54:@0.037229:0.974518:0.056728:0.974518:0.056728:0.957377:0.037229:0.957377:0.000000:0.000000
Funciones trigonométricas:@0.073089:0.043661:0.311884:0.043661:0.311884:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4.1 Función secante:@0.293660:0.235348:0.448789:0.235348:0.448789:0.218401:0.293660:0.218401:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función secante se denota como :@0.293660:0.260394:0.564087:0.260394:0.564087:0.244682:0.293660:0.244682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sec:@0.565001:0.260394:0.588833:0.260394:0.588833:0.244959:0.565001:0.244959:0.000000:0.000000:0.000000
, para       en el que está definida :@0.588876:0.260394:0.859113:0.260394:0.859113:0.244682:0.588876:0.244682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.634286:0.260394:0.641741:0.260394:0.641741:0.244959:0.634286:0.244959:0.000000
[:@0.646601:0.260256:0.661934:0.260256:0.661934:0.246207:0.646601:0.246207:0.000000
R:@0.666812:0.259534:0.680102:0.259534:0.680102:0.246637:0.666812:0.246637:0.000000
Sec x:@0.859978:0.260394:0.896240:0.260394:0.896240:0.244959:0.859978:0.244959:0.000000:0.000000:0.000000:0.000000:0.000000
( ). Se :@0.883852:0.260394:0.930941:0.260394:0.930941:0.244682:0.883852:0.244682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
suele notar y definir como :@0.293660:0.277036:0.487231:0.277036:0.487231:0.261323:0.293660:0.261323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sec x:@0.492643:0.307449:0.528426:0.307449:0.528426:0.292014:0.492643:0.292014:0.000000:0.000000:0.000000:0.000000:0.000000
( )   :@0.516167:0.307449:0.556368:0.307449:0.556368:0.291736:0.516167:0.291736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.537096:0.306894:0.552429:0.306894:0.552429:0.293179:0.537096:0.293179:0.000000
1:@0.572711:0.299342:0.581693:0.299342:0.581693:0.283630:0.572711:0.283630:0.000000
cos( ):@0.557488:0.313710:0.599567:0.313710:0.599567:0.297997:0.557488:0.297997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.587234:0.313710:0.594689:0.313710:0.594689:0.298275:0.587234:0.298275:0.000000
,            :@0.600039:0.307440:0.650732:0.307440:0.650732:0.291728:0.600039:0.291728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cos x:@0.650567:0.307440:0.687952:0.307440:0.687952:0.292005:0.650567:0.292005:0.000000:0.000000:0.000000:0.000000:0.000000
( )   0.:@0.675693:0.307440:0.727932:0.307440:0.727932:0.291728:0.675693:0.291728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
?:@0.696622:0.307981:0.711955:0.307981:0.711955:0.292809:0.696622:0.292809:0.000000
Determinemos el subconjunto de   en el que :@0.293650:0.332486:0.632012:0.332486:0.632012:0.316774:0.293650:0.316774:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.543124:0.331626:0.556414:0.331626:0.556414:0.318729:0.543124:0.318729:0.000000
Cos x:@0.631865:0.332486:0.669250:0.332486:0.669250:0.317051:0.631865:0.317051:0.000000:0.000000:0.000000:0.000000:0.000000
( )   0.:@0.656991:0.332486:0.709231:0.332486:0.709231:0.316774:0.656991:0.316774:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.677920:0.331931:0.693253:0.331931:0.693253:0.318216:0.677920:0.318216:0.000000
Tenemos :@0.293650:0.357532:0.363958:0.357532:0.363958:0.341819:0.293650:0.341819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cos x:@0.363837:0.357532:0.401222:0.357532:0.401222:0.342097:0.363837:0.342097:0.000000:0.000000:0.000000:0.000000:0.000000
( )   0 :@0.388963:0.357532:0.442031:0.357532:0.442031:0.341819:0.388963:0.341819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.409892:0.356977:0.425225:0.356977:0.425225:0.343262:0.409892:0.343262:0.000000
⇔:@0.441939:0.357116:0.461119:0.357116:0.461119:0.340128:0.441939:0.340128:0.000000
         :@0.461027:0.357532:0.536274:0.357521:0.536274:0.341808:0.461027:0.341819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.464985:0.357532:0.472440:0.357532:0.472440:0.342097:0.464985:0.342097:0.000000
5:@0.476324:0.356977:0.491657:0.356977:0.491657:0.343262:0.476324:0.343262:0.000000
p:@0.498369:0.351333:0.510647:0.351333:0.510647:0.337617:0.498369:0.337617:0.000000
2:@0.499841:0.366255:0.508824:0.366255:0.508824:0.350543:0.499841:0.350543:0.000000
1 p:@0.517002:0.356966:0.555970:0.356966:0.555970:0.343250:0.517002:0.343250:0.000000:0.000000:0.000000
k:@0.536201:0.357521:0.543766:0.357521:0.543766:0.342086:0.536201:0.342086:0.000000
,          , luego,:@0.555878:0.357521:0.673585:0.357521:0.673585:0.341808:0.555878:0.341808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.578758:0.357521:0.586324:0.357521:0.586324:0.342086:0.578758:0.342086:0.000000
[:@0.590208:0.357382:0.605541:0.357382:0.605541:0.343334:0.590208:0.343334:0.000000
Z:@0.609406:0.356661:0.621684:0.356661:0.621684:0.343764:0.609406:0.343764:0.000000
{      | :@0.293685:0.384189:0.354043:0.384189:0.354043:0.368477:0.293685:0.368477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.298490:0.384189:0.305944:0.384189:0.305944:0.368754:0.298490:0.368754:0.000000
[:@0.309828:0.384051:0.325162:0.384051:0.325162:0.370002:0.309828:0.370002:0.000000
R:@0.329027:0.383330:0.342317:0.383330:0.342317:0.370432:0.329027:0.370432:0.000000
Cos x:@0.353951:0.384189:0.391336:0.384189:0.391336:0.368754:0.353951:0.368754:0.000000:0.000000:0.000000:0.000000:0.000000
( )   0}   :@0.379076:0.384189:0.456111:0.384189:0.456111:0.368477:0.379076:0.368477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.400006:0.383635:0.415339:0.383635:0.415339:0.369919:0.400006:0.369919:0.000000
5:@0.436838:0.383635:0.452172:0.383635:0.452172:0.369919:0.436838:0.369919:0.000000
p:@0.465632:0.377170:0.477910:0.377170:0.477910:0.363454:0.465632:0.363454:0.000000
2:@0.467105:0.392092:0.476088:0.392092:0.476088:0.376379:0.467105:0.376379:0.000000
1 p:@0.482040:0.385009:0.521008:0.385009:0.521008:0.371293:0.482040:0.371293:0.000000:0.000000:0.000000
 :@0.497281:0.385231:0.501312:0.385231:0.501312:0.369518:0.497281:0.369518:0.000000
k:@0.501239:0.385231:0.508804:0.385231:0.508804:0.369795:0.501239:0.369795:0.000000
 |       .:@0.520916:0.385231:0.587109:0.384193:0.587109:0.368480:0.520916:0.369518:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.536617:0.385231:0.544183:0.385231:0.544183:0.369795:0.536617:0.369795:0.000000
[:@0.548048:0.385411:0.563382:0.385411:0.563382:0.371363:0.548048:0.371363:0.000000
Z:@0.567247:0.384634:0.579525:0.384634:0.579525:0.371737:0.567247:0.371737:0.000000
5:@0.456618:0.390091:0.461076:0.390091:0.461076:0.365010:0.456618:0.365010:0.000000
5:@0.583400:0.390091:0.578942:0.390091:0.578942:0.365010:0.583400:0.365010:0.000000
Por lo tanto, la función secante queda definida como sigue: :@0.293660:0.409233:0.726912:0.409233:0.726912:0.393520:0.293660:0.393520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sec:@0.490820:0.453223:0.515565:0.453223:0.515565:0.436539:0.490820:0.436539:0.000000:0.000000:0.000000
: :@0.515504:0.453223:0.522665:0.453223:0.522665:0.437510:0.515504:0.437510:0.000000:0.000000
p:@0.562697:0.431660:0.574975:0.431660:0.574975:0.417945:0.562697:0.417945:0.000000
2:@0.564170:0.446582:0.573153:0.446582:0.573153:0.430870:0.564170:0.430870:0.000000
x:@0.535565:0.468411:0.543020:0.468411:0.543020:0.452976:0.535565:0.452976:0.000000
Sec x:@0.572140:0.468411:0.608200:0.468411:0.608200:0.452976:0.572140:0.452976:0.000000:0.000000:0.000000:0.000000:0.000000
( ) :@0.595867:0.468411:0.617109:0.468411:0.617109:0.452698:0.595867:0.452698:0.000000:0.000000:0.000000:0.000000
5 :@0.617109:0.467856:0.637044:0.467856:0.637044:0.454141:0.617109:0.454141:0.000000:0.000000
1 p:@0.580890:0.439153:0.619858:0.439153:0.619858:0.425437:0.580890:0.425437:0.000000:0.000000:0.000000
 :@0.596131:0.439375:0.600163:0.439375:0.600163:0.423662:0.596131:0.423662:0.000000
k:@0.600089:0.439375:0.607654:0.439375:0.607654:0.423939:0.600089:0.423939:0.000000
 |      :@0.619766:0.439375:0.666171:0.439375:0.666171:0.423662:0.619766:0.423662:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.635468:0.439375:0.643033:0.439375:0.643033:0.423939:0.635468:0.423939:0.000000
[:@0.646899:0.439555:0.662232:0.439555:0.662232:0.425506:0.646899:0.425506:0.000000
Z:@0.666097:0.438778:0.678375:0.438778:0.678375:0.425881:0.666097:0.425881:0.000000
5:@0.523563:0.475221:0.528021:0.475221:0.528021:0.416165:0.523563:0.416165:0.000000
5:@0.554918:0.443726:0.559376:0.443726:0.559376:0.418644:0.554918:0.418644:0.000000
5:@0.685535:0.443924:0.681078:0.443924:0.681078:0.418842:0.685535:0.418842:0.000000
R:@0.530819:0.438971:0.545317:0.438971:0.545317:0.424901:0.530819:0.424901:0.000000
\:@0.545317:0.439304:0.550900:0.439304:0.550900:0.424342:0.545317:0.424342:0.000000
R:@0.714176:0.440091:0.728674:0.440091:0.728674:0.426021:0.714176:0.426021:0.000000
→:@0.689972:0.441220:0.709791:0.441220:0.709791:0.424185:0.689972:0.424185:0.000000
→:@0.546034:0.470767:0.565853:0.470767:0.565853:0.453732:0.546034:0.453732:0.000000
1:@0.651666:0.461225:0.660649:0.461225:0.660649:0.445512:0.651666:0.445512:0.000000
Cos x:@0.636447:0.475592:0.674108:0.475592:0.674108:0.460157:0.636447:0.460157:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.661775:0.475592:0.678986:0.475592:0.678986:0.459879:0.661775:0.459879:0.000000:0.000000:0.000000
Determinemos el recorrido de esta función, esto es,  :@0.293660:0.491312:0.674541:0.491312:0.674541:0.475600:0.293660:0.475600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 p:@0.534745:0.516637:0.573713:0.516637:0.573713:0.502921:0.534745:0.502921:0.000000:0.000000:0.000000
 :@0.549986:0.516859:0.554017:0.516859:0.554017:0.501146:0.549986:0.501146:0.000000
k:@0.553944:0.516859:0.561509:0.516859:0.561509:0.501424:0.553944:0.501424:0.000000
 |      :@0.573621:0.516859:0.620026:0.516859:0.620026:0.501146:0.573621:0.501146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.589322:0.516859:0.596888:0.516859:0.596888:0.501424:0.589322:0.501424:0.000000
[:@0.600753:0.517039:0.616087:0.517039:0.616087:0.502991:0.600753:0.502991:0.000000
Z:@0.619952:0.516262:0.632230:0.516262:0.632230:0.503365:0.619952:0.503365:0.000000
5:@0.397064:0.522487:0.401522:0.522487:0.401522:0.497406:0.397064:0.497406:0.000000
5:@0.512207:0.522487:0.516665:0.522487:0.516665:0.497406:0.512207:0.497406:0.000000
5 5:@0.641730:0.522612:0.643878:0.522060:0.643878:0.496979:0.641730:0.497530:0.000000:0.000000:0.000000
    :@0.281237:0.547954:0.297141:0.547954:0.297141:0.532241:0.281237:0.532241:0.000000:0.000000:0.000000:0.000000
Rec  Sec:@0.297067:0.547954:0.352867:0.547954:0.352867:0.532519:0.297067:0.532519:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.324476:0.547954:0.329353:0.547954:0.329353:0.532241:0.324476:0.532241:0.000000
)  ]:@0.352793:0.547954:0.381667:0.547954:0.381667:0.532241:0.352793:0.532241:0.000000:0.000000:0.000000:0.000000
5 2` 2:@0.361548:0.547732:0.431422:0.547732:0.431422:0.534016:0.361548:0.534016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,  1] :@0.409020:0.547954:0.449074:0.547954:0.449074:0.532241:0.409020:0.532241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
<:@0.448982:0.548134:0.464315:0.548134:0.464315:0.534086:0.448982:0.534086:0.000000
 :@0.464223:0.547732:0.468825:0.547732:0.468825:0.534016:0.464223:0.534016:0.000000
[1,  [.:@0.468733:0.547954:0.509708:0.547954:0.509708:0.532241:0.468733:0.532241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
`:@0.489515:0.547732:0.501793:0.547732:0.501793:0.534016:0.489515:0.534016:0.000000
Rec Sec x:@0.297757:0.518277:0.366471:0.518277:0.366471:0.502842:0.297757:0.502842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 (:@0.321925:0.518277:0.330761:0.518277:0.330761:0.502564:0.321925:0.502564:0.000000:0.000000
( )) :@0.354201:0.518277:0.380037:0.518277:0.380037:0.502564:0.354201:0.502564:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.379945:0.518055:0.395278:0.518055:0.395278:0.504340:0.379945:0.504340:0.000000
Sec x x:@0.402347:0.517445:0.462060:0.517445:0.462060:0.502010:0.402347:0.502010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) |   :@0.425860:0.517445:0.465999:0.517445:0.465999:0.501732:0.425860:0.501732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[ :@0.465925:0.517625:0.485768:0.517625:0.485768:0.503577:0.465925:0.503577:0.000000:0.000000
R :@0.485676:0.516849:0.503476:0.516849:0.503476:0.503951:0.485676:0.503951:0.000000:0.000000
\:@0.503384:0.517223:0.508501:0.517223:0.508501:0.503508:0.503384:0.503508:0.000000
p:@0.517538:0.509601:0.529815:0.509601:0.529815:0.495885:0.517538:0.495885:0.000000
2:@0.519005:0.524522:0.527988:0.524522:0.527988:0.508809:0.519005:0.508809:0.000000
.:@0.650418:0.521224:0.653621:0.521224:0.653621:0.505511:0.650418:0.505511:0.000000
La función secante es periódica de período 2 .:@0.293660:0.575077:0.633753:0.575077:0.633753:0.559365:0.293660:0.559365:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.618364:0.574523:0.630642:0.574523:0.630642:0.560807:0.618364:0.560807:0.000000
La función secante es par. En efecto, como :@0.293660:0.598861:0.604774:0.598861:0.604774:0.583149:0.293660:0.583149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cos:@0.604430:0.598861:0.629618:0.598861:0.629618:0.583426:0.604430:0.583426:0.000000:0.000000:0.000000
 (:@0.629556:0.598861:0.638391:0.598861:0.638391:0.583149:0.629556:0.583149:0.000000:0.000000
2 5:@0.638299:0.598307:0.684998:0.598307:0.684998:0.584591:0.638299:0.584591:0.000000:0.000000:0.000000
x:@0.653540:0.598861:0.660995:0.598861:0.660995:0.583426:0.653540:0.583426:0.000000
)   :@0.660922:0.598861:0.688937:0.598861:0.688937:0.583149:0.660922:0.583149:0.000000:0.000000:0.000000:0.000000
Cos x:@0.688864:0.598861:0.726249:0.598861:0.726249:0.583426:0.688864:0.583426:0.000000:0.000000:0.000000:0.000000:0.000000
( ),   :@0.713990:0.598861:0.746055:0.598861:0.746055:0.583149:0.713990:0.583149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
;:@0.745945:0.598307:0.758222:0.598307:0.758222:0.584591:0.745945:0.584591:0.000000
x:@0.758130:0.598861:0.765585:0.598861:0.765585:0.583426:0.758130:0.583426:0.000000
    , se sigue que::@0.765512:0.598861:0.903235:0.598861:0.903235:0.583149:0.765512:0.583149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.769469:0.598723:0.784802:0.598723:0.784802:0.584674:0.769469:0.584674:0.000000
R:@0.788668:0.598002:0.801958:0.598002:0.801958:0.585104:0.788668:0.585104:0.000000
5:@0.784443:0.630171:0.779985:0.630171:0.779985:0.605090:0.784443:0.605090:0.000000
5:@0.654924:0.630041:0.659382:0.630041:0.659382:0.604960:0.654924:0.604960:0.000000
p:@0.660252:0.617155:0.672530:0.617155:0.672530:0.603439:0.660252:0.603439:0.000000
2:@0.661725:0.632077:0.670708:0.632077:0.670708:0.616364:0.661725:0.616364:0.000000
Sec:@0.294942:0.624418:0.318529:0.624418:0.318529:0.608983:0.294942:0.608983:0.000000:0.000000:0.000000
(:@0.318466:0.624418:0.323344:0.624418:0.323344:0.608705:0.318466:0.608705:0.000000
2 5:@0.323271:0.624196:0.369970:0.624196:0.369970:0.610480:0.323271:0.610480:0.000000:0.000000:0.000000
x:@0.338512:0.624418:0.345967:0.624418:0.345967:0.608983:0.338512:0.608983:0.000000
)                                   :@0.345893:0.624418:0.522916:0.624418:0.522916:0.608705:0.345893:0.608705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.433088:0.624196:0.448422:0.624196:0.448422:0.610480:0.433088:0.610480:0.000000
5:@0.503643:0.624196:0.518977:0.624196:0.518977:0.610480:0.503643:0.610480:0.000000
Sec x:@0.522842:0.624418:0.558626:0.624418:0.558626:0.608983:0.522842:0.608983:0.000000:0.000000:0.000000:0.000000:0.000000
( ),   :@0.546356:0.624418:0.578432:0.624418:0.578432:0.608705:0.546356:0.608705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
;:@0.578322:0.624196:0.590599:0.624196:0.590599:0.610480:0.578322:0.610480:0.000000
x:@0.590507:0.624418:0.597962:0.624418:0.597962:0.608983:0.590507:0.608983:0.000000
     \          :@0.597889:0.624418:0.695392:0.624418:0.695392:0.608705:0.597889:0.608705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.601846:0.624598:0.617179:0.624598:0.617179:0.610550:0.601846:0.610550:0.000000
R:@0.621045:0.623822:0.634335:0.623822:0.634335:0.610924:0.621045:0.610924:0.000000
1 p:@0.676119:0.624196:0.715088:0.624196:0.715088:0.610480:0.676119:0.610480:0.000000:0.000000:0.000000
k:@0.695318:0.624418:0.702883:0.624418:0.702883:0.608983:0.695318:0.608983:0.000000
 |         .:@0.714995:0.624418:0.784630:0.624418:0.784630:0.608705:0.714995:0.608705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.730697:0.624418:0.738262:0.624418:0.738262:0.608983:0.730697:0.608983:0.000000
[:@0.742128:0.624598:0.757461:0.624598:0.757461:0.610550:0.742128:0.610550:0.000000
Z:@0.761327:0.623822:0.773604:0.623822:0.773604:0.610924:0.761327:0.610924:0.000000
1:@0.391990:0.617513:0.400973:0.617513:0.400973:0.601800:0.391990:0.601800:0.000000
Cos:@0.376767:0.631880:0.402096:0.631880:0.402096:0.616445:0.376767:0.616445:0.000000:0.000000:0.000000
(:@0.402096:0.631880:0.406974:0.631880:0.406974:0.616168:0.402096:0.616168:0.000000
2:@0.406974:0.631492:0.422307:0.631492:0.422307:0.617776:0.406974:0.617776:0.000000
x:@0.422307:0.631880:0.429762:0.631880:0.429762:0.616445:0.422307:0.616445:0.000000
):@0.429762:0.631880:0.434640:0.631880:0.434640:0.616168:0.429762:0.616168:0.000000
1:@0.474836:0.617513:0.483819:0.617513:0.483819:0.601800:0.474836:0.601800:0.000000
Cos x:@0.459613:0.631880:0.497274:0.631880:0.497274:0.616445:0.459613:0.616445:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.484942:0.631880:0.502152:0.631880:0.502152:0.616168:0.484942:0.616168:0.000000:0.000000:0.000000
Por otro lado, el grafo de la función secante se nota  (:@0.293660:0.657375:0.671101:0.657375:0.671101:0.641662:0.293660:0.641662:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
G Sec x:@0.655492:0.657375:0.706314:0.657375:0.706314:0.641940:0.655492:0.641940:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( )) y se define como el conjunto::@0.694165:0.657375:0.927083:0.657375:0.927083:0.641662:0.694165:0.641662:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 5:@0.804590:0.688404:0.806839:0.688404:0.806839:0.663322:0.804590:0.663322:0.000000:0.000000:0.000000
5:@0.489719:0.688404:0.494177:0.688404:0.494177:0.663322:0.489719:0.663322:0.000000
5:@0.673699:0.688404:0.678157:0.688404:0.678157:0.663322:0.673699:0.663322:0.000000
p:@0.682801:0.675227:0.695079:0.675227:0.695079:0.661512:0.682801:0.661512:0.000000
2:@0.684274:0.690149:0.693257:0.690149:0.693257:0.674437:0.684274:0.674437:0.000000
   ( , :@0.481372:0.682651:0.512554:0.682651:0.512554:0.666938:0.481372:0.666938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x Sec x:@0.498012:0.682651:0.548246:0.682651:0.548246:0.667215:0.498012:0.667215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ))     |       \          :@0.535976:0.682651:0.715933:0.682651:0.715933:0.666938:0.535976:0.666938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.561720:0.682831:0.577053:0.682831:0.577053:0.668782:0.561720:0.668782:0.000000
R:@0.580919:0.682054:0.594209:0.682054:0.594209:0.669157:0.580919:0.669157:0.000000
2:@0.594133:0.676752:0.599370:0.676752:0.599370:0.667591:0.594133:0.667591:0.000000
x:@0.611048:0.682651:0.618503:0.682651:0.618503:0.667215:0.611048:0.667215:0.000000
[:@0.622387:0.682831:0.637720:0.682831:0.637720:0.668782:0.622387:0.668782:0.000000
R:@0.641586:0.682054:0.654876:0.682054:0.654876:0.669157:0.641586:0.669157:0.000000
1 p:@0.696660:0.682429:0.735628:0.682429:0.735628:0.668713:0.696660:0.668713:0.000000:0.000000:0.000000
k:@0.715859:0.682651:0.723424:0.682651:0.723424:0.667215:0.715859:0.667215:0.000000
 |           .:@0.735536:0.682651:0.813086:0.682651:0.813086:0.666938:0.735536:0.666938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.751228:0.682651:0.758794:0.682651:0.758794:0.667215:0.751228:0.667215:0.000000
[:@0.762669:0.682831:0.778002:0.682831:0.778002:0.668782:0.762669:0.668782:0.000000
Z:@0.781867:0.682054:0.794145:0.682054:0.794145:0.669157:0.781867:0.669157:0.000000
G Sec x:@0.403068:0.684200:0.454488:0.684200:0.454488:0.668765:0.403068:0.668765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.413900:0.684200:0.418778:0.684200:0.418778:0.668487:0.413900:0.668487:0.000000
( )) :@0.442217:0.684200:0.468054:0.684200:0.468054:0.668487:0.442217:0.668487:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.467962:0.683978:0.483295:0.683978:0.483295:0.670262:0.467962:0.670262:0.000000
4.2 Función cosecante:@0.293660:0.715222:0.467123:0.715222:0.467123:0.698275:0.293660:0.698275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función cosecante se designa con :@0.293660:0.739006:0.564177:0.739006:0.564177:0.723293:0.293660:0.723293:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Csc:@0.563860:0.739006:0.587642:0.739006:0.587642:0.723571:0.563860:0.723571:0.000000:0.000000:0.000000
 y se define como: :@0.587587:0.739006:0.722862:0.739006:0.722862:0.723293:0.587587:0.723293:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Csc x:@0.487266:0.770065:0.528405:0.770065:0.528405:0.752421:0.487266:0.752421:0.000000:0.000000:0.000000:0.000000:0.000000
( ) :@0.514392:0.770065:0.538420:0.770065:0.538420:0.752104:0.514392:0.752104:0.000000:0.000000:0.000000:0.000000
5:@0.538315:0.769811:0.555842:0.769811:0.555842:0.754133:0.538315:0.754133:0.000000
,:@0.604216:0.769019:0.608024:0.769019:0.608024:0.751375:0.604216:0.751375:0.000000
Sen x:@0.646024:0.769019:0.689347:0.769019:0.689347:0.751375:0.646024:0.751375:0.000000:0.000000:0.000000:0.000000:0.000000
( ) :@0.675250:0.769019:0.699531:0.769019:0.699531:0.751058:0.675250:0.751058:0.000000:0.000000:0.000000:0.000000
? :@0.699531:0.769637:0.722319:0.769637:0.722319:0.752294:0.699531:0.752294:0.000000:0.000000
0:@0.722319:0.769019:0.732587:0.769019:0.732587:0.751058:0.722319:0.751058:0.000000
 :@0.732596:0.768379:0.737856:0.768379:0.737856:0.752701:0.732596:0.752701:0.000000
1:@0.571864:0.761595:0.582132:0.761595:0.582132:0.743634:0.571864:0.743634:0.000000
Sen x:@0.554463:0.778018:0.597786:0.778018:0.597786:0.760374:0.554463:0.760374:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.583689:0.778018:0.603362:0.778018:0.603362:0.760057:0.583689:0.760057:0.000000:0.000000:0.000000
Determinemos el subconjunto de   en el que :@0.317377:0.804735:0.655739:0.804735:0.655739:0.789022:0.317377:0.789022:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.566851:0.803875:0.580141:0.803875:0.580141:0.790978:0.566851:0.790978:0.000000
Sen x:@0.655592:0.804735:0.693216:0.804735:0.693216:0.789300:0.655592:0.789300:0.000000:0.000000:0.000000:0.000000:0.000000
( )   0. Tenemos: :@0.680957:0.804735:0.809812:0.804735:0.809812:0.789022:0.680957:0.789022:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.701886:0.804180:0.717219:0.804180:0.717219:0.790464:0.701886:0.790464:0.000000
Sen x:@0.513856:0.828519:0.551480:0.828519:0.551480:0.813083:0.513856:0.813083:0.000000:0.000000:0.000000:0.000000:0.000000
( )   0 :@0.539221:0.828519:0.592289:0.828519:0.592289:0.812806:0.539221:0.812806:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.560150:0.827964:0.575484:0.827964:0.575484:0.814248:0.560150:0.814248:0.000000
⇔:@0.592197:0.828103:0.611378:0.828103:0.611378:0.811114:0.592197:0.811114:0.000000
     :@0.611286:0.828519:0.645854:0.828519:0.645854:0.812806:0.611286:0.812806:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.615243:0.828519:0.622698:0.828519:0.622698:0.813083:0.615243:0.813083:0.000000
5 p:@0.626582:0.827964:0.665550:0.827964:0.665550:0.814248:0.626582:0.814248:0.000000:0.000000:0.000000
k:@0.645781:0.828519:0.653346:0.828519:0.653346:0.813083:0.645781:0.813083:0.000000
,         ,:@0.665458:0.828519:0.730417:0.828519:0.730417:0.812806:0.665458:0.812806:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.684381:0.828519:0.691946:0.828519:0.691946:0.813083:0.684381:0.813083:0.000000
[:@0.695830:0.828380:0.711163:0.828380:0.711163:0.814332:0.695830:0.814332:0.000000
Z:@0.715029:0.827659:0.727307:0.827659:0.727307:0.814762:0.715029:0.814762:0.000000
con lo que :@0.317377:0.852303:0.399050:0.852303:0.399050:0.836590:0.317377:0.836590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
{      | :@0.497345:0.876087:0.557702:0.876087:0.557702:0.860374:0.497345:0.860374:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.502149:0.876087:0.509604:0.876087:0.509604:0.860651:0.502149:0.860651:0.000000
[:@0.513488:0.875948:0.528821:0.875948:0.528821:0.861900:0.513488:0.861900:0.000000
R:@0.532687:0.875227:0.545977:0.875227:0.545977:0.862329:0.532687:0.862329:0.000000
Sen x:@0.557610:0.876087:0.595235:0.876087:0.595235:0.860651:0.557610:0.860651:0.000000:0.000000:0.000000:0.000000:0.000000
( )   0}   {:@0.582975:0.876087:0.664814:0.876087:0.664814:0.860374:0.582975:0.860374:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.603904:0.875532:0.619238:0.875532:0.619238:0.861816:0.603904:0.861816:0.000000
5 p:@0.640737:0.875532:0.684491:0.875532:0.684491:0.861816:0.640737:0.861816:0.000000:0.000000:0.000000
k:@0.664722:0.876087:0.672287:0.876087:0.672287:0.860651:0.664722:0.860651:0.000000
 |      }.:@0.684399:0.876087:0.746966:0.876087:0.746966:0.860374:0.684399:0.860374:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.696125:0.876087:0.703690:0.876087:0.703690:0.860651:0.696125:0.860651:0.000000
[:@0.707574:0.875948:0.722907:0.875948:0.722907:0.861900:0.707574:0.861900:0.000000
Z:@0.726773:0.875227:0.739050:0.875227:0.739050:0.862329:0.726773:0.862329:0.000000
De este resultado, la función cosecante queda definida como se indica::@0.317377:0.899871:0.831164:0.899871:0.831164:0.884158:0.317377:0.884158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En la Figura 5.12., se muestra el gráfico del conjunto  (:@0.317377:0.923655:0.715058:0.923655:0.715058:0.907942:0.317377:0.907942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
G Sec:@0.699283:0.923655:0.738785:0.923655:0.738785:0.908219:0.699283:0.908219:0.000000:0.000000:0.000000:0.000000:0.000000
) al que lo denominamos :@0.738785:0.923655:0.925932:0.923655:0.925932:0.907942:0.738785:0.907942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
representación gráfica de la función secante.:@0.317377:0.940296:0.643679:0.940296:0.643679:0.924584:0.317377:0.924584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tema 4. Funciones secante y cosecante:@0.073089:0.098522:0.645247:0.098522:0.645247:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuál es el recorrido de las funciones secante y cosecante?:@0.293660:0.162647:0.717204:0.162647:0.717204:0.146935:0.293660:0.146935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reto matemático:@0.302768:0.140138:0.425244:0.140138:0.425244:0.124732:0.302768:0.124732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Secante: :@0.082576:0.314263:0.144379:0.314263:0.144379:0.299109:0.082576:0.299109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se utiliza en el :@0.144287:0.314263:0.239986:0.314263:0.239986:0.299979:0.144287:0.299979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diseño de estructuras, :@0.082572:0.329392:0.230754:0.329392:0.230754:0.315108:0.082572:0.315108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como puentes y :@0.082572:0.344521:0.193662:0.344521:0.193662:0.330237:0.082572:0.330237:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
edificios, donde es :@0.082572:0.359650:0.208337:0.359650:0.208337:0.345366:0.082572:0.345366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
necesario calcular :@0.082572:0.374779:0.203751:0.374779:0.203751:0.360495:0.082572:0.360495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ángulos y distancias. La :@0.082572:0.389908:0.239496:0.389908:0.239496:0.375624:0.082572:0.375624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
secante puede ayudar :@0.082572:0.405037:0.232695:0.405037:0.232695:0.390753:0.082572:0.390753:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a determinar la relación :@0.082572:0.420166:0.241425:0.420166:0.241425:0.405882:0.082572:0.405882:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entre la longitud de un :@0.082572:0.435295:0.237801:0.435295:0.237801:0.421011:0.082572:0.421011:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lado de un triángulo y el :@0.082572:0.450424:0.246924:0.450424:0.246924:0.436140:0.082572:0.436140:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ángulo opuesto.:@0.082572:0.465553:0.190258:0.465553:0.190258:0.451269:0.082572:0.451269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cosecante:@0.082572:0.484250:0.154349:0.484250:0.154349:0.469095:0.082572:0.469095:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: en la :@0.154260:0.484250:0.195995:0.484250:0.195995:0.469965:0.154260:0.469965:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ingeniería de caminos, :@0.082572:0.499379:0.234887:0.499379:0.234887:0.485094:0.082572:0.485094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se puede aplicar para :@0.082572:0.514508:0.226952:0.514508:0.226952:0.500223:0.082572:0.500223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
calcular pendientes y :@0.082572:0.529636:0.226059:0.529636:0.226059:0.515352:0.082572:0.515352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
alturas de rampas, lo que :@0.082572:0.544765:0.251042:0.544765:0.251042:0.530481:0.082572:0.530481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es crucial para el diseño :@0.082572:0.559894:0.242900:0.559894:0.242900:0.545610:0.082572:0.545610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de carreteras y accesos. :@0.082572:0.575023:0.239946:0.575023:0.239946:0.560739:0.082572:0.560739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad :@0.078581:0.243005:0.230966:0.243005:0.230966:0.227599:0.078581:0.227599:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemáticas e :@0.078581:0.258134:0.178352:0.258134:0.178352:0.243850:0.078581:0.243850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ingeniería :@0.078581:0.273263:0.148053:0.273263:0.148053:0.258978:0.078581:0.258978:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y arquitectura:@0.078581:0.288392:0.169946:0.288392:0.169946:0.274107:0.078581:0.274107:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 5.12.:@0.221614:0.940006:0.281803:0.940006:0.281803:0.928578:0.221614:0.928578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.272791:0.863121:0.277535:0.863121:0.277535:0.853299:0.272791:0.853299:0.000000
0:@0.154068:0.858666:0.158151:0.858666:0.158151:0.851524:0.154068:0.851524:0.000000
1 2 3 4 5 6:@0.170183:0.850446:0.227647:0.850446:0.227647:0.843304:0.170183:0.843304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.163071:0.846871:0.167154:0.846871:0.167154:0.839729:0.163071:0.839729:0.000000
2:@0.143509:0.850193:0.150478:0.850193:0.150478:0.843959:0.143509:0.843959:0.000000
1:@0.150060:0.850446:0.154143:0.850446:0.154143:0.843304:0.150060:0.843304:0.000000
2:@0.151056:0.868947:0.158025:0.868947:0.158025:0.862713:0.151056:0.862713:0.000000
1:@0.157607:0.869199:0.161690:0.869199:0.161690:0.862057:0.157607:0.862057:0.000000
2:@0.132866:0.850193:0.139836:0.850193:0.139836:0.843959:0.132866:0.843959:0.000000
2:@0.139417:0.850446:0.143500:0.850446:0.143500:0.843304:0.139417:0.843304:0.000000
2:@0.122223:0.850193:0.129193:0.850193:0.129193:0.843959:0.122223:0.843959:0.000000
3:@0.128775:0.850446:0.132858:0.850446:0.132858:0.843304:0.128775:0.843304:0.000000
2:@0.111581:0.850193:0.118550:0.850193:0.118550:0.843959:0.111581:0.843959:0.000000
4:@0.118132:0.850446:0.122215:0.850446:0.122215:0.843304:0.118132:0.843304:0.000000
2:@0.100938:0.850193:0.107908:0.850193:0.107908:0.843959:0.100938:0.843959:0.000000
5:@0.107489:0.850446:0.111572:0.850446:0.111572:0.843304:0.107489:0.843304:0.000000
y:@0.150781:0.781750:0.155537:0.781750:0.155537:0.771928:0.150781:0.771928:0.000000
p:@0.174910:0.859341:0.180686:0.859341:0.180686:0.852889:0.174910:0.852889:0.000000
2:@0.175689:0.865905:0.179915:0.865905:0.179915:0.858513:0.175689:0.858513:0.000000
p:@0.141943:0.859341:0.147719:0.859341:0.147719:0.852889:0.141943:0.852889:0.000000
2:@0.142713:0.865905:0.146939:0.865905:0.146939:0.858513:0.142713:0.858513:0.000000
3:@0.108485:0.859602:0.112711:0.859602:0.112711:0.852210:0.108485:0.852210:0.000000
p 2p:@0.112711:0.859341:0.137145:0.859015:0.137145:0.852562:0.112711:0.852889:0.000000:0.000000:0.000000:0.000000
2:@0.111377:0.865905:0.115603:0.865905:0.115603:0.858513:0.111377:0.858513:0.000000
3:@0.208393:0.859602:0.212619:0.859602:0.212619:0.852210:0.208393:0.852210:0.000000
p:@0.212619:0.859341:0.218395:0.859341:0.218395:0.852889:0.212619:0.852889:0.000000
2:@0.211493:0.865905:0.215719:0.865905:0.215719:0.858513:0.211493:0.858513:0.000000
5:@0.240768:0.859602:0.244994:0.859602:0.244994:0.852210:0.240768:0.852210:0.000000
p:@0.244994:0.859341:0.250770:0.859341:0.250770:0.852889:0.244994:0.852889:0.000000
2:@0.243833:0.865905:0.248059:0.865905:0.248059:0.858513:0.243833:0.858513:0.000000
p:@0.191970:0.859015:0.197746:0.859015:0.197746:0.852562:0.191970:0.852562:0.000000
2 p:@0.085654:0.859341:0.102869:0.859341:0.102869:0.852889:0.085654:0.852889:0.000000:0.000000:0.000000
2:@0.092867:0.859602:0.097093:0.859602:0.097093:0.852210:0.092867:0.852210:0.000000
–:@0.136617:0.862427:0.140947:0.862427:0.140947:0.855035:0.136617:0.855035:0.000000
–:@0.103164:0.862427:0.107494:0.862427:0.107494:0.855035:0.103164:0.855035:0.000000
2:@0.223517:0.859602:0.227743:0.859602:0.227743:0.852210:0.223517:0.852210:0.000000
p:@0.227743:0.859341:0.233519:0.859341:0.233519:0.852889:0.227743:0.852889:0.000000
3:@0.257057:0.859602:0.261283:0.859602:0.261283:0.852210:0.257057:0.852210:0.000000
p:@0.261283:0.859341:0.267059:0.859341:0.267059:0.852889:0.261283:0.852889:0.000000
y Sec x:@0.185747:0.774194:0.220027:0.774194:0.220027:0.765318:0.185747:0.765318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 = :@0.190042:0.774194:0.200140:0.774194:0.200140:0.765159:0.190042:0.765159:0.000000:0.000000:0.000000
( ) =            .:@0.212936:0.774194:0.260268:0.774194:0.260268:0.765159:0.212936:0.765159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.245349:0.770007:0.250515:0.770007:0.250515:0.760972:0.245349:0.760972:0.000000
Cos x:@0.235707:0.779017:0.257363:0.779017:0.257363:0.770142:0.235707:0.770142:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.250271:0.779017:0.260167:0.779017:0.260167:0.769983:0.250271:0.769983:0.000000:0.000000:0.000000
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