.395032:0.514848:0.453144:0.514848:0.453144:0.498414:0.395032:0.498414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cos x y:@0.453033:0.514848:0.512526:0.514848:0.512526:0.498442:0.453033:0.498442:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.475895:0.514848:0.480773:0.514848:0.480773:0.498414:0.475895:0.498414:0.000000 – :@0.491339:0.515430:0.505052:0.515430:0.505052:0.497776:0.491339:0.497776:0.000000:0.000000 )]:@0.512360:0.514848:0.522042:0.514848:0.522042:0.498414:0.512360:0.498414:0.000000:0.000000 senx seny:@0.248805:0.550156:0.313764:0.550156:0.313764:0.533750:0.248805:0.533750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = :@0.313764:0.550156:0.345701:0.550156:0.345701:0.533723:0.313764:0.533723:0.000000:0.000000:0.000000:0.000000:0.000000 –:@0.332558:0.550739:0.341762:0.550739:0.341762:0.533085:0.332558:0.533085:0.000000 1:@0.350304:0.542307:0.359287:0.542307:0.359287:0.525873:0.350304:0.525873:0.000000 2:@0.350304:0.558075:0.359287:0.558075:0.359287:0.541641:0.350304:0.541641:0.000000 :@0.359287:0.558075:0.362600:0.558075:0.362600:0.541669:0.359287:0.541669:0.000000 [:@0.369080:0.550156:0.377915:0.550156:0.377915:0.533723:0.369080:0.533723:0.000000:0.000000 cos x:@0.377823:0.550156:0.412944:0.550156:0.412944:0.533750:0.377823:0.533750:0.000000:0.000000:0.000000:0.000000:0.000000 ( + ) :@0.400685:0.550156:0.460950:0.550156:0.460950:0.533723:0.400685:0.533723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.431664:0.550156:0.439138:0.550156:0.439138:0.533750:0.431664:0.533750:0.000000 –:@0.447807:0.550739:0.457011:0.550739:0.457011:0.533085:0.447807:0.533085:0.000000 cos x y:@0.460877:0.550156:0.521068:0.550156:0.521068:0.533750:0.460877:0.533750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( :@0.483738:0.550156:0.499955:0.550156:0.499955:0.533723:0.483738:0.533723:0.000000:0.000000:0.000000 – :@0.499882:0.550739:0.513595:0.550739:0.513595:0.533085:0.499882:0.533085:0.000000:0.000000 )]:@0.520903:0.550156:0.530585:0.550156:0.530585:0.533723:0.520903:0.533723:0.000000:0.000000 b. Identidades de suma a producto:@0.073089:0.591804:0.349080:0.591804:0.349080:0.575134:0.073089:0.575134:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 senx:@0.261774:0.625878:0.292662:0.625878:0.292662:0.609472:0.261774:0.609472:0.000000:0.000000:0.000000:0.000000 + :@0.292625:0.625878:0.311511:0.625878:0.311511:0.609444:0.292625:0.609444:0.000000:0.000000:0.000000 seny:@0.311419:0.625878:0.342325:0.625878:0.342325:0.609472:0.311419:0.609472:0.000000:0.000000:0.000000:0.000000 = 2:@0.342288:0.625878:0.370083:0.625878:0.370083:0.609444:0.342288:0.609444:0.000000:0.000000:0.000000:0.000000 sen:@0.369972:0.625878:0.393478:0.625878:0.393478:0.609472:0.369972:0.609472:0.000000:0.000000:0.000000 :@0.393423:0.625878:0.397454:0.625878:0.397454:0.609444:0.393423:0.609444:0.000000 x:@0.401115:0.621240:0.408570:0.621240:0.408570:0.604834:0.401115:0.604834:0.000000 + :@0.408496:0.621240:0.427382:0.621240:0.427382:0.604806:0.408496:0.604806:0.000000:0.000000:0.000000 y:@0.427290:0.621240:0.434763:0.621240:0.434763:0.604834:0.427290:0.604834:0.000000 2:@0.413448:0.638783:0.422431:0.638783:0.422431:0.622349:0.413448:0.622349:0.000000 :@0.422431:0.638783:0.425744:0.638783:0.425744:0.622377:0.422431:0.622377:0.000000 cos:@0.447782:0.625874:0.470707:0.625874:0.470707:0.609468:0.447782:0.609468:0.000000:0.000000:0.000000 :@0.470644:0.625874:0.474675:0.625874:0.474675:0.609440:0.470644:0.609440:0.000000 x y:@0.479229:0.619975:0.511110:0.619975:0.511110:0.603569:0.479229:0.603569:0.000000:0.000000:0.000000 :@0.486610:0.619975:0.503710:0.619975:0.503710:0.603541:0.486610:0.603541:0.000000:0.000000:0.000000 –:@0.490568:0.620558:0.499771:0.620558:0.499771:0.602903:0.490568:0.602903:0.000000 2:@0.490678:0.637518:0.499661:0.637518:0.499661:0.621085:0.490678:0.621085:0.000000 :@0.499661:0.637518:0.502974:0.637518:0.502974:0.621112:0.499661:0.621112:0.000000 senx seny:@0.262667:0.666905:0.341450:0.666905:0.341450:0.650499:0.262667:0.650499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.293518:0.666905:0.310618:0.666905:0.310618:0.650471:0.293518:0.650471:0.000000:0.000000:0.000000 –:@0.297475:0.667488:0.306679:0.667488:0.306679:0.649833:0.297475:0.649833:0.000000 = 2:@0.341414:0.666905:0.369209:0.666905:0.369209:0.650471:0.341414:0.650471:0.000000:0.000000:0.000000:0.000000 cos:@0.369098:0.666905:0.392022:0.666905:0.392022:0.650499:0.369098:0.650499:0.000000:0.000000:0.000000 :@0.391960:0.666905:0.395991:0.666905:0.395991:0.650471:0.391960:0.650471:0.000000 x:@0.399636:0.659598:0.407091:0.659598:0.407091:0.643192:0.399636:0.643192:0.000000 + :@0.407017:0.659598:0.425903:0.659598:0.425903:0.643164:0.407017:0.643164:0.000000:0.000000:0.000000 y:@0.425811:0.659598:0.433284:0.659598:0.433284:0.643192:0.425811:0.643192:0.000000 2:@0.411969:0.677141:0.420951:0.677141:0.420951:0.660707:0.411969:0.660707:0.000000 :@0.420951:0.677141:0.424265:0.677141:0.424265:0.660735:0.420951:0.660735:0.000000 sen:@0.446305:0.666913:0.469811:0.666913:0.469811:0.650507:0.446305:0.650507:0.000000:0.000000:0.000000 :@0.469756:0.666913:0.473787:0.666913:0.473787:0.650479:0.469756:0.650479:0.000000 x y:@0.478340:0.660121:0.510221:0.660121:0.510221:0.643715:0.478340:0.643715:0.000000:0.000000:0.000000 :@0.485721:0.660121:0.502822:0.660121:0.502822:0.643687:0.485721:0.643687:0.000000:0.000000:0.000000 –:@0.489679:0.660704:0.498883:0.660704:0.498883:0.643049:0.489679:0.643049:0.000000 2:@0.489789:0.677664:0.498772:0.677664:0.498772:0.661231:0.489789:0.661231:0.000000 :@0.498772:0.677664:0.502085:0.677664:0.502085:0.661258:0.498772:0.661258:0.000000 cosx:@0.262644:0.707051:0.293012:0.707051:0.293012:0.690645:0.262644:0.690645:0.000000:0.000000:0.000000:0.000000 + :@0.292961:0.707051:0.311846:0.707051:0.311846:0.690617:0.292961:0.690617:0.000000:0.000000:0.000000 cosy:@0.311754:0.707051:0.342079:0.707051:0.342079:0.690645:0.311754:0.690645:0.000000:0.000000:0.000000:0.000000 = 2:@0.342034:0.707051:0.369829:0.707051:0.369829:0.690617:0.342034:0.690617:0.000000:0.000000:0.000000:0.000000 cos:@0.369719:0.707051:0.392643:0.707051:0.392643:0.690645:0.369719:0.690645:0.000000:0.000000:0.000000 :@0.392581:0.707051:0.396612:0.707051:0.396612:0.690617:0.392581:0.690617:0.000000 x:@0.400258:0.699744:0.407713:0.699744:0.407713:0.683338:0.400258:0.683338:0.000000 + :@0.407640:0.699744:0.426525:0.699744:0.426525:0.683310:0.407640:0.683310:0.000000:0.000000:0.000000 y:@0.426433:0.699744:0.433907:0.699744:0.433907:0.683338:0.426433:0.683338:0.000000 2:@0.412591:0.717287:0.421574:0.717287:0.421574:0.700853:0.412591:0.700853:0.000000 :@0.421574:0.717287:0.424887:0.717287:0.424887:0.700881:0.421574:0.700881:0.000000 cos:@0.446927:0.707057:0.469852:0.707057:0.469852:0.690651:0.446927:0.690651:0.000000:0.000000:0.000000 :@0.469789:0.707057:0.473820:0.707057:0.473820:0.690624:0.469789:0.690624:0.000000 x y:@0.478374:0.701160:0.510255:0.701160:0.510255:0.684753:0.478374:0.684753:0.000000:0.000000:0.000000 :@0.485755:0.701160:0.502855:0.701160:0.502855:0.684726:0.485755:0.684726:0.000000:0.000000:0.000000 –:@0.489712:0.701742:0.498916:0.701742:0.498916:0.684088:0.489712:0.684088:0.000000 2:@0.489823:0.718703:0.498806:0.718703:0.498806:0.702269:0.489823:0.702269:0.000000 :@0.498806:0.718703:0.502119:0.718703:0.502119:0.702297:0.498806:0.702297:0.000000 cosx cosy:@0.258388:0.746301:0.336056:0.746301:0.336056:0.729894:0.258388:0.729894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.288705:0.746301:0.305806:0.746301:0.305806:0.729867:0.288705:0.729867:0.000000:0.000000:0.000000 –:@0.292663:0.746883:0.301866:0.746883:0.301866:0.729229:0.292663:0.729229:0.000000 = 2:@0.336012:0.746301:0.372900:0.746301:0.372900:0.729867:0.336012:0.729867:0.000000:0.000000:0.000000:0.000000:0.000000 –:@0.354806:0.746883:0.364009:0.746883:0.364009:0.729229:0.354806:0.729229:0.000000 sen:@0.372826:0.746301:0.396332:0.746301:0.396332:0.729894:0.372826:0.729894:0.000000:0.000000:0.000000 :@0.396277:0.746301:0.400308:0.746301:0.400308:0.729867:0.396277:0.729867:0.000000 x:@0.403925:0.738995:0.411380:0.738995:0.411380:0.722588:0.403925:0.722588:0.000000 + :@0.411306:0.738995:0.430192:0.738995:0.430192:0.722561:0.411306:0.722561:0.000000:0.000000:0.000000 y:@0.430100:0.738995:0.437573:0.738995:0.437573:0.722588:0.430100:0.722588:0.000000 2:@0.416257:0.756538:0.425240:0.756538:0.425240:0.740104:0.416257:0.740104:0.000000 :@0.425240:0.756538:0.428553:0.756538:0.428553:0.740132:0.425240:0.740132:0.000000 sen:@0.450594:0.746309:0.474100:0.746309:0.474100:0.729903:0.450594:0.729903:0.000000:0.000000:0.000000 :@0.474045:0.746309:0.478076:0.746309:0.478076:0.729876:0.474045:0.729876:0.000000 x y:@0.482629:0.741305:0.514510:0.741305:0.514510:0.724899:0.482629:0.724899:0.000000:0.000000:0.000000 :@0.490010:0.741305:0.507111:0.741305:0.507111:0.724872:0.490010:0.724872:0.000000:0.000000:0.000000 –:@0.493968:0.741888:0.503171:0.741888:0.503171:0.724234:0.493968:0.724234:0.000000 2:@0.494078:0.758849:0.503061:0.758849:0.503061:0.742415:0.494078:0.742415:0.000000 :@0.503061:0.758849:0.506374:0.758849:0.506374:0.742443:0.503061:0.742443:0.000000 Ejercicios resueltos:@0.073086:0.804600:0.219926:0.804600:0.219926:0.787930:0.073086:0.787930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Demuestra las siguientes identidades:@0.073089:0.831973:0.386150:0.831973:0.386150:0.815304:0.073089:0.815304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cosx:@0.326530:0.856941:0.356899:0.856941:0.356899:0.840535:0.326530:0.840535:0.000000:0.000000:0.000000:0.000000 secx senx :@0.310130:0.874484:0.376543:0.874484:0.376543:0.858078:0.310130:0.858078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = :@0.378347:0.865123:0.397233:0.865123:0.397233:0.848689:0.378347:0.848689:0.000000:0.000000:0.000000 cscx senx:@0.397141:0.865123:0.472500:0.865123:0.472500:0.848717:0.397141:0.848717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –:@0.429261:0.865706:0.438465:0.865706:0.438465:0.848051:0.429261:0.848051:0.000000 Considermos tres formas posibles de hacerlo::@0.103214:0.899627:0.431345:0.899627:0.431345:0.883193:0.103214:0.883193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Relación entre radianes y :@0.740294:0.186502:0.908498:0.186502:0.908498:0.171562:0.740294:0.171562:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 grados :@0.740294:0.201631:0.789367:0.201631:0.789367:0.186691:0.740294:0.186691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 :@0.740294:0.216760:0.763135:0.216760:0.763135:0.201820:0.740294:0.201820:0.000000:0.000000:0.000000 p:@0.748393:0.216256:0.759554:0.216256:0.759554:0.203787:0.748393:0.203787:0.000000 Rad:@0.763069:0.216760:0.787975:0.216760:0.787975:0.201845:0.763069:0.201845:0.000000:0.000000:0.000000 = 360°:@0.787918:0.216760:0.834238:0.216760:0.834238:0.201820:0.787918:0.201820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.740310:0.231385:0.751472:0.231385:0.751472:0.218916:0.740310:0.218916:0.000000 :@0.751388:0.231889:0.755053:0.231889:0.755053:0.216949:0.751388:0.216949:0.000000 Rad:@0.754986:0.231889:0.779893:0.231889:0.779893:0.216974:0.754986:0.216974:0.000000:0.000000:0.000000 = 180°:@0.779836:0.231889:0.826155:0.231889:0.826155:0.216949:0.779836:0.216949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 por tanto::@0.740310:0.254166:0.805064:0.254166:0.805064:0.239226:0.740310:0.239226:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 Rad = :@0.740310:0.271754:0.794354:0.271754:0.794354:0.256814:0.740310:0.256814:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 180°:@0.798206:0.264881:0.824502:0.264881:0.824502:0.251435:0.798206:0.251435:0.000000:0.000000:0.000000:0.000000 p:@0.806324:0.276103:0.816369:0.276103:0.816369:0.264881:0.806324:0.264881:0.000000 y:@0.830071:0.271751:0.848227:0.271751:0.848227:0.256811:0.830071:0.256811:0.000000:0.000000:0.000000:0.000000 1° = :@0.740294:0.301240:0.770415:0.301240:0.770415:0.286300:0.740294:0.286300:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.782413:0.292168:0.792458:0.292168:0.792458:0.280946:0.782413:0.280946:0.000000 180°:@0.774295:0.304865:0.800591:0.304865:0.800591:0.291419:0.774295:0.291419:0.000000:0.000000:0.000000:0.000000 = Rad:@0.805405:0.301235:0.847752:0.301235:0.847752:0.286295:0.805405:0.286295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • Para pasar de Rad a:@0.740294:0.331493:0.881805:0.331493:0.881805:0.316553:0.740294:0.316553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 grados, se multiplica por:@0.754524:0.346622:0.915959:0.346622:0.915959:0.331682:0.754524:0.331682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 180°:@0.816624:0.360911:0.842919:0.360911:0.842919:0.347465:0.816624:0.347465:0.000000:0.000000:0.000000:0.000000 p:@0.824741:0.372133:0.834787:0.372133:0.834787:0.360911:0.824741:0.360911:0.000000 • Para pasar de grados a:@0.740294:0.390951:0.901970:0.390951:0.901970:0.376011:0.740294:0.376011:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Rad, se multiplica por:@0.754524:0.406080:0.895795:0.406080:0.895795:0.391140:0.754524:0.391140:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.825118:0.419349:0.835163:0.419349:0.835163:0.408127:0.825118:0.408127:0.000000 180°:@0.817000:0.432046:0.843296:0.432046:0.843296:0.418600:0.817000:0.418600:0.000000:0.000000:0.000000:0.000000 Competencia :@0.740294:0.146688:0.848854:0.146688:0.848854:0.129741:0.740294:0.129741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.740294:0.163330:0.837769:0.163330:0.837769:0.146383:0.740294:0.146383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 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