{"id":4698,"date":"2022-09-01T13:24:41","date_gmt":"2022-09-01T11:24:41","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/goniometricke-funkce-priklad-1\/"},"modified":"2022-09-01T13:40:00","modified_gmt":"2022-09-01T11:40:00","slug":"goniometricke-funkce-priklad-1","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/goniometricke-funkce-priklad-1\/","title":{"rendered":"Goniometrick\u00e9 funkce &#8211; p\u0159\u00edklad 1"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong><\/p>\n<p style=\"text-align: center\" data-mce-style=\"text-align: center;\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-4697\" src=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/gonio-1-300x143.png\" alt=\"\" width=\"485\" height=\"231\" data-mce-src=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/gonio-1-300x143.png\" srcset=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/gonio-1-300x143.png 300w, https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/gonio-1.png 504w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/p>\n<p>M\u00e1me obd\u00e9ln\u00edk ABCD s obsahem 28 cm2, ve kter\u00e9m je um\u00edst\u011bn troj\u00faheln\u00edk CDE. Obd\u00e9ln\u00edk a troj\u00faheln\u00edk maj\u00ed spole\u010dnou stranu CD.<br \/>D\u00e1le plat\u00ed, \u017ee:&nbsp;<em><strong>|BC| = 4 cm<\/strong><\/em>,&nbsp;<strong><em>|CE| = 5 cm<\/em><\/strong>,&nbsp;<strong><em>|DE| = 3 cm<\/em><\/strong>.<br \/><strong>Vypo\u010d\u00edtejte velikost \u00fahlu \u03c6.<\/strong><\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><br \/>1) Nejd\u0159\u00edve zjist\u00edme d\u00e9lku strany a, a to pomoc\u00ed vzore\u010dku na v\u00fdpo\u010det obsahu:<br \/>$$S=a\\cdot b$$<br \/>2) Dosad\u00edme:<br \/>$$28 = a\\cdot 4$$<br \/>3) P\u0159evedeme 4 na druhou stranu a t\u00edm se n\u00e1m n\u00e1soben\u00ed p\u0159evede na d\u011blen\u00ed:<br \/>$$a = 7$$<br \/>4) Pou\u017eijeme vzorec:<br \/>$$a^{2}=c^{2}+d^{2}-2\\cdot c\\cdot d\\cdot cos(\\phi)$$<br \/>5) Dosad\u00edme:<br \/>$$49=9+25-2\\cdot 3\\cdot 5\\cdot cos(\\phi)$$<br \/>6) Cosinus nech\u00e1me na jedn\u00e9 stran\u011b a \u010d\u00edsla na druh\u00e9:<br \/>$$30cos(\\phi)=-15$$<br \/>7) P\u0159evedeme na 1cos(~gamma):<br \/>$$cos(\\phi)=-0,5$$<br \/>8) P\u0159evedeme desetinn\u00e9 \u010d\u00edslo na stupn\u011b (lze vypo\u010d\u00edtat na kalkula\u010dce):<br \/>$$\\phi=120\u00b0$$<\/p>\n<p>\u010casov\u00e1 n\u00e1ro\u010dnost: 5 minut<\/p>\n<p>Jedn\u00e1 se o p\u0159\u00edklad z maturitn\u00edho testu.<\/p>\n","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-4698","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>Goniometrick\u00e9 funkce - p\u0159\u00edklad 1 | 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\/goniometricke-funkce-priklad-1\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Goniometrick\u00e9 funkce - p\u0159\u00edklad 1 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: M\u00e1me obd\u00e9ln\u00edk ABCD s obsahem 28 cm2, ve kter\u00e9m je um\u00edst\u011bn troj\u00faheln\u00edk CDE. Obd\u00e9ln\u00edk a troj\u00faheln\u00edk maj\u00ed spole\u010dnou stranu CD.D\u00e1le plat\u00ed, \u017ee:&nbsp;|BC| = 4 cm,&nbsp;|CE| = 5 cm,&nbsp;|DE| = 3 cm.Vypo\u010d\u00edtejte velikost \u00fahlu \u03c6. \u0158e\u0161en\u00ed:1) Nejd\u0159\u00edve zjist\u00edme d\u00e9lku strany a, a to pomoc\u00ed vzore\u010dku na v\u00fdpo\u010det obsahu:$$S=acdot b$$2) Dosad\u00edme:$$28 = acdot 4$$3) P\u0159evedeme 4 ... 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