203:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento espacial:@0.721207:0.043660:0.914624:0.043660:0.914624:0.024915:0.721207:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tema 4. Relaciones trigonométricas:@0.073089:0.097853:0.600199:0.097853:0.600199:0.066611:0.073089:0.066611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Indaga.:@0.293660:0.167993:0.350240:0.167993:0.350240:0.151323:0.293660:0.151323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ¿Qué es una razón trigonométrica?:@0.350139:0.167993:0.607652:0.167993:0.607652:0.151559:0.350139:0.151559:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reto matemático:@0.302768:0.138558:0.437491:0.138558:0.437491:0.121611:0.302768:0.121611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Nombre:@0.098077:0.647272:0.158352:0.647272:0.158352:0.631651:0.098077:0.631651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Razón trigonométrica:@0.199415:0.647272:0.360376:0.647272:0.360376:0.631651:0.199415:0.631651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.435923:0.647272:0.512079:0.647272:0.512079:0.631651:0.435923:0.631651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En la figura:@0.596925:0.647272:0.679975:0.647272:0.679975:0.631651:0.596925:0.631651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Seno:@0.080706:0.685480:0.114542:0.685480:0.114542:0.670540:0.080706:0.670540:0.000000:0.000000:0.000000:0.000000
cateto opuesto:@0.429566:0.675807:0.517385:0.675807:0.517385:0.662495:0.429566:0.662495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hipotenusa:@0.442165:0.691601:0.507470:0.691601:0.507470:0.678289:0.442165:0.678289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.634163:0.676608:0.642495:0.676608:0.642495:0.661842:0.634163:0.661842:0.000000
c:@0.634676:0.694157:0.641568:0.694157:0.641568:0.679391:0.634676:0.679391:0.000000
Coseno:@0.080706:0.732681:0.131276:0.732681:0.131276:0.717741:0.080706:0.717741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cateto adyacente:@0.423808:0.723008:0.524002:0.723008:0.524002:0.709696:0.423808:0.709696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hipotenusa:@0.441327:0.738802:0.506632:0.738802:0.506632:0.725490:0.441327:0.725490:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.633833:0.723808:0.642166:0.723808:0.642166:0.709042:0.633833:0.709042:0.000000
c:@0.634539:0.741360:0.641431:0.741360:0.641431:0.726594:0.634539:0.726594:0.000000
Tangente:@0.080706:0.779880:0.143391:0.779880:0.143391:0.764941:0.080706:0.764941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cateto opuesto:@0.429628:0.770209:0.517462:0.770209:0.517462:0.756897:0.429628:0.756897:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cateto adyacente:@0.423410:0.786003:0.523605:0.786003:0.523605:0.772691:0.423410:0.772691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.634163:0.771009:0.642495:0.771009:0.642495:0.756243:0.634163:0.756243:0.000000
b:@0.633973:0.788561:0.642306:0.788561:0.642306:0.773795:0.633973:0.773795:0.000000
Cosecante:@0.080706:0.827082:0.150620:0.827082:0.150620:0.812142:0.080706:0.812142:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hipotenusa:@0.440746:0.817408:0.506051:0.817408:0.506051:0.804097:0.440746:0.804097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cateto opuesto:@0.430070:0.833202:0.517889:0.833202:0.517889:0.819891:0.430070:0.819891:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.634680:0.818208:0.641571:0.818208:0.641571:0.803443:0.634680:0.803443:0.000000
a:@0.634166:0.835757:0.642499:0.835757:0.642499:0.820992:0.634166:0.820992:0.000000
Secante:@0.080706:0.874281:0.133886:0.874281:0.133886:0.859341:0.080706:0.859341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hipotenusa:@0.441290:0.864609:0.506595:0.864609:0.506595:0.851298:0.441290:0.851298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cateto adyacente:@0.423606:0.880403:0.523801:0.880403:0.523801:0.867092:0.423606:0.867092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.634539:0.865409:0.641431:0.865409:0.641431:0.850644:0.634539:0.850644:0.000000
b:@0.633833:0.882962:0.642166:0.882962:0.642166:0.868196:0.633833:0.868196:0.000000
Cotangente:@0.080706:0.921482:0.160157:0.921482:0.160157:0.906542:0.080706:0.906542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cateto adyacente:@0.414912:0.911779:0.531037:0.911779:0.531037:0.898237:0.414912:0.898237:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cateto opuesto:@0.424676:0.927846:0.526475:0.927846:0.526475:0.914304:0.424676:0.914304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.633973:0.912610:0.642306:0.912610:0.642306:0.897844:0.633973:0.897844:0.000000
a:@0.634156:0.930159:0.642489:0.930159:0.642489:0.915393:0.634156:0.915393:0.000000
Observemos los siguientes triángulos rectángulos, que a su vez tienen un ángulo agudo :@0.073089:0.214267:0.710735:0.214267:0.710735:0.197834:0.073089:0.197834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
congruente.:@0.073089:0.230909:0.161589:0.230909:0.161589:0.214475:0.073089:0.214475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.169905:0.258077:0.178901:0.258077:0.178901:0.243173:0.169905:0.243173:0.000000
B:@0.169905:0.342035:0.177932:0.342035:0.177932:0.327131:0.169905:0.327131:0.000000
A:@0.304737:0.342035:0.313717:0.342035:0.313717:0.327131:0.304737:0.327131:0.000000
E:@0.330957:0.342035:0.338332:0.342035:0.338332:0.327131:0.330957:0.327131:0.000000
f:@0.382680:0.342035:0.386944:0.342035:0.386944:0.327131:0.382680:0.327131:0.000000
i:@0.555906:0.342035:0.559351:0.342035:0.559351:0.327131:0.555906:0.327131:0.000000
D:@0.460622:0.342035:0.471090:0.342035:0.471090:0.327131:0.460622:0.327131:0.000000
H:@0.512127:0.342035:0.522211:0.342035:0.522211:0.327131:0.512127:0.327131:0.000000
I:@0.512127:0.281183:0.515605:0.281183:0.515605:0.266279:0.512127:0.266279:0.000000
G:@0.606608:0.342035:0.616508:0.342035:0.616508:0.327131:0.606608:0.327131:0.000000
F:@0.330957:0.273763:0.338265:0.273763:0.338265:0.258858:0.330957:0.258858:0.000000
c:@0.227212:0.342035:0.234169:0.342035:0.234169:0.327131:0.227212:0.327131:0.000000
b:@0.241827:0.293354:0.250239:0.293354:0.250239:0.278450:0.241827:0.278450:0.000000
α:@0.271677:0.324851:0.280573:0.324851:0.280573:0.309921:0.271677:0.309921:0.000000
α:@0.427913:0.324851:0.436810:0.324851:0.436810:0.309921:0.427913:0.309921:0.000000
α:@0.575271:0.324851:0.584167:0.324851:0.584167:0.309921:0.575271:0.309921:0.000000
d:@0.320690:0.306079:0.329101:0.306079:0.329101:0.291174:0.320690:0.291174:0.000000
e:@0.400723:0.299993:0.407796:0.299993:0.407796:0.285089:0.400723:0.285089:0.000000
g:@0.502545:0.309203:0.510957:0.309203:0.510957:0.294299:0.502545:0.294299:0.000000
h:@0.562328:0.303118:0.570956:0.303118:0.570956:0.288214:0.562328:0.288214:0.000000
a:@0.159687:0.299439:0.168099:0.299439:0.168099:0.284535:0.159687:0.284535:0.000000
Los triángulos anteriores son semejantes por el criterio de semejanza ángulo-ángulo. Si :@0.073089:0.375205:0.710768:0.375205:0.710768:0.358771:0.073089:0.358771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se conoce uno de los ángulos agudos del triángulo, la razón entre dos lados del triángulo :@0.073089:0.391847:0.710816:0.391847:0.710816:0.375413:0.073089:0.375413:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es constante.:@0.073089:0.408489:0.168184:0.408489:0.168184:0.392055:0.073089:0.392055:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En todo triángulo rectángulo, los catetos son los lados :@0.073678:0.437626:0.490006:0.437626:0.490006:0.421192:0.073678:0.421192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que forman el ángulo recto y la hipotenusa es el lado más :@0.073678:0.454268:0.490105:0.454268:0.490105:0.437834:0.073678:0.437834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
grande del triángulo opuesto al ángulo recto.:@0.073678:0.470910:0.402345:0.470910:0.402345:0.454476:0.073678:0.454476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El cateto adyacente es aquel que forma un lado del :@0.073678:0.498272:0.489840:0.498272:0.489840:0.481838:0.073678:0.481838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ángulo agudo que se está empleando.:@0.073678:0.514913:0.353175:0.514913:0.353175:0.498480:0.073678:0.498480:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.624315:0.431207:0.629913:0.431207:0.629913:0.422081:0.624315:0.422081:0.000000
b:@0.567428:0.502272:0.574506:0.502272:0.574506:0.490865:0.567428:0.490865:0.000000
c:@0.555873:0.466517:0.561577:0.466517:0.561577:0.455110:0.555873:0.455110:0.000000
A:@0.509713:0.499873:0.515839:0.499873:0.515839:0.490748:0.509713:0.490748:0.000000
C:@0.624314:0.499873:0.630300:0.499873:0.630300:0.490748:0.624314:0.490748:0.000000
Hipotenusa:@0.518836:0.454089:0.579540:0.454089:0.579540:0.443366:0.518836:0.443366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cateto:@0.519792:0.503312:0.554409:0.503312:0.554409:0.492590:0.519792:0.492590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
adyacente:@0.519792:0.510764:0.574092:0.510764:0.574092:0.500042:0.519792:0.500042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cateto:@0.625030:0.447604:0.659646:0.447604:0.659646:0.436881:0.625030:0.436881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
opuesto:@0.625030:0.455056:0.668317:0.455056:0.668317:0.444333:0.625030:0.444333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
90º:@0.596339:0.488944:0.614958:0.488944:0.614958:0.477455:0.596339:0.477455:0.000000:0.000000:0.000000
4.1 Razones trigonométricas:@0.073089:0.558838:0.296807:0.558838:0.296807:0.541891:0.073089:0.541891:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El valor de cada razón trigonométrica es independiente de la medida de los lados del :@0.073089:0.585486:0.710635:0.585486:0.710635:0.569052:0.073089:0.569052:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
triángulo rectángulo, porque solo depende del valor del ángulo agudo empleado.:@0.073089:0.602128:0.667544:0.602128:0.667544:0.585694:0.073089:0.585694:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.740294:0.222929:0.848854:0.222929:0.848854:0.205982:0.740294:0.205982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.740294:0.239571:0.837769:0.239571:0.837769:0.222624:0.740294:0.222624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Hace más de 5000 años, :@0.744288:0.259169:0.906784:0.259169:0.906784:0.244229:0.744288:0.244229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los matemáticos egipcios :@0.744288:0.274298:0.915412:0.274298:0.915412:0.259358:0.744288:0.259358:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conocían la relación entre :@0.744288:0.289427:0.918140:0.289427:0.918140:0.274487:0.744288:0.274487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el valor de las razones :@0.744288:0.304556:0.891320:0.304556:0.891320:0.289616:0.744288:0.289616:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de las longitudes de los :@0.744288:0.319685:0.902985:0.319685:0.902985:0.304745:0.744288:0.304745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lados y la medida de los :@0.744288:0.334814:0.905670:0.334814:0.905670:0.319874:0.744288:0.319874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ángulos agudos en un :@0.744288:0.349942:0.895696:0.349942:0.895696:0.335003:0.744288:0.335003:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
triángulo rectángulo. :@0.744288:0.365071:0.886283:0.365071:0.886283:0.350132:0.744288:0.350132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Esos valores eran útiles :@0.744288:0.380200:0.898382:0.380200:0.898382:0.365261:0.744288:0.365261:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en la determinación de :@0.744288:0.395329:0.901038:0.395329:0.901038:0.380389:0.744288:0.380389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
distancias imposibles :@0.744288:0.410458:0.887881:0.410458:0.887881:0.395518:0.744288:0.395518:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de medir directamente, :@0.744288:0.425587:0.903034:0.425587:0.903034:0.410647:0.744288:0.410647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por ello, se establecieron :@0.744288:0.440716:0.911143:0.440716:0.911143:0.425776:0.744288:0.425776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
razones trigonométricas.:@0.744288:0.455845:0.906931:0.455845:0.906931:0.440905:0.744288:0.440905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los:@0.744288:0.523925:0.766169:0.523925:0.766169:0.508985:0.744288:0.508985:0.000000:0.000000:0.000000
 Lineamientos de :@0.765923:0.523925:0.872893:0.523925:0.872893:0.509011:0.765923:0.509011:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
educación inclusiva:@0.744286:0.539054:0.864984:0.539054:0.864984:0.524140:0.744286:0.524140:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, :@0.864854:0.539054:0.871430:0.539054:0.871430:0.524114:0.864854:0.524114:0.000000:0.000000
entregados al país :@0.744286:0.554183:0.865085:0.554183:0.865085:0.539243:0.744286:0.539243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en marzo de 2014 :@0.744286:0.569312:0.864305:0.569312:0.864305:0.554372:0.744286:0.554372:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se convierten en un :@0.744286:0.584441:0.875878:0.584441:0.875878:0.569501:0.744286:0.569501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
documento pionero :@0.744286:0.599570:0.879352:0.599570:0.879352:0.584630:0.744286:0.584630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en América Latina, ya :@0.744286:0.614699:0.884761:0.614699:0.884761:0.599759:0.744286:0.599759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que responde al interés :@0.744286:0.629828:0.899187:0.629828:0.899187:0.614888:0.744286:0.614888:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
demostrado por las :@0.744286:0.644957:0.873539:0.644957:0.873539:0.630017:0.744286:0.630017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
instituciones de educación :@0.744286:0.660086:0.921230:0.660086:0.921230:0.645146:0.744286:0.645146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
superior de desarrollar :@0.744286:0.675215:0.891593:0.675215:0.891593:0.660275:0.744286:0.660275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
este modelo educativo :@0.744286:0.690344:0.896586:0.690344:0.896586:0.675404:0.744286:0.675404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como núcleo vital de una :@0.744286:0.705473:0.912127:0.705473:0.912127:0.690533:0.744286:0.690533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sociedad que busca la :@0.744286:0.720602:0.890925:0.720602:0.890925:0.705662:0.744286:0.705662:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
paz desde la reparación :@0.744286:0.735730:0.900258:0.735730:0.900258:0.720791:0.744286:0.720791:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y la reconciliación. En él :@0.744286:0.750859:0.899235:0.750859:0.899235:0.735920:0.744286:0.735920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se abre el camino para :@0.744286:0.765988:0.892910:0.765988:0.892910:0.751048:0.744286:0.751048:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lograr que la educación :@0.744286:0.781117:0.899888:0.781117:0.899888:0.766177:0.744286:0.766177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
superior de Colombia :@0.744286:0.796246:0.887734:0.796246:0.887734:0.781306:0.744286:0.781306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
\potencie y valore la :@0.744286:0.811375:0.877644:0.811375:0.877644:0.796435:0.744286:0.796435:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diversidad (entendiendo :@0.744286:0.826504:0.906386:0.826504:0.906386:0.811564:0.744286:0.811564:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y protegiendo las :@0.744286:0.841633:0.859899:0.841633:0.859899:0.826693:0.744286:0.826693:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
particularidades), :@0.744286:0.856762:0.858381:0.856762:0.858381:0.841822:0.744286:0.841822:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
promueva el respeto a :@0.744286:0.871891:0.892761:0.871891:0.892761:0.856951:0.744286:0.856951:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ser diferente y facilite :@0.744286:0.887020:0.883236:0.887020:0.883236:0.872080:0.744286:0.872080:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la participación de la :@0.744286:0.902149:0.881031:0.902149:0.881031:0.887209:0.744286:0.887209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunidad dentro de una :@0.744286:0.917278:0.918697:0.917278:0.918697:0.902338:0.744286:0.902338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
estructura intercultural\.:@0.744286:0.932407:0.896287:0.932407:0.896287:0.917467:0.744286:0.917467:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interculturalidad:@0.744526:0.495914:0.875874:0.495914:0.875874:0.478967:0.744526:0.478967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 4 (Ev. 1 G. 10) Reconoce el significado de las razones trigonométricas en un triángulo rectángulo para ángulos agudos, en particular, seno, coseno y tangente. :@0.043679:0.965272:0.898864:0.965272:0.898864:0.953320:0.043679:0.953320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.895208:0.965272:0.898139:0.965272:0.898139:0.953320:0.895208:0.953320:0.000000
EC. Conoce y calcula las razones trigonométricas seno, coseno y tangente para los ángulos agudos de un triángulo rectángulo y las utiliza para resolver triángulos.:@0.043681:0.977375:0.894946:0.977375:0.894946:0.965423:0.043681:0.965423:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@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