{"id":8306,"date":"2026-09-19T17:46:13","date_gmt":"2026-09-19T14:46:13","guid":{"rendered":"https:\/\/www.schooler.org.ua\/scho-take-sichna-funktsija-praktichnij-posibnik-z-osnov-trigonometriyi\/"},"modified":"2026-09-19T17:46:13","modified_gmt":"2026-09-19T14:46:13","slug":"scho-take-sichna-funktsija-praktichnij-posibnik-z-osnov-trigonometriyi","status":"publish","type":"post","link":"https:\/\/www.schooler.org.ua\/cs\/co-je-funkce-secant-prakticky-pruvodce-zaklady-trigonometrie\/","title":{"rendered":"Co je funkce secant? Praktick\u00fd pr\u016fvodce z\u00e1klady trigonometrie"},"content":{"rendered":"

Funkce secant<\/strong> je jednou ze \u0161esti nejd\u016fle\u017eit\u011bj\u0161\u00edch goniometrick\u00fdch funkc\u00ed, kter\u00e9 byste m\u011bli zn\u00e1t. M\u016f\u017eete se s t\u00edm setkat p\u0159i studiu z\u00e1kladn\u00ed geometrie nebo kalkulu. I kdy\u017e je \u010dasto zast\u00edn\u011bn sinusem a kosinusem, hraje zvl\u00e1\u0161tn\u00ed roli v porozum\u011bn\u00ed pravo\u00fahl\u00fdm troj\u00faheln\u00edk\u016fm a pokro\u010dil\u00e9 matematice. <\/p>\n

V pravo\u00fahl\u00e9m troj\u00faheln\u00edku ABC<\/em> se se\u010dna \u00fahlu A<\/em> ur\u010d\u00ed jednodu\u0161e. Toto je pom\u011br d\u00e9lky p\u0159epony k noze soused\u00edc\u00ed s \u00fahlem A<\/em>. <\/p>\n

$$ \\sec A = \\frac{\\text{D\u00e9lka p\u0159epony}}{\\text{D\u00e9lka nohy soused\u00edc\u00ed s \u00fahlem } A} $$<\/p>\n

Dal\u0161\u00edmi p\u011bti funkcemi v t\u00e9to \u0159ad\u011b jsou sinus (sin<\/em> ), kosinus (cos<\/em> ), tangens (tan<\/em> ), kotangens (csc<\/em> ) a kotangens (cot<\/em> ). Pochopen\u00ed t\u011bchto vztah\u016f v\u00e1m pom\u016f\u017ee rychleji \u0159e\u0161it probl\u00e9my. <\/p>\n

Pro\u010d byste m\u011bli v\u011bnovat pozornost secantu<\/h3>\n

V\u011bt\u0161ina student\u016f se zam\u011b\u0159uje na sinus a kosinus, proto\u017ee jsou nejb\u011b\u017en\u011bj\u0161\u00ed. Sekanta je v\u0161ak p\u0159evr\u00e1cen\u00e1 hodnota kosinusu. To znamen\u00e1:<\/p>\n

$$ \\frac{1}{\\sec A} = \\cos A $$<\/p>\n

Tento pom\u011br je u\u017eite\u010dn\u00fd. Pokud zn\u00e1te kosinus \u00fahlu, m\u016f\u017eete pou\u017e\u00edt p\u0159evr\u00e1cenou hodnotu a z\u00edskat hodnotu se\u010dny. K tomu nepot\u0159ebujete samostatnou tabulku. <\/p>\n

Je zde tak\u00e9 d\u016fle\u017eit\u00e1 identita spojuj\u00edc\u00ed se\u010dnu a te\u010dnu. Podle definice te\u010dny ($ \\tan A = \\frac{\\text{opa\u010dn\u00e1 strana}}{\\text{sousedn\u00ed strana}} $) a Pythagorovy v\u011bty z\u00edsk\u00e1me:<\/p>\n

$$ \\tan^2 A + 1 = \\sec^2 A $$<\/p>\n

Tato identita je u\u017eite\u010dn\u00e1 pro zjednodu\u0161en\u00ed rovnic. P\u0159i \u0159e\u0161en\u00ed slo\u017eit\u00fdch \u00faloh trigonometrie m\u016f\u017eete p\u0159ep\u00ednat mezi \u010dleny te\u010dny a se\u010dny. <\/p>\n

Chov\u00e1n\u00ed funkce sekantu<\/h3>\n

Kdy\u017e vykresl\u00edte funkci se\u010dny, vypad\u00e1 jako \u0159ada k\u0159ivek ve tvaru U. Nen\u00ed to hladk\u00e1 vlna jako sinus nebo kosinus. <\/p>\n

Pokud je \u00fahel A<\/em> vyj\u00e1d\u0159en v radi\u00e1nech, je perioda t\u00e9to funkce $2\\pi$. Je d\u016fle\u017eit\u00e9 v\u011bd\u011bt n\u00e1sleduj\u00edc\u00ed:<\/p>\n

    \n
  • V bod\u011b 0 je hodnota 1.<\/li>\n
  • V bod\u011b $\\pi$ je hodnota -1. <\/li>\n
  • Funkce m\u00e1 nespojitost v bod\u011b $\\pi\/2$. Pokud se p\u0159ibl\u00ed\u017e\u00edte zleva, m\u00e1 tendenci k kladn\u00e9mu nekone\u010dnu, a pokud se p\u0159ibl\u00ed\u017e\u00edte zprava, m\u00e1 tendenci k z\u00e1porn\u00e9mu nekone\u010dnu. <\/li>\n
  • K opakovan\u00e9mu prasknut\u00ed doch\u00e1z\u00ed v bod\u011b $3\\pi\/2$. P\u0159i p\u0159ibl\u00ed\u017een\u00ed zleva m\u00e1 funkce sklon k z\u00e1porn\u00e9mu nekone\u010dnu a zprava k kladn\u00e9mu nekone\u010dnu. <\/li>\n<\/ul>\n

    Funkce je sud\u00e1. To znamen\u00e1, \u017ee $\\sec(-A) = \\sec A$. Graf je symetrick\u00fd podle osy y. <\/p>\n

    Diferenciace a integrace<\/h3>\n

    Pokud studujete kalkul, m\u011bli byste v\u011bd\u011bt, jak pracovat se sekanty v diferenciaci a integraci. <\/p>\n

    Derivace $\\sec x$ vzhledem k $x$ se rovn\u00e1:<\/p>\n

    $$ \\frac{d}{dx}(\\sec x) = \\sec x \\tan x $$<\/p>\n

    Neur\u010dit\u00e9 integr\u00e1ly jsou je\u0161t\u011b slo\u017eit\u011bj\u0161\u00ed. Zahrnuj\u00ed p\u0159irozen\u00e9 logaritmy. <\/p>\n

    $$ \\int \\sec x \\, dx = \\ln |\\sec x + \\tan x| +C$$<\/p>\n

    kde $C$ je integra\u010dn\u00ed konstanta a $\\ln$ je p\u0159irozen\u00fd logaritmus. <\/p>\n

    \u010casto kladen\u00e9 ot\u00e1zky o sexu<\/h3>\n

    **Jako j\u00e1<\/p>\n","protected":false},"excerpt":{"rendered":"

    Funkce secant je jednou ze \u0161esti nejd\u016fle\u017eit\u011bj\u0161\u00edch goniometrick\u00fdch funkc\u00ed, kter\u00e9 byste m\u011bli zn\u00e1t. M\u016f\u017eete se s t\u00edm setkat p\u0159i studiu z\u00e1kladn\u00ed geometrie nebo kalkulu. I kdy\u017e je \u010dasto zast\u00edn\u011bn sinusem a kosinusem, hraje zvl\u00e1\u0161tn\u00ed roli v porozum\u011bn\u00ed pravo\u00fahl\u00fdm troj\u00faheln\u00edk\u016fm a pokro\u010dil\u00e9 matematice. V pravo\u00fahl\u00e9m troj\u00faheln\u00edku ABC se se\u010dna \u00fahlu A ur\u010d\u00ed jednodu\u0161e. Toto je pom\u011br […]<\/p>\n","protected":false},"author":1,"featured_media":8303,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":""},"categories":[50],"tags":[],"wpm_language_slugs":{"cs":"co-je-funkce-secant-prakticky-pruvodce-zaklady-trigonometrie","de":"was-ist-die-sekantenfunktion-ein-praktischer-leitfaden-zu-den","en":"what-is-the-secant-function-a-practical-guide-to-the-basics-of","es":"que-es-la-funcion-secante-una-guia-practica-sobre-los-conceptos","fr":"quest-ce-que-la-fonction-secante-un-guide-pratique-sur-les-bases-de-la","id":"apa-fungsi-garis-potongnya-panduan-praktis-dasar-dasar-trigonometri","it":"cose-la-funzione-secante-una-guida-pratica-alle-basi-della","nl":"wat-is-de-secansfunctie-een-praktische-gids-voor-de-basisprincipes-van","pl":"co-to-jest-funkcja-sieczna-praktyczny-przewodnik-po-podstawach","pt":"qual-e-a-funcao-secante-um-guia-pratico-para-os-fundamentos-da","ru-ru":"chto-takoe-funktsija-sekansa-prakticheskoe-rukovodstvo-po-osnovam","uk-ua":"scho-take-sichna-funktsija-praktichnij-posibnik-z-osnov-trigonometriyi"},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/posts\/8306"}],"collection":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/comments?post=8306"}],"version-history":[{"count":0,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/posts\/8306\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/media\/8303"}],"wp:attachment":[{"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/media?parent=8306"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/categories?post=8306"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.schooler.org.ua\/cs\/wp-json\/wp\/v2\/tags?post=8306"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}