39:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000
Pensamiento espacial, numérico y variacional:@0.525225:0.043660:0.930049:0.043660:0.930049:0.024915:0.525225:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 4 (Ev. 1) Reconoce el significado de las razones trigonométricas en un triángulo rectángulo para ángulos agudos, en particular, seno, coseno y tangente.:@0.083241:0.971366:0.906536:0.971366:0.906536:0.959939:0.083241:0.959939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 3:@0.073089:0.136836:0.148872:0.136836:0.148872:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.148835:0.136836:0.152866:0.136836:0.152866:0.121124:0.148835:0.121124:0.000000
Teniendo en cuenta que la longitud de la circunferencia unitaria es 2 , justifica el valor de   en cada una de las gráficas :@0.073089:0.161633:0.931044:0.161633:0.931044:0.145920:0.073089:0.145920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.567784:0.161078:0.580061:0.161078:0.580061:0.147362:0.567784:0.147362:0.000000
t:@0.724190:0.161633:0.729565:0.161633:0.729565:0.146197:0.724190:0.146197:0.000000
dadas.:@0.073070:0.179287:0.119302:0.179287:0.119302:0.163574:0.073070:0.163574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.157192:0.210246:0.165205:0.210246:0.165205:0.192656:0.157192:0.192656:0.000000
0:@0.159422:0.289069:0.169054:0.289069:0.169054:0.271449:0.159422:0.271449:0.000000
2:@0.146712:0.335314:0.163152:0.335314:0.163152:0.320608:0.146712:0.320608:0.000000
1:@0.163152:0.335908:0.172784:0.335908:0.172784:0.318288:0.163152:0.318288:0.000000
2:@0.083260:0.288475:0.099700:0.288475:0.099700:0.273769:0.083260:0.273769:0.000000
1:@0.099700:0.289069:0.109332:0.289069:0.109332:0.271449:0.099700:0.271449:0.000000
1 P(0, 1):@0.162008:0.228670:0.223249:0.228298:0.223249:0.210678:0.162008:0.211049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.233335:0.289069:0.242966:0.289069:0.242966:0.271449:0.233335:0.271449:0.000000
x:@0.265860:0.289069:0.273853:0.289069:0.273853:0.271479:0.265860:0.271479:0.000000
y:@0.375346:0.210246:0.383359:0.210246:0.383359:0.192656:0.375346:0.192656:0.000000
0:@0.377577:0.289069:0.387208:0.289069:0.387208:0.271449:0.377577:0.271449:0.000000
2:@0.364867:0.335314:0.381307:0.335314:0.381307:0.320608:0.364867:0.320608:0.000000
1:@0.381307:0.335908:0.390938:0.335908:0.390938:0.318288:0.381307:0.318288:0.000000
2:@0.301414:0.288475:0.317855:0.288475:0.317855:0.273769:0.301414:0.273769:0.000000
1:@0.317855:0.289069:0.327486:0.289069:0.327486:0.271449:0.317855:0.271449:0.000000
1:@0.380754:0.229815:0.390386:0.229815:0.390386:0.212194:0.380754:0.212194:0.000000
1:@0.451509:0.289069:0.461140:0.289069:0.461140:0.271449:0.451509:0.271449:0.000000
t :@0.306802:0.240164:0.316118:0.240164:0.316118:0.222573:0.306802:0.222573:0.000000:0.000000
5 p:@0.316118:0.239569:0.350045:0.239569:0.350045:0.224863:0.316118:0.224863:0.000000:0.000000:0.000000
 :@0.332558:0.240164:0.336881:0.240164:0.336881:0.222543:0.332558:0.222543:0.000000
x:@0.484034:0.289069:0.492027:0.289069:0.492027:0.271479:0.484034:0.271479:0.000000
y:@0.595581:0.210246:0.603594:0.210246:0.603594:0.192656:0.595581:0.192656:0.000000
0:@0.596745:0.289233:0.606377:0.289233:0.606377:0.271613:0.596745:0.271613:0.000000
2:@0.585298:0.337187:0.601739:0.337187:0.601739:0.322481:0.585298:0.322481:0.000000
1P(0,  1):@0.601739:0.337782:0.678100:0.337787:0.678100:0.320167:0.601739:0.320162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.521669:0.288475:0.538109:0.288475:0.538109:0.273769:0.521669:0.273769:0.000000
1:@0.538109:0.289069:0.547740:0.289069:0.547740:0.271449:0.538109:0.271449:0.000000
1:@0.601008:0.229815:0.610640:0.229815:0.610640:0.212194:0.601008:0.212194:0.000000
1:@0.671763:0.289069:0.681394:0.289069:0.681394:0.271449:0.671763:0.271449:0.000000
x:@0.704288:0.289069:0.712281:0.289069:0.712281:0.271479:0.704288:0.271479:0.000000
y:@0.805345:0.210246:0.813358:0.210246:0.813358:0.192656:0.805345:0.192656:0.000000
0:@0.807575:0.289069:0.817206:0.289069:0.817206:0.271449:0.807575:0.271449:0.000000
2:@0.794865:0.335314:0.811305:0.335314:0.811305:0.320608:0.794865:0.320608:0.000000
1:@0.811305:0.335908:0.820937:0.335908:0.820937:0.318288:0.811305:0.318288:0.000000
2:@0.731413:0.288475:0.747853:0.288475:0.747853:0.273769:0.731413:0.273769:0.000000
1:@0.747853:0.289069:0.757485:0.289069:0.757485:0.271449:0.747853:0.271449:0.000000
1:@0.810753:0.229815:0.820384:0.229815:0.820384:0.212194:0.810753:0.212194:0.000000
1:@0.881507:0.289069:0.891138:0.289069:0.891138:0.271449:0.881507:0.271449:0.000000
x:@0.914033:0.289069:0.922026:0.289069:0.922026:0.271479:0.914033:0.271479:0.000000
2:@0.255325:0.251252:0.264956:0.251252:0.264956:0.233632:0.255325:0.233632:0.000000
t :@0.224635:0.244873:0.233950:0.244873:0.233950:0.227282:0.224635:0.227282:0.000000:0.000000
5:@0.233950:0.244278:0.250390:0.244278:0.250390:0.229572:0.233950:0.229572:0.000000
p:@0.253232:0.237557:0.266396:0.237557:0.266396:0.222851:0.253232:0.222851:0.000000
2:@0.545371:0.246871:0.555002:0.246871:0.555002:0.229251:0.545371:0.229251:0.000000
t :@0.511898:0.240492:0.521214:0.240492:0.521214:0.222901:0.511898:0.222901:0.000000:0.000000
5:@0.521214:0.239897:0.537654:0.239897:0.537654:0.225191:0.521214:0.225191:0.000000
3:@0.540503:0.233509:0.549486:0.233509:0.549486:0.217075:0.540503:0.217075:0.000000
p:@0.549484:0.233164:0.562648:0.233164:0.562648:0.218458:0.549484:0.218458:0.000000
2:@0.646798:0.337192:0.663238:0.337192:0.663238:0.322486:0.646798:0.322486:0.000000
P(1, 0):@0.880456:0.271707:0.927851:0.271701:0.927851:0.254081:0.880456:0.254087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P( 1, 0):@0.328477:0.273574:0.388006:0.273574:0.388006:0.257140:0.328477:0.257140:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.342595:0.273019:0.357928:0.273019:0.357928:0.259304:0.342595:0.259304:0.000000
t :@0.709803:0.313475:0.719119:0.313475:0.719119:0.295884:0.709803:0.295884:0.000000:0.000000
5 p:@0.719119:0.312880:0.762676:0.312880:0.762676:0.298174:0.719119:0.298174:0.000000:0.000000:0.000000
 2:@0.735559:0.313475:0.749512:0.313475:0.749512:0.295854:0.735559:0.295854:0.000000:0.000000
Solución:@0.073089:0.370084:0.139222:0.370084:0.139222:0.353415:0.073089:0.353415:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En la primera gráfica, tenemos que :@0.073089:0.394880:0.333167:0.394880:0.333167:0.379168:0.073089:0.379168:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.363245:0.400452:0.372227:0.400452:0.372227:0.384739:0.363245:0.384739:0.000000
t :@0.332560:0.394072:0.341248:0.394072:0.341248:0.378637:0.332560:0.378637:0.000000:0.000000
5:@0.341248:0.393510:0.356581:0.393510:0.356581:0.379794:0.341248:0.379794:0.000000
p:@0.361165:0.386784:0.373442:0.386784:0.373442:0.373068:0.361165:0.373068:0.000000
, puesto que el arco verde nos muestra un desplazamiento igual a la cuarta :@0.374281:0.394882:0.930848:0.394882:0.930848:0.379169:0.374281:0.379169:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
parte de la circunferencia unitaria  (:@0.073089:0.412532:0.340640:0.414931:0.340640:0.399219:0.073089:0.396819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2 ):@0.340349:0.414931:0.366411:0.414626:0.366411:0.398914:0.340349:0.399219:0.000000:0.000000:0.000000
2:@0.383544:0.420969:0.392527:0.420969:0.392527:0.405256:0.383544:0.405256:0.000000
 :@0.340640:0.414931:0.343954:0.414931:0.343954:0.399496:0.340640:0.399496:0.000000
p 5:@0.349255:0.414072:0.381744:0.414072:0.381744:0.400356:0.349255:0.400356:0.000000:0.000000:0.000000
p:@0.381292:0.408812:0.393570:0.408812:0.393570:0.395096:0.381292:0.395096:0.000000
4:@0.323726:0.421257:0.332709:0.421257:0.332709:0.405544:0.323726:0.405544:0.000000
1:@0.323910:0.409191:0.332893:0.409191:0.332893:0.393479:0.323910:0.393479:0.000000
. En la segunda gráfica, tenemos que :@0.394349:0.412532:0.666532:0.412532:0.666532:0.396819:0.394349:0.396819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t   :@0.666775:0.412532:0.694276:0.412532:0.694276:0.397097:0.666775:0.397097:0.000000:0.000000:0.000000:0.000000
5 p:@0.675703:0.411977:0.706829:0.411977:0.706829:0.398262:0.675703:0.398262:0.000000:0.000000:0.000000
, puesto que el arco verde nos :@0.706756:0.412532:0.930998:0.412532:0.930998:0.396819:0.706756:0.396819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
muestra un desplazamiento igual a la mitad de la circunferencia unitaria  2(:@0.073068:0.430186:0.616421:0.431933:0.616421:0.416220:0.073068:0.414474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.616421:0.431933:0.619735:0.431933:0.619735:0.416497:0.616421:0.416497:0.000000
p 5p:@0.625036:0.431073:0.669901:0.430706:0.669901:0.416990:0.625036:0.417357:0.000000:0.000000:0.000000:0.000000
):@0.637314:0.431627:0.642191:0.431627:0.642191:0.415915:0.637314:0.415915:0.000000
2:@0.599503:0.438258:0.608486:0.438258:0.608486:0.422545:0.599503:0.422545:0.000000
1:@0.599687:0.426192:0.608670:0.426192:0.608670:0.410480:0.599687:0.410480:0.000000
En la tercera gráfica, tenemos que :@0.073089:0.454981:0.329618:0.454981:0.329618:0.439269:0.073089:0.439269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.362686:0.462542:0.372317:0.462542:0.372317:0.445694:0.362686:0.445694:0.000000
t :@0.329213:0.456163:0.338528:0.456163:0.338528:0.439613:0.329213:0.439613:0.000000:0.000000
5:@0.338527:0.455562:0.354967:0.455562:0.354967:0.440856:0.338527:0.440856:0.000000
3:@0.357818:0.449181:0.366801:0.449181:0.366801:0.433468:0.357818:0.433468:0.000000
p:@0.366801:0.448836:0.379965:0.448836:0.379965:0.434130:0.366801:0.434130:0.000000
, puesto que el arco verde nos muestra un desplazamiento igual a las tres :@0.379975:0.454981:0.931121:0.454981:0.931121:0.439269:0.379975:0.439269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuartas partes de la circunferencia unitaria  2(:@0.073089:0.472632:0.401138:0.473420:0.401138:0.457707:0.073089:0.456919:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.446944:0.479458:0.455927:0.479458:0.455927:0.463745:0.446944:0.463745:0.000000
 :@0.401138:0.473420:0.404452:0.473420:0.404452:0.457985:0.401138:0.457985:0.000000
p 5:@0.409753:0.472560:0.442242:0.472560:0.442242:0.458844:0.409753:0.458844:0.000000:0.000000:0.000000
):@0.422031:0.473115:0.426909:0.473115:0.426909:0.457402:0.422031:0.457402:0.000000
3:@0.441790:0.467855:0.450773:0.467855:0.450773:0.452142:0.441790:0.452142:0.000000
p:@0.450773:0.467300:0.463050:0.467300:0.463050:0.453585:0.450773:0.453585:0.000000
4:@0.384224:0.479745:0.393207:0.479745:0.393207:0.464032:0.384224:0.464032:0.000000
3:@0.384408:0.467680:0.393391:0.467680:0.393391:0.451967:0.384408:0.451967:0.000000
En la última gráfica, tenemos que     2 , puesto que el arco verde nos muestra un desplazamiento igual a la :@0.073089:0.497429:0.931044:0.497429:0.931044:0.481717:0.073089:0.481717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.338821:0.497429:0.344196:0.497429:0.344196:0.481994:0.338821:0.481994:0.000000
5 p:@0.350326:0.496875:0.393381:0.496875:0.393381:0.483159:0.350326:0.483159:0.000000:0.000000:0.000000
circunferencia unitaria que tiene longitud (2 ).:@0.073058:0.515084:0.410665:0.515084:0.410665:0.499371:0.073058:0.499371:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.390472:0.514529:0.402750:0.514529:0.402750:0.500813:0.390472:0.500813:0.000000
1.3 Razones trigonométricas de un ángulo agudo:@0.073058:0.538868:0.445823:0.538868:0.445823:0.522198:0.073058:0.522198:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Antes de entrar a definir y trabajar las razones y las funciones trigonométricas, consideremos las figuras 1 y 2.:@0.073058:0.563664:0.856739:0.563664:0.856739:0.547951:0.073058:0.547951:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 1:@0.133265:0.650589:0.197378:0.650589:0.197378:0.633642:0.133265:0.633642:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ca:@0.386692:0.685485:0.407502:0.685485:0.407502:0.664842:0.386692:0.664842:0.000000:0.000000
co:@0.446462:0.652143:0.469075:0.652143:0.469075:0.631500:0.446462:0.631500:0.000000:0.000000
O:@0.312564:0.679702:0.327477:0.679702:0.327477:0.659094:0.312564:0.659094:0.000000
R:@0.440149:0.616083:0.451387:0.616083:0.451387:0.595475:0.440149:0.595475:0.000000
S:@0.436381:0.686861:0.446508:0.686861:0.446508:0.666253:0.436381:0.666253:0.000000
hip:@0.351015:0.634020:0.381004:0.634020:0.381004:0.613377:0.351015:0.613377:0.000000:0.000000:0.000000
u:@0.356102:0.670742:0.367663:0.670742:0.367663:0.653513:0.356102:0.653513:0.000000
Figura 2:@0.559106:0.650589:0.623219:0.650589:0.623219:0.633642:0.559106:0.633642:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.781173:0.601791:0.787572:0.601791:0.787572:0.588574:0.781173:0.588574:0.000000
0:@0.782954:0.664744:0.790646:0.664744:0.790646:0.651289:0.782954:0.651289:0.000000
2:@0.772803:0.701677:0.785933:0.701677:0.785933:0.689932:0.772803:0.689932:0.000000
1:@0.785933:0.702152:0.793625:0.702152:0.793625:0.688697:0.785933:0.688697:0.000000
2:@0.722127:0.664269:0.735257:0.664269:0.735257:0.652524:0.722127:0.652524:0.000000
1:@0.735257:0.664744:0.742949:0.664744:0.742949:0.651289:0.735257:0.651289:0.000000
1:@0.785492:0.617419:0.793184:0.617419:0.793184:0.603964:0.785492:0.603964:0.000000
1:@0.842000:0.664744:0.849692:0.664744:0.849692:0.651289:0.842000:0.651289:0.000000
x:@0.885142:0.664744:0.891526:0.664744:0.891526:0.651526:0.885142:0.651526:0.000000
Q:@0.829816:0.664744:0.839983:0.664744:0.839983:0.651526:0.829816:0.651526:0.000000
O:@0.793137:0.664744:0.803303:0.664744:0.803303:0.651526:0.793137:0.651526:0.000000
R:@0.866259:0.617419:0.873919:0.617419:0.873919:0.604202:0.866259:0.604202:0.000000
S:@0.863689:0.665670:0.870593:0.665670:0.870593:0.652453:0.863689:0.652453:0.000000
t:@0.843828:0.648971:0.848430:0.648971:0.848430:0.635753:0.843828:0.635753:0.000000
P( ,  ):@0.832069:0.631632:0.867314:0.631632:0.867314:0.618177:0.832069:0.618177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.844159:0.631632:0.863137:0.631632:0.863137:0.618415:0.844159:0.618415:0.000000:0.000000:0.000000
u:@0.808961:0.654683:0.816842:0.654683:0.816842:0.642938:0.808961:0.642938:0.000000
En la Figura 1 tenemos: triángulo rectángulo :@0.080201:0.729731:0.393552:0.729731:0.393552:0.714732:0.080201:0.714732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
OSR:@0.393552:0.729731:0.421120:0.729731:0.421120:0.714997:0.393552:0.714997:0.000000:0.000000:0.000000
 en donde :@0.421120:0.729731:0.497008:0.729731:0.497008:0.714732:0.421120:0.714732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el lador   se define como el cateto opuesto (co) al ángulo :@0.080201:0.745616:0.494495:0.745616:0.494495:0.730617:0.080201:0.730617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
RS:@0.135935:0.745616:0.153312:0.745616:0.153312:0.729691:0.135935:0.729691:0.000000:0.000000
u:@0.080201:0.760972:0.088986:0.760972:0.088986:0.747880:0.080201:0.747880:0.000000
, el lado :@0.088986:0.761501:0.146442:0.761501:0.146442:0.746503:0.088986:0.746503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
OS:@0.146442:0.761501:0.165471:0.761501:0.165471:0.746768:0.146442:0.746768:0.000000:0.000000
 es el cateto adyacente (ca) al ángulo   y el :@0.165471:0.761501:0.467192:0.761501:0.467192:0.746503:0.165471:0.746503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.426885:0.760972:0.435671:0.760972:0.435671:0.747880:0.426885:0.747880:0.000000
lado :@0.080201:0.777387:0.114657:0.777387:0.114657:0.762388:0.080201:0.762388:0.000000:0.000000:0.000000:0.000000:0.000000
OR:@0.114657:0.777387:0.134529:0.777387:0.134529:0.762653:0.114657:0.762653:0.000000:0.000000
 como hipotenusa ( ):@0.134529:0.777387:0.284634:0.777387:0.284634:0.762388:0.134529:0.762388:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.270912:0.777387:0.279978:0.777387:0.279978:0.762653:0.270912:0.762653:0.000000
En la Figura 2 tenemos: una circunferencia unitaria, siendo :@0.507640:0.748714:0.916593:0.748714:0.916593:0.733715:0.507640:0.733715:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P x y:@0.507640:0.764599:0.541815:0.764599:0.541815:0.749865:0.507640:0.749865:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ) el punto trigonométrico determinado por  . :@0.516003:0.764599:0.859364:0.764599:0.859364:0.749601:0.516003:0.749601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.847328:0.764599:0.852458:0.764599:0.852458:0.749865:0.847328:0.749865:0.000000
Además, en el plano cartesiano se ha colocado el triángulo :@0.507640:0.780484:0.922163:0.780484:0.922163:0.765486:0.507640:0.765486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rectángulo :@0.507640:0.796370:0.587814:0.796370:0.587814:0.781371:0.507640:0.781371:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ORS,:@0.587814:0.796370:0.618563:0.796370:0.618563:0.781636:0.587814:0.781636:0.000000:0.000000:0.000000:0.000000
 de tal manera que el ángulo   quede en :@0.618563:0.796370:0.906878:0.796370:0.906878:0.781371:0.618563:0.781371:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.823154:0.795840:0.831940:0.795840:0.831940:0.782748:0.823154:0.782748:0.000000
posición normal.:@0.507640:0.812255:0.624062:0.812255:0.624062:0.797257:0.507640:0.797257:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El :@0.507640:0.831715:0.523401:0.831715:0.523401:0.816716:0.507640:0.816716:0.000000:0.000000:0.000000
D:@0.523401:0.831185:0.535120:0.831185:0.535120:0.818093:0.523401:0.818093:0.000000
OQP:@0.535120:0.831715:0.566150:0.831715:0.566150:0.816981:0.535120:0.816981:0.000000:0.000000:0.000000
 es semejante con :@0.566150:0.831715:0.696207:0.831715:0.696207:0.816716:0.566150:0.816716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.696207:0.831185:0.707927:0.831185:0.707927:0.818093:0.696207:0.818093:0.000000
OSR:@0.707927:0.831715:0.735495:0.831715:0.735495:0.816981:0.707927:0.816981:0.000000:0.000000:0.000000
.:@0.735495:0.831715:0.738552:0.831715:0.738552:0.816716:0.735495:0.816716:0.000000
Sen:@0.608066:0.860765:0.633634:0.860765:0.633634:0.845330:0.608066:0.845330:0.000000:0.000000:0.000000
 u 5:@0.633634:0.860210:0.667374:0.860210:0.667374:0.846494:0.633634:0.846494:0.000000:0.000000:0.000000:0.000000
5:@0.704667:0.860210:0.720001:0.860210:0.720001:0.846494:0.704667:0.846494:0.000000
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y:@0.809209:0.858837:0.816682:0.858837:0.816682:0.843402:0.809209:0.843402:0.000000
Cos :@0.608073:0.893369:0.636714:0.893369:0.636714:0.877934:0.608073:0.877934:0.000000:0.000000:0.000000:0.000000
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 :@0.821202:0.914992:0.825050:0.914992:0.825050:0.899993:0.821202:0.899993:0.000000
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1:@0.260011:0.826754:0.269397:0.826754:0.269397:0.810550:0.260011:0.810550:0.000000
1:@0.328967:0.881245:0.338353:0.881245:0.338353:0.865041:0.328967:0.865041:0.000000
x:@0.381612:0.881245:0.389863:0.881245:0.389863:0.865041:0.381612:0.865041:0.000000
Q:@0.314098:0.881245:0.326505:0.881245:0.326505:0.865069:0.314098:0.865069:0.000000
t:@0.331217:0.863086:0.336834:0.863086:0.336834:0.846909:0.331217:0.846909:0.000000
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5:@0.326024:0.842575:0.342046:0.842575:0.342046:0.829051:0.326024:0.829051:0.000000
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x y:@0.347143:0.843122:0.370302:0.843122:0.370302:0.826945:0.347143:0.826945:0.000000:0.000000:0.000000
u:@0.286041:0.866455:0.295011:0.866455:0.295011:0.853842:0.286041:0.853842:0.000000
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