{"id":876,"date":"2025-09-06T18:39:41","date_gmt":"2025-09-07T00:39:41","guid":{"rendered":"https:\/\/portal.pronea.gt\/?p=876"},"modified":"2025-09-07T10:34:30","modified_gmt":"2025-09-07T16:34:30","slug":"temporary-title-790-2-2-2-2-2-2-2-2-2","status":"publish","type":"post","link":"https:\/\/portal.pronea.gt\/?p=876","title":{"rendered":"\u00c1ngulos y funciones trigonom\u00e9tricas: midiendo el mundo con matem\u00e1ticas"},"content":{"rendered":"<div id=\"cmsmasters_row_0j6royqael\" class=\"cmsmasters_row cmsmasters_color_scheme_default cmsmasters_row_top_default cmsmasters_row_bot_default cmsmasters_row_fullwidth\">\n<div class=\"cmsmasters_row_outer_parent\">\n<div class=\"cmsmasters_row_outer\">\n<div class=\"cmsmasters_row_inner cmsmasters_row_fullwidth cmsmasters_row_no_margin\">\n<div class=\"cmsmasters_row_margin\">\n<div id=\"cmsmasters_column_69dy6p9ke\" class=\"cmsmasters_column one_first\">\n<div class=\"cmsmasters_column_inner\"><div class=\"cmsmasters_text\" data-animation=\"fadeInRight\" data-delay=\"0\">\n<p data-start=\"2346\" data-end=\"2612\">Las matem\u00e1ticas no solo est\u00e1n en los n\u00fameros, tambi\u00e9n en las formas, las distancias y los \u00e1ngulos que nos rodean. A trav\u00e9s de las <strong data-start=\"2476\" data-end=\"2505\">funciones trigonom\u00e9tricas<\/strong>, es posible calcular alturas, trayectorias y dimensiones que a simple vista parecen imposibles de medir.<\/p>\n<p data-start=\"2614\" data-end=\"2712\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f3a5.svg\" alt=\"\ud83c\udfa5\" \/> <strong data-start=\"2617\" data-end=\"2639\">Mira el video aqu\u00ed<\/strong><\/p>\n<iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/-gb5j_1_MaI?si=fQFDnS6yFstdXJbj\" width=\"1220\" height=\"630\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe>\n<hr data-start=\"2714\" data-end=\"2717\" \/>\n<h2 data-start=\"2719\" data-end=\"2748\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f50e.svg\" alt=\"\ud83d\udd0e\" \/> \u00bfQu\u00e9 son los \u00e1ngulos?<\/h2>\n<p data-start=\"2749\" data-end=\"2975\">Un <strong data-start=\"2752\" data-end=\"2762\">\u00e1ngulo<\/strong> es la abertura formada por dos l\u00edneas que se encuentran en un punto. Se mide en grados (\u00b0) o radianes, y est\u00e1 presente en todo lo que nos rodea: desde el giro de una puerta hasta la inclinaci\u00f3n de una escalera.<\/p>\n<hr data-start=\"2977\" data-end=\"2980\" \/>\n<h2 data-start=\"2982\" data-end=\"3029\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/270d.svg\" alt=\"\u270d\ufe0f\" \/> \u00bfQu\u00e9 son las funciones trigonom\u00e9tricas?<\/h2>\n<p data-start=\"3030\" data-end=\"3118\">Las funciones trigonom\u00e9tricas son relaciones que surgen de los tri\u00e1ngulos rect\u00e1ngulos:<\/p>\n<ul data-start=\"3119\" data-end=\"3333\">\n<li data-start=\"3119\" data-end=\"3185\">\n<p data-start=\"3121\" data-end=\"3185\"><strong data-start=\"3121\" data-end=\"3136\">Seno (sen):<\/strong> relaciona el cateto opuesto con la hipotenusa.<\/p>\n<\/li>\n<li data-start=\"3186\" data-end=\"3256\">\n<p data-start=\"3188\" data-end=\"3256\"><strong data-start=\"3188\" data-end=\"3205\">Coseno (cos):<\/strong> relaciona el cateto adyacente con la hipotenusa.<\/p>\n<\/li>\n<li data-start=\"3257\" data-end=\"3333\">\n<p data-start=\"3259\" data-end=\"3333\"><strong data-start=\"3259\" data-end=\"3278\">Tangente (tan):<\/strong> relaciona el cateto opuesto con el cateto adyacente.<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"3335\" data-end=\"3338\" \/>\n<h2 data-start=\"3340\" data-end=\"3376\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f30d.svg\" alt=\"\ud83c\udf0d\" \/> Aplicaciones en la vida real<\/h2>\n<p data-start=\"3377\" data-end=\"3422\">Las funciones trigonom\u00e9tricas se usan para:<\/p>\n<ul data-start=\"3423\" data-end=\"3651\">\n<li data-start=\"3423\" data-end=\"3479\">\n<p data-start=\"3425\" data-end=\"3479\">Calcular la altura de un edificio o una monta\u00f1a. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f3d4.svg\" alt=\"\ud83c\udfd4\ufe0f\" \/><\/p>\n<\/li>\n<li data-start=\"3480\" data-end=\"3538\">\n<p data-start=\"3482\" data-end=\"3538\">Determinar la distancia entre dos puntos inaccesibles.<\/p>\n<\/li>\n<li data-start=\"3539\" data-end=\"3595\">\n<p data-start=\"3541\" data-end=\"3595\">Dise\u00f1ar puentes, rampas y construcciones seguras. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f309.svg\" alt=\"\ud83c\udf09\" \/><\/p>\n<\/li>\n<li data-start=\"3596\" data-end=\"3651\">\n<p data-start=\"3598\" data-end=\"3651\">Analizar trayectorias de aviones o sat\u00e9lites. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/2708.svg\" alt=\"\u2708\ufe0f\" \/><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f6f0.svg\" alt=\"\ud83d\udef0\ufe0f\" \/><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"3653\" data-end=\"3656\" \/>\n<h2 data-start=\"3658\" data-end=\"3685\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f393.svg\" alt=\"\ud83c\udf93\" \/> Aprender con PRONEA<\/h2>\n<p data-start=\"3686\" data-end=\"3965\">El <strong data-start=\"3689\" data-end=\"3744\">Programa Nacional de Educaci\u00f3n Alternativa \u2013PRONEA\u2013<\/strong> del Ministerio de Educaci\u00f3n de Guatemala ofrece a j\u00f3venes y adultos la oportunidad de comprender la trigonometr\u00eda de forma clara y pr\u00e1ctica, demostrando que aprender matem\u00e1ticas es \u00fatil y necesario para la vida diaria.<\/p>\n<hr data-start=\"3967\" data-end=\"3970\" \/>\n<h2 data-start=\"3972\" data-end=\"3989\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/2705.svg\" alt=\"\u2705\" \/> Conclusi\u00f3n<\/h2>\n<p data-start=\"3990\" data-end=\"4227\">Los <strong data-start=\"3994\" data-end=\"4037\">\u00e1ngulos y las funciones trigonom\u00e9tricas<\/strong> son herramientas poderosas que permiten medir y entender el mundo. Aprenderlas es descubrir que las matem\u00e1ticas no solo est\u00e1n en los libros, sino en cada rinc\u00f3n de nuestra vida cotidiana.<\/p>\n<p data-start=\"4229\" data-end=\"4280\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f449.svg\" alt=\"\ud83d\udc49\" \/> <strong data-start=\"4232\" data-end=\"4278\">PRONEA: La educaci\u00f3n que transforma vidas.<\/strong><\/p>\n<\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":879,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"image","meta":{"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"footnotes":""},"categories":[33,39],"tags":[],"class_list":["post-876","post","type-post","status-publish","format-image","has-post-thumbnail","hentry","category-matematicas","category-recursos","post_format-post-format-image"],"_links":{"self":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/876","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=876"}],"version-history":[{"count":2,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/876\/revisions"}],"predecessor-version":[{"id":878,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/876\/revisions\/878"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/media\/879"}],"wp:attachment":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=876"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=876"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=876"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}