182:@0.053974:0.966765:0.079386:0.966765:0.079386:0.950778:0.053974:0.950778:0.000000:0.000000:0.000000
Funciones secante y cosecante:@0.404235:0.127666:0.770559:0.127666:0.770559:0.083007:0.404235:0.083007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199646:0.111077:0.307805:0.111077:0.307805:0.095605:0.199646:0.095605:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cómo se define la :@0.199884:0.139704:0.326090:0.139704:0.326090:0.124641:0.199884:0.124641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función secante?:@0.153341:0.155546:0.261887:0.155546:0.261887:0.140483:0.153341:0.140483:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.196639:0.363493:0.196639:0.363493:0.181166:0.199646:0.181166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuál es el recorrido de :@0.199884:0.225267:0.353058:0.225267:0.353058:0.210204:0.199884:0.210204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la función secante y cosecante?:@0.153341:0.241109:0.356168:0.241109:0.356168:0.226046:0.153341:0.226046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Función secante:@0.404236:0.157916:0.534119:0.157916:0.534119:0.140233:0.404236:0.140233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función secante se denota como Sec, para       en el que está :@0.404236:0.174623:0.895913:0.174623:0.895913:0.158126:0.404236:0.158126:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.737718:0.174739:0.745193:0.174739:0.745193:0.158270:0.737718:0.158270:0.000000
:@0.750548:0.174407:0.766596:0.174407:0.766596:0.159760:0.750548:0.159760:0.000000
R:@0.772648:0.173536:0.785953:0.173536:0.785953:0.160674:0.772648:0.160674:0.000000
definida Sec( ). Se suele notar y definir como :@0.404231:0.191974:0.728714:0.191974:0.728714:0.175476:0.404231:0.175476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.496779:0.192090:0.504254:0.192090:0.504254:0.175621:0.496779:0.175621:0.000000
sec( ) =              ,            cos( ) ≠ 0.:@0.527644:0.221398:0.768345:0.221398:0.768345:0.204900:0.527644:0.204900:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.556253:0.221514:0.563728:0.221514:0.563728:0.205045:0.556253:0.205045:0.000000
x:@0.724574:0.221514:0.732049:0.221514:0.732049:0.205045:0.724574:0.205045:0.000000
Determinemos el subconjunto de   en el que cos( ) = 0.:@0.404231:0.256100:0.807484:0.256096:0.807484:0.239599:0.404231:0.239602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.648092:0.255010:0.661397:0.255010:0.661397:0.242147:0.648092:0.242147:0.000000
x:@0.763713:0.256212:0.771188:0.256212:0.771188:0.239743:0.763713:0.239743:0.000000
Tenemos cos( ) = 0     =       + :@0.404245:0.280576:0.637414:0.280576:0.637414:0.264078:0.404245:0.264078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.502555:0.280691:0.510030:0.280691:0.510030:0.264222:0.502555:0.264222:0.000000
⇔:@0.547702:0.279932:0.566904:0.279932:0.566904:0.262990:0.547702:0.262990:0.000000
x:@0.571046:0.280692:0.578521:0.280692:0.578521:0.264223:0.571046:0.264223:0.000000
kπ,:@0.637414:0.280692:0.658048:0.280692:0.658048:0.264223:0.637414:0.264223:0.000000:0.000000:0.000000
          , luego,:@0.658048:0.280576:0.773192:0.280576:0.773192:0.264078:0.658048:0.264078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.678758:0.280692:0.687003:0.280692:0.687003:0.264223:0.678758:0.264223:0.000000
:@0.691145:0.280359:0.707193:0.280359:0.707193:0.265712:0.691145:0.265712:0.000000
Z:@0.712103:0.279489:0.724395:0.279489:0.724395:0.266627:0.712103:0.266627:0.000000
{      | cos( ) = 0} =        +   |      :@0.404245:0.315278:0.676850:0.315278:0.676850:0.298780:0.404245:0.298780:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.410101:0.315393:0.417576:0.315393:0.417576:0.298925:0.410101:0.298925:0.000000
:@0.421718:0.315061:0.437766:0.315061:0.437766:0.300414:0.421718:0.300414:0.000000
R:@0.442670:0.314191:0.455974:0.314191:0.455974:0.301329:0.442670:0.301329:0.000000
x:@0.498762:0.315393:0.506237:0.315393:0.506237:0.298925:0.498762:0.298925:0.000000
kπ k:@0.608671:0.315393:0.652133:0.315393:0.652133:0.298925:0.608671:0.298925:0.000000:0.000000:0.000000:0.000000
:@0.656275:0.315061:0.672323:0.315061:0.672323:0.300414:0.656275:0.300414:0.000000
Z  :@0.677232:0.314191:0.698737:0.314191:0.698737:0.301329:0.677232:0.301329:0.000000:0.000000:0.000000
.:@0.698737:0.315278:0.701492:0.315278:0.701492:0.298780:0.698737:0.298780:0.000000
Por lo tanto, la función secante queda definida como sigue: :@0.404229:0.346885:0.828561:0.346885:0.828561:0.330387:0.404229:0.330387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404229:0.391390:0.408371:0.391390:0.408371:0.374892:0.404229:0.374892:0.000000
     Sec: :@0.464529:0.391390:0.516563:0.391390:0.516563:0.374892:0.464529:0.374892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Determinemos el recorrido de esta función, esto es,  :@0.404229:0.450570:0.776545:0.450570:0.776545:0.434072:0.404229:0.434072:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rec  Sec:@0.404229:0.485387:0.460888:0.485387:0.460888:0.468919:0.404229:0.468919:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.432202:0.485272:0.438155:0.485272:0.438155:0.468774:0.432202:0.468774:0.000000
) =    sec( ) |       \        +   |            .:@0.460888:0.485272:0.761669:0.485275:0.761669:0.468777:0.460888:0.468774:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x:@0.526966:0.485387:0.561161:0.485387:0.561161:0.468919:0.526966:0.468919:0.000000:0.000000:0.000000
:@0.565303:0.485055:0.581351:0.485055:0.581351:0.470408:0.565303:0.470408:0.000000
R:@0.586269:0.484188:0.599574:0.484188:0.599574:0.471326:0.586269:0.471326:0.000000
kπ k:@0.657349:0.485390:0.700811:0.485390:0.700811:0.468922:0.657349:0.468922:0.000000:0.000000:0.000000:0.000000
:@0.704953:0.485058:0.721001:0.485058:0.721001:0.470411:0.704953:0.470411:0.000000
Z:@0.725912:0.484188:0.738204:0.484188:0.738204:0.471326:0.725912:0.471326:0.000000
Rec  Sec:@0.404240:0.520092:0.460897:0.520092:0.460897:0.503623:0.404240:0.503623:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.432214:0.519976:0.438166:0.519976:0.438166:0.503479:0.432214:0.503479:0.000000
) = ]–∞, –1]   [1, ∞[.:@0.460899:0.519976:0.614867:0.519976:0.614867:0.503479:0.460899:0.503479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.551504:0.519759:0.567552:0.519759:0.567552:0.505113:0.551504:0.505113:0.000000
La función secante es periódica de período 2 .:@0.404240:0.554678:0.734713:0.554678:0.734713:0.538180:0.404240:0.538180:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
π:@0.722421:0.554793:0.731958:0.554793:0.731958:0.538325:0.722421:0.538325:0.000000
La función secante es par. En efecto, como cos(– ) = cos( ),        , :@0.404240:0.572029:0.895918:0.572029:0.895918:0.555531:0.404240:0.555531:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.744330:0.572144:0.751805:0.572144:0.751805:0.555675:0.744330:0.555675:0.000000
x:@0.805497:0.572144:0.812972:0.572144:0.812972:0.555675:0.805497:0.555675:0.000000
∀:@0.833615:0.579615:0.845188:0.579615:0.845188:0.560616:0.833615:0.560616:0.000000
x:@0.845102:0.572144:0.852577:0.572144:0.852577:0.555675:0.845102:0.555675:0.000000
:@0.856559:0.571510:0.871212:0.571510:0.871212:0.558137:0.856559:0.558137:0.000000
R:@0.875208:0.571060:0.889118:0.571060:0.889118:0.557613:0.875208:0.557613:0.000000
se sigue que::@0.404250:0.589379:0.491560:0.589379:0.491560:0.572882:0.404250:0.572882:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sec (– ) =                =              = sec( ),        \        +   |         .:@0.405463:0.620307:0.890554:0.620309:0.890554:0.603811:0.405463:0.603809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.448714:0.620423:0.456189:0.620423:0.456189:0.603954:0.448714:0.603954:0.000000
x:@0.655717:0.620423:0.663192:0.620423:0.663192:0.603954:0.655717:0.603954:0.000000
∀:@0.684309:0.627895:0.695882:0.627895:0.695882:0.608896:0.684309:0.608896:0.000000
x:@0.695890:0.620425:0.703365:0.620425:0.703365:0.603956:0.695890:0.603956:0.000000
:@0.707506:0.619790:0.722159:0.619790:0.722159:0.606417:0.707506:0.606417:0.000000
R :@0.726302:0.619340:0.745028:0.619340:0.745028:0.605893:0.726302:0.605893:0.000000:0.000000
kπ k:@0.798662:0.620425:0.842125:0.620425:0.842125:0.603956:0.798662:0.603956:0.000000:0.000000:0.000000:0.000000
:@0.846267:0.620092:0.862315:0.620092:0.862315:0.605445:0.846267:0.605445:0.000000
Z:@0.867224:0.619222:0.879515:0.619222:0.879515:0.606360:0.867224:0.606360:0.000000
Por otro lado, el grafo de la función secante se nota  (sec) y se define :@0.404241:0.655010:0.895867:0.655010:0.895867:0.638513:0.404241:0.638513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
G:@0.767426:0.655126:0.778870:0.655126:0.778870:0.638657:0.767426:0.638657:0.000000
como el conjunto::@0.404241:0.672361:0.534126:0.672361:0.534126:0.655864:0.404241:0.655864:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
G:@0.447800:0.704908:0.459244:0.704908:0.459244:0.688440:0.447800:0.688440:0.000000
(sec) =   ( , sec( ))   :@0.459244:0.704793:0.612429:0.704800:0.612429:0.688302:0.459244:0.688295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.527132:0.704908:0.534607:0.704908:0.534607:0.688440:0.527132:0.688440:0.000000
x:@0.570111:0.704908:0.577586:0.704908:0.577586:0.688440:0.570111:0.688440:0.000000
:@0.593634:0.704281:0.608286:0.704281:0.608286:0.690908:0.593634:0.690908:0.000000
R  :@0.612429:0.703831:0.636108:0.703831:0.636108:0.690384:0.612429:0.690384:0.000000:0.000000:0.000000
2:@0.626338:0.698447:0.631291:0.698447:0.631291:0.688828:0.626338:0.688828:0.000000
|      \        +   |           .:@0.636108:0.704800:0.848206:0.704800:0.848206:0.688302:0.636108:0.688302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.645259:0.704915:0.652734:0.704915:0.652734:0.688446:0.645259:0.688446:0.000000
:@0.656874:0.704281:0.671527:0.704281:0.671527:0.690908:0.656874:0.690908:0.000000
R :@0.675669:0.703831:0.694395:0.703831:0.694395:0.690384:0.675669:0.690384:0.000000:0.000000
kπ k:@0.748030:0.704915:0.791492:0.704915:0.791492:0.688446:0.748030:0.688446:0.000000:0.000000:0.000000:0.000000
:@0.795634:0.704583:0.811682:0.704583:0.811682:0.689936:0.795634:0.689936:0.000000
Z:@0.816591:0.703713:0.828883:0.703713:0.828883:0.690850:0.816591:0.690850:0.000000
 :@0.404238:0.722150:0.408380:0.722150:0.408380:0.705653:0.404238:0.705653:0.000000
Función cosecante:@0.404236:0.748026:0.552955:0.748026:0.552955:0.730344:0.404236:0.730344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función cosecante se designa con :@0.404236:0.764734:0.666665:0.764734:0.666665:0.748236:0.404236:0.748236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Csc:@0.666666:0.764850:0.690225:0.764850:0.690225:0.748381:0.666666:0.748381:0.000000:0.000000:0.000000
 y se define como: :@0.690229:0.764734:0.822562:0.764734:0.822562:0.748236:0.690229:0.748236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
csc( ) =              ,             sen( ) ≠ 0.:@0.525434:0.794158:0.770584:0.794158:0.770584:0.777660:0.525434:0.777660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.553850:0.794273:0.561325:0.794273:0.561325:0.777805:0.553850:0.777805:0.000000
x:@0.726814:0.794273:0.734289:0.794273:0.734289:0.777805:0.726814:0.777805:0.000000
Determinemos el subconjunto de   en el que sen( ) = 0. Tenemos: :@0.404236:0.828859:0.883984:0.828856:0.883984:0.812359:0.404236:0.812362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.648092:0.827769:0.661397:0.827769:0.661397:0.814907:0.648092:0.814907:0.000000
x:@0.764214:0.828972:0.771689:0.828972:0.771689:0.812503:0.764214:0.812503:0.000000
sen( ) = 0   x = :@0.542415:0.853335:0.667998:0.853335:0.667998:0.836837:0.542415:0.836838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.572411:0.853451:0.579886:0.853451:0.579886:0.836982:0.572411:0.836982:0.000000
⇔:@0.617568:0.852690:0.636770:0.852690:0.636770:0.835748:0.617568:0.835748:0.000000
kπ,    k:@0.667998:0.853450:0.713445:0.853450:0.713445:0.836981:0.667998:0.836981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
    ,:@0.713445:0.853335:0.753592:0.853335:0.753592:0.836837:0.713445:0.836837:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.717587:0.853118:0.733635:0.853118:0.733635:0.838471:0.717587:0.838471:0.000000
Z:@0.738545:0.852248:0.750837:0.852248:0.750837:0.839385:0.738545:0.839385:0.000000
con lo que :@0.404235:0.870685:0.484069:0.870685:0.484069:0.854188:0.404235:0.854188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
{      | sen( ) = 0} = {:@0.522004:0.888036:0.688854:0.888036:0.688854:0.871538:0.522004:0.871538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.527860:0.888152:0.535335:0.888152:0.535335:0.871683:0.527860:0.871683:0.000000
:@0.539477:0.887819:0.555525:0.887819:0.555525:0.873172:0.539477:0.873172:0.000000
R:@0.560439:0.886949:0.573744:0.886949:0.573744:0.874087:0.560439:0.874087:0.000000
x:@0.617033:0.888152:0.624508:0.888152:0.624508:0.871683:0.617033:0.871683:0.000000
kπ | k:@0.688854:0.888152:0.728001:0.888152:0.728001:0.871683:0.688854:0.871683:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
    }.:@0.728001:0.888036:0.774001:0.888036:0.774001:0.871538:0.728001:0.871538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.732143:0.887819:0.748191:0.887819:0.748191:0.873172:0.732143:0.873172:0.000000
Z:@0.753100:0.886949:0.765391:0.886949:0.765391:0.874087:0.753100:0.874087:0.000000
De este resultado, la función cosecante queda definida como se indica: :@0.404243:0.919716:0.895937:0.919716:0.895937:0.903218:0.404243:0.903218:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.609021:0.214124:0.617517:0.214124:0.617517:0.197626:0.609021:0.197626:0.000000
cos( ):@0.591817:0.230463:0.634740:0.230463:0.634740:0.213965:0.591817:0.213965:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.621312:0.230578:0.628787:0.230578:0.628787:0.214110:0.621312:0.214110:0.000000
1:@0.607835:0.785997:0.616331:0.785997:0.616331:0.769500:0.607835:0.769500:0.000000
sen( ):@0.590380:0.802336:0.633804:0.802336:0.633804:0.785838:0.590380:0.785838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.620376:0.802452:0.627851:0.802452:0.627851:0.785983:0.620376:0.785983:0.000000
π:@0.600206:0.273286:0.610609:0.273286:0.610609:0.256789:0.600206:0.256789:0.000000
2:@0.601150:0.289625:0.609646:0.289625:0.609646:0.273127:0.601150:0.273127:0.000000
π:@0.576081:0.307958:0.586484:0.307958:0.586484:0.291460:0.576081:0.291460:0.000000
2:@0.577025:0.324296:0.585521:0.324296:0.585521:0.307799:0.577025:0.307799:0.000000
R:@0.547488:0.379590:0.560792:0.379590:0.560792:0.366728:0.547488:0.366728:0.000000
          +   |      :@0.560791:0.380677:0.686748:0.380677:0.686748:0.364180:0.560791:0.364180:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
\:@0.565800:0.380677:0.571348:0.380677:0.567472:0.364180:0.561924:0.364180:0.000000
kπ k:@0.618568:0.380793:0.662030:0.380793:0.662030:0.364324:0.618568:0.364324:0.000000:0.000000:0.000000:0.000000
:@0.666172:0.380461:0.682220:0.380461:0.682220:0.365814:0.666172:0.365814:0.000000
Z    R:@0.687131:0.379590:0.742690:0.379590:0.742690:0.366728:0.687131:0.366728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.708636:0.388776:0.724780:0.388776:0.724780:0.368914:0.708636:0.368914:0.000000
.:@0.742690:0.380677:0.745445:0.380677:0.745445:0.364180:0.742690:0.364180:0.000000
x   sec ( ) =              .:@0.547494:0.415379:0.701788:0.415379:0.701788:0.398881:0.547494:0.398881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.559631:0.423478:0.575776:0.423478:0.575776:0.403615:0.559631:0.403615:0.000000
x:@0.612667:0.415495:0.620142:0.415495:0.620142:0.399026:0.612667:0.399026:0.000000
π:@0.583559:0.373543:0.593962:0.373543:0.593962:0.357046:0.583559:0.357046:0.000000
2:@0.584503:0.389882:0.592999:0.389882:0.592999:0.373384:0.584503:0.373384:0.000000
1:@0.665823:0.407946:0.674319:0.407946:0.674319:0.391448:0.665823:0.391448:0.000000
cos( ):@0.648619:0.424284:0.691542:0.424284:0.691542:0.407787:0.648619:0.407787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.678114:0.424400:0.685589:0.424400:0.685589:0.407931:0.678114:0.407931:0.000000
π:@0.766766:0.613262:0.777170:0.613262:0.777170:0.596764:0.766766:0.596764:0.000000
2:@0.767710:0.629600:0.776206:0.629600:0.776206:0.613103:0.767710:0.613103:0.000000
1:@0.506200:0.613619:0.514696:0.613619:0.514696:0.597121:0.506200:0.597121:0.000000
cos(– ):@0.483736:0.629957:0.537159:0.629957:0.537159:0.613460:0.483736:0.613460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.523731:0.630073:0.531206:0.630073:0.531206:0.613604:0.523731:0.613604:0.000000
1:@0.578511:0.613619:0.587007:0.613619:0.587007:0.597121:0.578511:0.597121:0.000000
cos( ):@0.561307:0.629957:0.604230:0.629957:0.604230:0.613460:0.561307:0.613460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.590803:0.630073:0.598278:0.630073:0.598278:0.613604:0.590803:0.613604:0.000000
π:@0.716509:0.697501:0.726912:0.697501:0.726912:0.681003:0.716509:0.681003:0.000000
2:@0.717453:0.713840:0.725949:0.713840:0.725949:0.697342:0.717453:0.697342:0.000000
π:@0.626785:0.478037:0.637188:0.478037:0.637188:0.461539:0.626785:0.461539:0.000000
2:@0.627729:0.494375:0.636225:0.494375:0.636225:0.477877:0.627729:0.477877:0.000000
En la Figura 5.12., se muestra el :@0.153344:0.350610:0.354220:0.350610:0.354220:0.335547:0.153344:0.335547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
gráfico del conjunto  (:@0.153344:0.366452:0.303877:0.366452:0.303877:0.351389:0.153344:0.351389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
G sec:@0.287994:0.366558:0.323015:0.366558:0.323015:0.351521:0.287994:0.351521:0.000000:0.000000:0.000000:0.000000:0.000000
) al :@0.323017:0.366452:0.346605:0.366452:0.346605:0.351389:0.323017:0.351389:0.000000:0.000000:0.000000:0.000000:0.000000
que lo denominamos repre-:@0.153344:0.382294:0.334713:0.382294:0.334713:0.367231:0.153344:0.367231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sentación gráfica de la función :@0.153344:0.398136:0.355203:0.398136:0.355203:0.383073:0.153344:0.383073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
secante.:@0.153344:0.413978:0.205359:0.413978:0.205359:0.398915:0.153344:0.398915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.302154:0.614127:0.313634:0.614127:0.313634:0.604103:0.302154:0.604103:0.000000
 :@0.313634:0.614835:0.316516:0.614835:0.316516:0.603359:0.313634:0.603359:0.000000
Figura 5.12.:@0.316516:0.614835:0.370994:0.614835:0.370994:0.603359:0.316516:0.603359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.353368:0.529580:0.357917:0.529580:0.357917:0.519556:0.353368:0.519556:0.000000
0:@0.234610:0.524978:0.238304:0.524978:0.238304:0.517806:0.234610:0.517806:0.000000
1 2 3 4 5 6:@0.250742:0.516781:0.307860:0.516781:0.307860:0.509608:0.250742:0.509608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.243623:0.513216:0.247316:0.513216:0.247316:0.506044:0.243623:0.506044:0.000000
–1:@0.226828:0.516781:0.234668:0.516781:0.234668:0.509608:0.226828:0.509608:0.000000:0.000000
–1:@0.232290:0.535483:0.240130:0.535483:0.240130:0.528310:0.232290:0.528310:0.000000:0.000000
–2:@0.216140:0.516781:0.223980:0.516781:0.223980:0.509608:0.216140:0.509608:0.000000:0.000000
–3:@0.205452:0.516781:0.213292:0.516781:0.213292:0.509608:0.205452:0.509608:0.000000:0.000000
–4:@0.194764:0.516781:0.202604:0.516781:0.202604:0.509608:0.194764:0.509608:0.000000:0.000000
–5:@0.184076:0.516781:0.191916:0.516781:0.191916:0.509608:0.184076:0.509608:0.000000:0.000000
y:@0.231162:0.448431:0.235841:0.448431:0.235841:0.438407:0.231162:0.438407:0.000000
π:@0.255828:0.525920:0.260510:0.525920:0.260510:0.518496:0.255828:0.518496:0.000000
2:@0.256253:0.532205:0.260076:0.532205:0.260076:0.524781:0.256253:0.524781:0.000000
π:@0.222824:0.525920:0.227506:0.525920:0.227506:0.518496:0.222824:0.518496:0.000000
2:@0.223249:0.532205:0.227073:0.532205:0.227073:0.524781:0.223249:0.524781:0.000000
3π –π:@0.188490:0.525920:0.213717:0.525920:0.213717:0.518496:0.188490:0.518496:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.190831:0.532205:0.194654:0.532205:0.194654:0.524781:0.190831:0.524781:0.000000
3π 2π:@0.288799:0.525920:0.312738:0.525920:0.312738:0.518496:0.288799:0.518496:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.291157:0.532205:0.294980:0.532205:0.294980:0.524781:0.291157:0.524781:0.000000
5π 3π:@0.321208:0.525920:0.346349:0.525920:0.346349:0.518496:0.321208:0.518496:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.323566:0.532205:0.327389:0.532205:0.327389:0.524781:0.323566:0.524781:0.000000
π:@0.272902:0.525920:0.277584:0.525920:0.277584:0.518496:0.272902:0.518496:0.000000
–2π:@0.167613:0.525920:0.180842:0.525920:0.180842:0.518496:0.167613:0.518496:0.000000:0.000000:0.000000
–:@0.216742:0.528737:0.221467:0.528737:0.221467:0.521313:0.216742:0.521313:0.000000
–:@0.183252:0.528737:0.187977:0.528737:0.187977:0.521313:0.183252:0.521313:0.000000
y:@0.270046:0.440859:0.274274:0.440859:0.274274:0.431802:0.270046:0.431802:0.000000
 = sec( ) =            .:@0.274274:0.440796:0.342426:0.440796:0.342426:0.431722:0.274274:0.431722:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.298813:0.440859:0.302924:0.440859:0.302924:0.431802:0.298813:0.431802:0.000000
1:@0.325039:0.436620:0.329712:0.436620:0.329712:0.427547:0.325039:0.427547:0.000000
cos( ):@0.315577:0.445606:0.339185:0.445606:0.339185:0.436533:0.315577:0.436533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.331799:0.445670:0.335911:0.445670:0.335911:0.436612:0.331799:0.436612:0.000000
M.5.1.72. Reconocer las funciones trigonométricas secante y cosecante, sus propiedades y las relaciones existentes entre estas funciones, y representarlas de manera gráfica con apoyo de las TIC. :@0.139925:0.937502:0.904043:0.937502:0.904043:0.927460:0.139925:0.927460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.901521:0.937502:0.904043:0.937502:0.904043:0.927460:0.901521:0.927460:0.000000
M.5.1.73. Reconocer y resolver (con apoyo de las TIC) aplicaciones, problemas o situaciones reales o hipotéticas que pueden ser modelizados con funciones trigonométricas, identificando :@0.139925:0.946304:0.904054:0.946304:0.904054:0.936262:0.139925:0.936262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las variables significativas presentes y las relaciones entre ellas, y juzgar la validez y pertinencia de los resultados obtenidos.:@0.139925:0.955105:0.632810:0.955105:0.632810:0.945063:0.139925:0.945063:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interculturalidad:@0.199644:0.720614:0.319958:0.720614:0.319958:0.705142:0.199644:0.705142:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática e historia:@0.193071:0.748967:0.346505:0.748967:0.346505:0.733495:0.193071:0.733495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los incas se destacaron en el :@0.153335:0.764387:0.342248:0.764387:0.342248:0.749324:0.153335:0.749324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
campo de las matemáticas.  :@0.153335:0.780229:0.336639:0.780229:0.336639:0.765166:0.153335:0.765166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Utilizaban :@0.153335:0.796071:0.222780:0.796071:0.222780:0.781008:0.153335:0.781008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
quipus y yupanas:@0.222780:0.796176:0.334000:0.796176:0.334000:0.781140:0.222780:0.781140:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.334002:0.796071:0.337784:0.796071:0.337784:0.781008:0.334002:0.781008:0.000000
para realizar diferentes opera-:@0.153335:0.811913:0.344237:0.811913:0.344237:0.796850:0.153335:0.796850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ciones aritméticas.:@0.153335:0.827755:0.272417:0.827755:0.272417:0.812692:0.153335:0.812692:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Indaga elabora:@0.153335:0.854831:0.268458:0.854831:0.268458:0.839359:0.153335:0.839359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y :@0.200967:0.854409:0.215672:0.854409:0.215672:0.839346:0.200967:0.839346:0.000000:0.000000:0.000000
 un resumen :@0.268461:0.854409:0.353720:0.854409:0.353720:0.839346:0.268461:0.839346:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en el cuaderno sobre el funcio-:@0.153335:0.870251:0.353699:0.870251:0.353699:0.855188:0.153335:0.855188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
namiento de estas herramientas :@0.153335:0.886093:0.364941:0.886093:0.364941:0.871030:0.153335:0.871030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de cálculo.:@0.153335:0.901935:0.221916:0.901935:0.221916:0.886872:0.153335:0.886872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000