{"id":3001,"date":"2022-05-27T16:52:41","date_gmt":"2022-05-27T14:52:41","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tangentova-veta\/"},"modified":"2022-05-29T19:58:04","modified_gmt":"2022-05-29T17:58:04","slug":"tangentova-veta","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tangentova-veta\/","title":{"rendered":"Tangentov\u00e1 v\u011bta vzorec a vyu\u017eit\u00ed"},"content":{"rendered":"<p>Tangentov\u00e1 v\u011bta, stejn\u011b jako v\u011bta sinov\u00e1 a kosinov\u00e1, se vztahuje na obecn\u00e9 troj\u00faheln\u00edky.<\/p>\n<ul>\n<li><strong>Co n\u00e1m tangentov\u00e1 v\u011bta \u0159\u00edk\u00e1?<\/strong><\/li>\n<\/ul>\n<p>$$\\frac{a-b}{a+b}=\\frac{tg\\frac{\\alpha-\\beta}{2}}{tg\\frac{\\alpha+\\beta}{2}}=\\frac{tg\\frac{\\alpha-\\beta}{2}}{cotg\\frac{\\gamma}{2}}$$<\/p>\n<p>$$\\frac{b-c}{b+c}=\\frac{tg\\frac{\\beta-\\gamma}{2}}{tg\\frac{\\beta+\\gamma}{2}}=\\frac{tg\\frac{\\beta-\\gamma}{2}}{cotg\\frac{\\alpha}{2}}$$<\/p>\n<p>$$\\frac{c-a}{c+a}=\\frac{tg\\frac{\\gamma-\\alpha}{2}}{tg\\frac{\\gamma+\\alpha}{2}}=\\frac{tg\\frac{\\gamma-\\alpha}{2}}{cotg\\frac{\\beta}{2}}$$<\/p>\n<ul>\n<li><strong>Kdy m\u016f\u017eeme tangentovou v\u011btu vyu\u017e\u00edt?<\/strong><\/li>\n<\/ul>\n<p>Kdy\u017e zn\u00e1me dv\u011b strany v troj\u00faheln\u00edku a \u00fahel proti jedn\u00e9 z nich.<\/p>\n<p>Kdy\u017e zn\u00e1me dva \u00fahly v troj\u00faheln\u00edku a stranu proti jednomu z nich.<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-3001","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Tangentov\u00e1 v\u011bta vzorec a vyu\u017eit\u00ed | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tangentova-veta\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Tangentov\u00e1 v\u011bta vzorec a vyu\u017eit\u00ed | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Tangentov\u00e1 v\u011bta, stejn\u011b jako v\u011bta sinov\u00e1 a kosinov\u00e1, se vztahuje na obecn\u00e9 troj\u00faheln\u00edky. Co n\u00e1m tangentov\u00e1 v\u011bta \u0159\u00edk\u00e1? $$frac{a-b}{a+b}=frac{tgfrac{alpha-beta}{2}}{tgfrac{alpha+beta}{2}}=frac{tgfrac{alpha-beta}{2}}{cotgfrac{gamma}{2}}$$ $$frac{b-c}{b+c}=frac{tgfrac{beta-gamma}{2}}{tgfrac{beta+gamma}{2}}=frac{tgfrac{beta-gamma}{2}}{cotgfrac{alpha}{2}}$$ $$frac{c-a}{c+a}=frac{tgfrac{gamma-alpha}{2}}{tgfrac{gamma+alpha}{2}}=frac{tgfrac{gamma-alpha}{2}}{cotgfrac{beta}{2}}$$ Kdy m\u016f\u017eeme tangentovou v\u011btu vyu\u017e\u00edt? Kdy\u017e zn\u00e1me dv\u011b strany v troj\u00faheln\u00edku a \u00fahel proti jedn\u00e9 z nich. Kdy\u017e zn\u00e1me dva \u00fahly v troj\u00faheln\u00edku a stranu proti jednomu z nich.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tangentova-veta\/\" \/>\n<meta property=\"og:site_name\" content=\"Studijni-svet.cz\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/studijnisvet\/\" \/>\n<meta property=\"article:modified_time\" content=\"2022-05-29T17:58:04+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Odhadovan\u00e1 doba \u010dten\u00ed\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minuta\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/tangentova-veta\\\/\",\"url\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/tangentova-veta\\\/\",\"name\":\"Tangentov\u00e1 v\u011bta vzorec a vyu\u017eit\u00ed | Studijni-svet.cz\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#website\"},\"datePublished\":\"2022-05-27T14:52:41+00:00\",\"dateModified\":\"2022-05-29T17:58:04+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/tangentova-veta\\\/#breadcrumb\"},\"inLanguage\":\"cs\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/tangentova-veta\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/tangentova-veta\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\u016f\",\"item\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Lekce\",\"item\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/lesson\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Matematika k maturit\u011b\",\"item\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/prehled\\\/matematika-k-maturite\\\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Tangentov\u00e1 v\u011bta vzorec a vyu\u017eit\u00ed\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#website\",\"url\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/\",\"name\":\"Akademie Studijni-svet.cz | Kurzy a podklady\",\"description\":\"Online akademie | Kurzy a podklady\",\"publisher\":{\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#organization\"},\"alternateName\":\"Akademie Studijni-svet.cz\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"cs\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#organization\",\"name\":\"Studijni-svet.cz\",\"url\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"cs\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/wp-content\\\/uploads\\\/2022\\\/01\\\/SS_logo-1.png\",\"contentUrl\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/wp-content\\\/uploads\\\/2022\\\/01\\\/SS_logo-1.png\",\"width\":66,\"height\":75,\"caption\":\"Studijni-svet.cz\"},\"image\":{\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/studijnisvet\\\/\",\"https:\\\/\\\/www.instagram.com\\\/studijnisvet.cz\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Tangentov\u00e1 v\u011bta vzorec a vyu\u017eit\u00ed | Studijni-svet.cz","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/tangentova-veta\/","og_locale":"cs_CZ","og_type":"article","og_title":"Tangentov\u00e1 v\u011bta vzorec a vyu\u017eit\u00ed | Studijni-svet.cz","og_description":"Tangentov\u00e1 v\u011bta, stejn\u011b jako v\u011bta sinov\u00e1 a kosinov\u00e1, se vztahuje na obecn\u00e9 troj\u00faheln\u00edky. Co n\u00e1m tangentov\u00e1 v\u011bta \u0159\u00edk\u00e1? $$frac{a-b}{a+b}=frac{tgfrac{alpha-beta}{2}}{tgfrac{alpha+beta}{2}}=frac{tgfrac{alpha-beta}{2}}{cotgfrac{gamma}{2}}$$ $$frac{b-c}{b+c}=frac{tgfrac{beta-gamma}{2}}{tgfrac{beta+gamma}{2}}=frac{tgfrac{beta-gamma}{2}}{cotgfrac{alpha}{2}}$$ $$frac{c-a}{c+a}=frac{tgfrac{gamma-alpha}{2}}{tgfrac{gamma+alpha}{2}}=frac{tgfrac{gamma-alpha}{2}}{cotgfrac{beta}{2}}$$ Kdy m\u016f\u017eeme tangentovou v\u011btu vyu\u017e\u00edt? Kdy\u017e zn\u00e1me dv\u011b strany v troj\u00faheln\u00edku a \u00fahel proti jedn\u00e9 z nich. 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