38:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000
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
1.1 Circunferencia unitaria:@0.293660:0.223146:0.491551:0.223146:0.491551:0.206476:0.293660:0.206476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La circunferencia unitaria es una circunferencia de radio igual a uno (:@0.293660:0.247235:0.787495:0.247235:0.787495:0.231522:0.293660:0.231522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.787030:0.247235:0.795976:0.247235:0.795976:0.231799:0.787030:0.231799:0.000000
5:@0.795902:0.246680:0.811235:0.246680:0.811235:0.232964:0.795902:0.232964:0.000000
1) y cuyo centro :@0.811143:0.247235:0.931015:0.247235:0.931015:0.231522:0.811143:0.231522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
coincide con el origen (0,0) del plano cartesiano :@0.293660:0.264889:0.704155:0.264889:0.704155:0.249176:0.293660:0.249176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
XY:@0.708191:0.264889:0.727188:0.264889:0.727188:0.249454:0.708191:0.249454:0.000000:0.000000
. La longitud de esta es :@0.727703:0.264889:0.930956:0.264889:0.930956:0.249176:0.727703:0.249176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.293679:0.282543:0.303582:0.282543:0.303582:0.267108:0.293679:0.267108:0.000000
   2 (1)  2 .:@0.303508:0.282543:0.409718:0.282543:0.409718:0.266830:0.303508:0.266830:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 p:@0.307466:0.281988:0.347833:0.281988:0.347833:0.268273:0.307466:0.268273:0.000000:0.000000:0.000000
5 p:@0.370179:0.281988:0.406607:0.281988:0.406607:0.268273:0.370179:0.268273:0.000000:0.000000:0.000000
La ecuación que describe todos los puntos de la circunferencia unitaria es:     :@0.293679:0.306632:0.869718:0.306613:0.869718:0.290901:0.293679:0.290919:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.833876:0.306632:0.841331:0.306632:0.841331:0.291197:0.833876:0.291197:0.000000
2:@0.841249:0.300549:0.846529:0.300549:0.846529:0.290823:0.841249:0.290823:0.000000
1:@0.850446:0.306058:0.865779:0.306058:0.865779:0.292343:0.850446:0.292343:0.000000
y:@0.869645:0.306613:0.877118:0.306613:0.877118:0.291178:0.869645:0.291178:0.000000
2 :@0.877040:0.300549:0.884584:0.300549:0.884584:0.291389:0.877040:0.291389:0.000000:0.000000
5:@0.884531:0.306058:0.899865:0.306058:0.899865:0.292343:0.884531:0.292343:0.000000
1.:@0.899773:0.306613:0.911884:0.306613:0.911884:0.290901:0.899773:0.290901:0.000000:0.000000
Esta circunferencia se utiliza con el fin de estudiar de 'manera fácil' las razones :@0.293658:0.330702:0.931236:0.330702:0.931236:0.314990:0.293658:0.314990:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
trigonométricas y las funciones trigonométricas, por medio de triángulos rectángulos :@0.293658:0.348356:0.930995:0.348356:0.930995:0.332644:0.293658:0.332644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
auxiliares.:@0.293658:0.366011:0.362910:0.366011:0.362910:0.350298:0.293658:0.350298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 1:@0.293658:0.390100:0.369441:0.390100:0.369441:0.373430:0.293658:0.373430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Prueba que el punto de coordenadas :@0.293658:0.414189:0.567868:0.414189:0.567868:0.398476:0.293658:0.398476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.571487:0.419228:0.577060:0.419228:0.577060:0.395154:0.571487:0.395154:0.000000
1:@0.587207:0.407187:0.595373:0.407187:0.595373:0.392902:0.587207:0.392902:0.000000
,:@0.605521:0.415361:0.608578:0.415361:0.608578:0.400363:0.605521:0.400363:0.000000
3:@0.625155:0.407187:0.633321:0.407187:0.633321:0.392902:0.625155:0.392902:0.000000
2:@0.643468:0.419228:0.649041:0.419228:0.649041:0.395154:0.643468:0.395154:0.000000
2:@0.587207:0.420010:0.595373:0.420010:0.595373:0.405725:0.587207:0.405725:0.000000
2:@0.625160:0.420010:0.633326:0.420010:0.633326:0.405725:0.625160:0.405725:0.000000
!:@0.616746:0.407862:0.622809:0.407862:0.622809:0.394766:0.616746:0.394766:0.000000
 está en la circunferencia unitaria.:@0.652874:0.414164:0.892859:0.414164:0.892859:0.398451:0.652874:0.398451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución: lo que tenemos que hacer es demostrar que este punto satisface la ecuación :@0.293657:0.438253:0.931360:0.438253:0.931360:0.422540:0.293657:0.422540:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.927326:0.438253:0.931358:0.438253:0.931358:0.422540:0.927326:0.422540:0.000000
x:@0.293657:0.455907:0.301112:0.455907:0.301112:0.440472:0.293657:0.440472:0.000000
2:@0.301048:0.449834:0.306328:0.449834:0.306328:0.440108:0.301048:0.440108:0.000000
   :@0.306289:0.455898:0.329519:0.455898:0.329519:0.440185:0.306289:0.440185:0.000000:0.000000:0.000000
1:@0.310247:0.455343:0.325580:0.455343:0.325580:0.441628:0.310247:0.441628:0.000000
y:@0.329445:0.455898:0.336919:0.455898:0.336919:0.440463:0.329445:0.440463:0.000000
2 :@0.336839:0.449834:0.344383:0.449834:0.344383:0.440674:0.336839:0.440674:0.000000:0.000000
5:@0.344332:0.455343:0.359665:0.455343:0.359665:0.441628:0.344332:0.441628:0.000000
1. :@0.359573:0.455898:0.375716:0.455898:0.375716:0.440185:0.359573:0.440185:0.000000:0.000000:0.000000
Veamos: :@0.293657:0.479987:0.357261:0.479987:0.357261:0.464274:0.293657:0.464274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 2:@0.360348:0.484528:0.395210:0.484528:0.395210:0.460454:0.360348:0.460454:0.000000:0.000000:0.000000
1:@0.373695:0.471648:0.381861:0.471648:0.381861:0.457364:0.373695:0.457364:0.000000
²:@0.399124:0.476691:0.404388:0.476691:0.404388:0.460979:0.399124:0.460979:0.000000
 :@0.404388:0.477952:0.409885:0.477952:0.409885:0.456526:0.404388:0.456526:0.000000
1 :@0.414751:0.481919:0.434686:0.481919:0.434686:0.468203:0.414751:0.468203:0.000000:0.000000
1:@0.434686:0.484528:0.440259:0.484528:0.440259:0.460454:0.434686:0.460454:0.000000
3:@0.449432:0.471648:0.457598:0.471648:0.457598:0.457364:0.449432:0.457364:0.000000
2:@0.465373:0.484528:0.470945:0.484528:0.470945:0.460454:0.465373:0.460454:0.000000
²:@0.474859:0.476691:0.480124:0.476691:0.480124:0.460979:0.474859:0.460979:0.000000
 :@0.480124:0.477952:0.485621:0.477952:0.485621:0.456526:0.480124:0.456526:0.000000
5:@0.493283:0.480153:0.508617:0.480153:0.508617:0.466438:0.493283:0.466438:0.000000
1:@0.520583:0.471648:0.528749:0.471648:0.528749:0.457364:0.520583:0.457364:0.000000
1:@0.540717:0.480153:0.556051:0.480153:0.556051:0.466438:0.540717:0.466438:0.000000
3:@0.568019:0.471648:0.576185:0.471648:0.576185:0.457364:0.568019:0.457364:0.000000
5:@0.585780:0.480153:0.601113:0.480153:0.601113:0.466438:0.585780:0.466438:0.000000
1, por tanto, el punto está en la circunferencia :@0.607924:0.481055:0.930649:0.479981:0.930649:0.464268:0.607924:0.465342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.373695:0.486147:0.381861:0.486147:0.381861:0.471863:0.373695:0.471863:0.000000
2:@0.449432:0.486147:0.457598:0.486147:0.457598:0.471863:0.449432:0.471863:0.000000
4:@0.520585:0.486147:0.528751:0.486147:0.528751:0.471863:0.520585:0.471863:0.000000
4:@0.568025:0.486147:0.576191:0.486147:0.576191:0.471863:0.568025:0.471863:0.000000
!:@0.441716:0.470786:0.447779:0.470786:0.447779:0.457690:0.441716:0.457690:0.000000
unitaria.:@0.293660:0.497631:0.351562:0.497631:0.351562:0.481919:0.293660:0.481919:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 2:@0.293660:0.521720:0.369443:0.521720:0.369443:0.505051:0.293660:0.505051:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El punto de coordenadas :@0.293660:0.545809:0.473801:0.545809:0.473801:0.530097:0.293660:0.530097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y :@0.473005:0.547039:0.483302:0.547039:0.483302:0.532305:0.473005:0.532305:0.000000:0.000000
5:@0.483302:0.546509:0.497938:0.546509:0.497938:0.533417:0.483302:0.533417:0.000000
2:@0.509241:0.538865:0.517407:0.538865:0.517407:0.524581:0.509241:0.524581:0.000000
2:@0.509241:0.551687:0.517407:0.551687:0.517407:0.537403:0.509241:0.537403:0.000000
!:@0.502017:0.539540:0.508080:0.539540:0.508080:0.526444:0.502017:0.526444:0.000000
 está en la circunferencia unitaria y es un punto del primer :@0.524884:0.545798:0.931174:0.545798:0.931174:0.530085:0.524884:0.530085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuadrante, encuentra el valor de  .:@0.293660:0.563448:0.535623:0.563448:0.535623:0.547736:0.293660:0.547736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.525223:0.563448:0.532678:0.563448:0.532678:0.548013:0.525223:0.548013:0.000000
Solución:@0.293642:0.587537:0.362612:0.587537:0.362612:0.570868:0.293642:0.570868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: es claro que :@0.362943:0.587537:0.473359:0.587537:0.473359:0.571825:0.362943:0.571825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y :@0.475797:0.587222:0.486093:0.587222:0.486093:0.572489:0.475797:0.572489:0.000000:0.000000
5:@0.486093:0.586693:0.500729:0.586693:0.500729:0.573601:0.486093:0.573601:0.000000
2:@0.512032:0.579048:0.520198:0.579048:0.520198:0.564763:0.512032:0.564763:0.000000
2:@0.512032:0.591869:0.520198:0.591869:0.520198:0.577585:0.512032:0.577585:0.000000
!:@0.504810:0.579723:0.510872:0.579723:0.510872:0.566627:0.504810:0.566627:0.000000
, entonces, al reemplazar este valor en la ecuación:@0.528316:0.587531:0.926993:0.587531:0.926993:0.571818:0.528316:0.571818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.293660:0.605182:0.301115:0.605182:0.301115:0.589746:0.293660:0.589746:0.000000
2:@0.301048:0.599118:0.306328:0.599118:0.306328:0.589391:0.301048:0.589391:0.000000
   :@0.306289:0.605182:0.329519:0.605182:0.329519:0.589469:0.306289:0.589469:0.000000:0.000000:0.000000
1:@0.310247:0.604627:0.325580:0.604627:0.325580:0.590911:0.310247:0.590911:0.000000
y:@0.329445:0.605182:0.336919:0.605182:0.336919:0.589746:0.329445:0.589746:0.000000
2 :@0.336839:0.599118:0.344383:0.599118:0.344383:0.589957:0.336839:0.589957:0.000000:0.000000
5:@0.344332:0.604627:0.359665:0.604627:0.359665:0.590911:0.344332:0.590911:0.000000
1, obtenemos::@0.359573:0.605182:0.463088:0.605182:0.463088:0.589469:0.359573:0.589469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x  :@0.387370:0.631220:0.402648:0.631220:0.402648:0.616486:0.387370:0.616486:0.000000:0.000000:0.000000
2:@0.394485:0.625432:0.399484:0.625432:0.399484:0.616688:0.394485:0.616688:0.000000
1:@0.402648:0.630690:0.417284:0.630690:0.417284:0.617598:0.402648:0.617598:0.000000
1:@0.420570:0.631445:0.424470:0.631445:0.424470:0.614593:0.420570:0.614593:0.000000
2:@0.433370:0.623046:0.441536:0.623046:0.441536:0.608762:0.433370:0.608762:0.000000
2:@0.449317:0.631039:0.453032:0.631039:0.453032:0.614990:0.449317:0.614990:0.000000
2:@0.454332:0.619059:0.459093:0.619059:0.459093:0.610731:0.454332:0.610731:0.000000
5:@0.463818:0.630007:0.477758:0.630007:0.477758:0.617538:0.463818:0.617538:0.000000
1:@0.478042:0.630826:0.486208:0.630826:0.486208:0.616542:0.478042:0.616542:0.000000
2:@0.433363:0.635869:0.441529:0.635869:0.441529:0.621585:0.433363:0.621585:0.000000
!:@0.427969:0.622794:0.434032:0.622794:0.434032:0.609698:0.427969:0.609698:0.000000
x  :@0.387370:0.657423:0.402648:0.657423:0.402648:0.642689:0.387370:0.642689:0.000000:0.000000:0.000000
2:@0.394485:0.651635:0.399484:0.651635:0.399484:0.642891:0.394485:0.642891:0.000000
1:@0.402648:0.656894:0.417284:0.656894:0.417284:0.643801:0.402648:0.643801:0.000000
1:@0.428349:0.649248:0.436515:0.649248:0.436515:0.634964:0.428349:0.634964:0.000000
5:@0.444297:0.656208:0.458236:0.656208:0.458236:0.643739:0.444297:0.643739:0.000000
1:@0.458521:0.657027:0.466687:0.657027:0.466687:0.642743:0.458521:0.642743:0.000000
2:@0.428349:0.662070:0.436515:0.662070:0.436515:0.647786:0.428349:0.647786:0.000000
x  :@0.387370:0.683184:0.402648:0.683184:0.402648:0.668450:0.387370:0.668450:0.000000:0.000000:0.000000
2:@0.394485:0.677396:0.399484:0.677396:0.399484:0.668652:0.394485:0.668652:0.000000
5:@0.402648:0.682654:0.417284:0.682654:0.417284:0.669562:0.402648:0.669562:0.000000
1 :@0.420573:0.682791:0.432404:0.682791:0.432404:0.668506:0.420573:0.668506:0.000000:0.000000
2:@0.432404:0.682286:0.446343:0.682286:0.446343:0.669817:0.432404:0.669817:0.000000
1:@0.452066:0.675012:0.460232:0.675012:0.460232:0.660727:0.452066:0.660727:0.000000
2:@0.452066:0.687833:0.460232:0.687833:0.460232:0.673549:0.452066:0.673549:0.000000
x:@0.387370:0.703837:0.394486:0.703837:0.394486:0.689104:0.387370:0.689104:0.000000
2:@0.394485:0.698049:0.399484:0.698049:0.399484:0.689304:0.394485:0.689304:0.000000
5:@0.401600:0.702623:0.415540:0.702623:0.415540:0.690155:0.401600:0.690155:0.000000
1:@0.418870:0.695664:0.427036:0.695664:0.427036:0.681380:0.418870:0.681380:0.000000
2:@0.418870:0.708486:0.427036:0.708486:0.427036:0.694202:0.418870:0.694202:0.000000
, por tanto :@0.429979:0.701515:0.509123:0.701515:0.509123:0.685802:0.429979:0.685802:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.508973:0.701958:0.519252:0.701958:0.519252:0.687224:0.508973:0.687224:0.000000:0.000000
5:@0.519252:0.701428:0.533888:0.701428:0.533888:0.688336:0.519252:0.688336:0.000000
1:@0.552326:0.693783:0.560492:0.693783:0.560492:0.679499:0.552326:0.679499:0.000000
5:@0.566164:0.700742:0.580104:0.700742:0.580104:0.688273:0.566164:0.688273:0.000000
2:@0.583434:0.693783:0.591600:0.693783:0.591600:0.679499:0.583434:0.679499:0.000000
2:@0.552326:0.706605:0.560492:0.706605:0.560492:0.692320:0.552326:0.692320:0.000000
2:@0.583434:0.706605:0.591600:0.706605:0.591600:0.692320:0.583434:0.692320:0.000000
!:@0.544432:0.702269:0.550495:0.702269:0.550495:0.678723:0.544432:0.678723:0.000000
!:@0.578189:0.693178:0.583612:0.693178:0.583612:0.681465:0.578189:0.681465:0.000000
1.2 Punto trigonométrico:@0.293660:0.724589:0.484847:0.724589:0.484847:0.707920:0.293660:0.707920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Es cualquier punto de la circunferencia unitaria y lo notamos  ( ) o  ( , ) en donde :@0.293660:0.748672:0.930947:0.748672:0.930947:0.732959:0.293660:0.732959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P t:@0.764094:0.748672:0.783440:0.748672:0.783440:0.733237:0.764094:0.733237:0.000000:0.000000:0.000000
P x y:@0.809689:0.748672:0.842123:0.748672:0.842123:0.733237:0.809689:0.733237:0.000000:0.000000:0.000000:0.000000:0.000000
suponemos que   es un número real y representa la distancia recorrida desde el punto :@0.293642:0.766326:0.930847:0.766326:0.930847:0.750614:0.293642:0.750614:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.417902:0.766326:0.423277:0.766326:0.423277:0.750891:0.417902:0.750891:0.000000
A:@0.293642:0.783980:0.303526:0.783980:0.303526:0.768545:0.293642:0.768545:0.000000
(1,0) a lo largo de la circunferencia unitaria y desplazándonos en sentido contrario al de :@0.303453:0.783980:0.931337:0.783980:0.931337:0.768268:0.303453:0.768268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las agujas del reloj, si :@0.293642:0.801635:0.446796:0.801635:0.446796:0.785922:0.293642:0.785922:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.446551:0.801635:0.451926:0.801635:0.451926:0.786199:0.446551:0.786199:0.000000
.:@0.451852:0.801080:0.467185:0.801080:0.467185:0.787364:0.451852:0.787364:0.000000
0 o en el sentido de las manecillas del reloj si :@0.467093:0.801635:0.794017:0.801635:0.794017:0.785922:0.467093:0.785922:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.793601:0.801635:0.798976:0.801635:0.798976:0.786199:0.793601:0.786199:0.000000
,:@0.798902:0.801080:0.814236:0.801080:0.814236:0.787364:0.798902:0.787364:0.000000
0.:@0.814144:0.801635:0.826256:0.801635:0.826256:0.785922:0.814144:0.785922:0.000000:0.000000
y:@0.463228:0.830986:0.470810:0.830986:0.470810:0.814341:0.463228:0.814341:0.000000
0:@0.465338:0.905571:0.474451:0.905571:0.474451:0.888898:0.465338:0.888898:0.000000
2:@0.453311:0.949328:0.468868:0.949328:0.468868:0.935413:0.453311:0.935413:0.000000
1:@0.468868:0.949891:0.477981:0.949891:0.477981:0.933218:0.468868:0.933218:0.000000
2:@0.393271:0.905008:0.408827:0.905008:0.408827:0.891093:0.393271:0.891093:0.000000
1:@0.408827:0.905571:0.417941:0.905571:0.417941:0.888898:0.408827:0.888898:0.000000
1:@0.468345:0.849502:0.477458:0.849502:0.477458:0.832829:0.468345:0.832829:0.000000
1:@0.535294:0.905571:0.544408:0.905571:0.544408:0.888898:0.535294:0.888898:0.000000
P( ,  ):@0.518076:0.861476:0.559834:0.861476:0.559834:0.844803:0.518076:0.844803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.532400:0.861476:0.554885:0.861476:0.554885:0.844831:0.532400:0.844831:0.000000:0.000000:0.000000
t :@0.533950:0.881891:0.542764:0.881891:0.542764:0.865246:0.533950:0.865246:0.000000:0.000000
.:@0.542764:0.881328:0.558321:0.881328:0.558321:0.867413:0.542764:0.867413:0.000000
 :@0.558321:0.881891:0.562411:0.881891:0.562411:0.865218:0.558321:0.865218:0.000000
0:@0.562411:0.881891:0.571039:0.881891:0.571039:0.865246:0.562411:0.865246:0.000000
x:@0.566071:0.905571:0.573634:0.905571:0.573634:0.888926:0.566071:0.888926:0.000000
y:@0.693511:0.830986:0.701093:0.830986:0.701093:0.814341:0.693511:0.814341:0.000000
0:@0.695621:0.905571:0.704735:0.905571:0.704735:0.888898:0.695621:0.888898:0.000000
2:@0.683594:0.949328:0.699151:0.949328:0.699151:0.935413:0.683594:0.935413:0.000000
1:@0.699151:0.949891:0.708264:0.949891:0.708264:0.933218:0.699151:0.933218:0.000000
2:@0.623554:0.905008:0.639111:0.905008:0.639111:0.891093:0.623554:0.891093:0.000000
1:@0.639111:0.905571:0.648224:0.905571:0.648224:0.888898:0.639111:0.888898:0.000000
1:@0.698628:0.849502:0.707741:0.849502:0.707741:0.832829:0.698628:0.832829:0.000000
1:@0.765578:0.905571:0.774691:0.905571:0.774691:0.888898:0.765578:0.888898:0.000000
P( ,  ):@0.628354:0.942124:0.670111:0.942124:0.670111:0.925451:0.628354:0.925451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.642678:0.942124:0.665162:0.942124:0.665162:0.925480:0.642678:0.925480:0.000000:0.000000:0.000000
t :@0.729124:0.946430:0.737939:0.946430:0.737939:0.929785:0.729124:0.929785:0.000000:0.000000
,:@0.737939:0.945867:0.753495:0.945867:0.753495:0.931952:0.737939:0.931952:0.000000
 :@0.753495:0.946430:0.757585:0.946430:0.757585:0.929757:0.753495:0.929757:0.000000
0:@0.757585:0.946430:0.766213:0.946430:0.766213:0.929785:0.757585:0.929785:0.000000
x:@0.796354:0.905571:0.803917:0.905571:0.803917:0.888926:0.796354:0.888926:0.000000
Tema 1. Circunferencia unitaria y punto trigonométrico:@0.073089:0.098522:0.889022:0.098522:0.889022:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En la circunferencia unitaria centrada en el origen, el punto   está en el eje   positivo :@0.310262:0.162925:0.914390:0.162925:0.914390:0.147212:0.310262:0.147212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.733923:0.162925:0.742685:0.162925:0.742685:0.147490:0.733923:0.147490:0.000000
x:@0.842103:0.162925:0.849558:0.162925:0.849558:0.147490:0.842103:0.147490:0.000000
¿Cuáles son las coordenadas de  ?:@0.310280:0.190287:0.558852:0.190287:0.558852:0.174574:0.310280:0.174574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.543150:0.190287:0.551912:0.190287:0.551912:0.174851:0.543150:0.174851:0.000000
Reto matemático:@0.302768:0.139600:0.437491:0.139600:0.437491:0.122653:0.302768:0.122653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.163477:0.144306:0.170692:0.144306:0.170692:0.128467:0.163477:0.128467:0.000000
0:@0.165486:0.215282:0.174158:0.215282:0.174158:0.199416:0.165486:0.199416:0.000000
1:@0.232057:0.215282:0.240729:0.215282:0.240729:0.199416:0.232057:0.199416:0.000000
P:@0.219511:0.203084:0.228432:0.203084:0.228432:0.187218:0.219511:0.187218:0.000000
x:@0.261344:0.215282:0.268542:0.215282:0.268542:0.199443:0.261344:0.199443:0.000000
x:@0.194524:0.257565:0.201721:0.257565:0.201721:0.241725:0.194524:0.241725:0.000000
       1:@0.201721:0.257565:0.272949:0.257571:0.272949:0.241705:0.201721:0.241699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.210696:0.257029:0.225499:0.257029:0.225499:0.243787:0.210696:0.243787:0.000000
y:@0.229391:0.257565:0.236607:0.257565:0.236607:0.241725:0.229391:0.241725:0.000000
5:@0.245581:0.257029:0.260385:0.257029:0.260385:0.243787:0.245581:0.243787:0.000000
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