{"id":496,"date":"2021-02-17T22:19:31","date_gmt":"2021-02-17T22:19:31","guid":{"rendered":"http:\/\/mxth.dk\/?p=496"},"modified":"2023-08-28T10:57:57","modified_gmt":"2023-08-28T08:57:57","slug":"trigonometriske-ligninger-et-par-eksempler","status":"publish","type":"post","link":"https:\/\/mxth.dk\/?p=496","title":{"rendered":"Trigonometriske Ligninger &#8211; Et Par Eksempler"},"content":{"rendered":"\n<p class=\" eplus-wrapper\">Der er her 4 eksempler hvor der gennemg\u00e5es hvorledes trigonometriske ligninger l\u00f8ses. De er alle med sinusfunktionen, men tilsvarende g\u00f8r sig g\u00e6ldende for cosinusfunktionen.<\/p>\n\n\n\n<h3 class=\" wp-block-heading eplus-wrapper\">Eksempel 1<\/h3>\n\n\n\n<p class=\" eplus-wrapper\">Vi ser her p\u00e5 en simpel trigonometrisk ligning nemlig <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/00\/ql_327b2d2cd911139c18c1931d3ae44b00_l3.png?resize=74%2C22&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#92;&#98;&#102;&#32;&#115;&#105;&#110;&#40;&#120;&#41;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"74\" style=\"vertical-align: -6px;\"\/>.<\/p>\n\n\n\n<figure class=\"wp-embed-aspect-16-9 wp-has-aspect-ratio wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube eplus-wrapper\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/FwoiDEWUP1M?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=da-DK&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><\/figure>\n\n\n\n<h3 class=\" wp-block-heading eplus-wrapper\">Eksempel 2<\/h3>\n\n\n\n<p class=\" eplus-wrapper\">Vi ser her p\u00e5 en igen simpel trigonometrisk ligning,nemlig <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/43\/ql_6c39f45f5d05437555aa7b822e8fa843_l3.png?resize=74%2C22&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#92;&#98;&#102;&#32;&#115;&#105;&#110;&#40;&#120;&#41;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"74\" style=\"vertical-align: -6px;\"\/>, men ser p\u00e5 et interval der ligger v\u00e6k fra y-aksen, nemlig intervallet fra otte til og med tolv.<\/p>\n\n\n\n<figure class=\"wp-embed-aspect-16-9 wp-has-aspect-ratio wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube eplus-wrapper\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/YZG_RfxA2FM?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=da-DK&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><\/figure>\n\n\n\n<h3 class=\" wp-block-heading eplus-wrapper\">Eksempel 3<\/h3>\n\n\n\n<p class=\" eplus-wrapper\">Vi ser nu p\u00e5 en ligning hvor udsvinget er st\u00f8rre, nemlig <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/c5\/ql_26abe53ce44b8b9df70fce10311015c5_l3.png?resize=96%2C16&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#92;&#98;&#102;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#115;&#105;&#110;&#40;&#120;&#41;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -3px;\"\/>. Derfor kan funktionensv\u00e6rdien v\u00e6re st\u00f8rre end 1. Man skal her v\u00e6re opm\u00e6rksom p\u00e5 at f\u00e5 isoleret sin(x) s\u00e5 det st\u00e5r alene p\u00e5 venstresiden s\u00e5ledes at ligningen ender med at ligne en klassisk trigonometrisk ligning af formen <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/1c\/ql_fd5ca81a810d1aff45aa91a8ffd92f1c_l3.png?resize=72%2C16&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#115;&#105;&#110;&#40;&#120;&#41;&#61;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -3px;\"\/>.<\/p>\n\n\n\n<figure class=\"wp-embed-aspect-16-9 wp-has-aspect-ratio wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube eplus-wrapper\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/zZg9ykkuqLk?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=da-DK&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><\/figure>\n\n\n\n<h3 class=\" wp-block-heading eplus-wrapper\">Eksempel 4<\/h3>\n\n\n\n<p class=\" eplus-wrapper\">Vi ser her i eksempel 4 p\u00e5 en trigonometrisk ligning, hvor x inde i sinusfunktionen ikke st\u00e5r alene, nemlig <img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/quicklatex.com\/cache3\/5e\/ql_828363ab5728a59c2991c74030c10b5e_l3.png?resize=97%2C16&#038;ssl=1\" class=\"ql-img-inline-formula \" alt=\"&#92;&#98;&#102;&#32;&#115;&#105;&#110;&#40;&#50;&#120;&#41;&#61;&#48;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"97\" style=\"vertical-align: -3px;\"\/>. Her skal man f\u00f8rst l\u00f8se ligningen p\u00e5 klassisk vis og derefter skal man isolere x. Man skal dog v\u00e6re opm\u00e6rksom p\u00e5 n\u00e5r man skal finde yderligere l\u00f8sninger, hvor man jo ligger perioden til. S\u00e5 her bliver vi n\u00f8d til at \u00e6ndre lidt p\u00e5 formlerne til den fuldst\u00e6ndige l\u00f8sning.<\/p>\n\n\n\n<figure class=\"wp-embed-aspect-16-9 wp-has-aspect-ratio wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube eplus-wrapper\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/gJD52rMKcz0?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=da-DK&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><\/figure>\n\n\n\n<h5 class=\" wp-block-heading eplus-wrapper\">Opgaver<\/h5>\n\n\n\n<table border=\"1\" width=\"100%\">\n    <thead>\n        <tr>\n            <th scope=\"col\" bgcolor=\"#3CB371\" width=\"33%\">Gr\u00f8n<\/th>\n            <th scope=\"col\" bgcolor=\"#FFA500\" width=\"33%\">Gul<\/th>\n            <th scope=\"col\" bgcolor=\"#DC143C\" width=\"33%\">R\u00f8d<\/th>\n        <\/tr>\n    <\/thead>\n    <tbody>\n        <tr>\n            <td><a href=\"https:\/\/matstxab2opgaver.systime.dk\/?id=c2781\" target=\"_blank\" rel=\"noopener noreferrer\">MatAB2stx-6.14<\/a><\/td>\n            <td><a href=\"https:\/\/matstxab2opgaver.systime.dk\/?id=c1375\" target=\"_blank\" rel=\"noopener noreferrer\">MatAB2stx-6.23<\/a><\/td>\n            <td><a href=\"https:\/\/matstxab2opgaver.systime.dk\/?id=c1370\" target=\"_blank\" rel=\"noopener noreferrer\">MatAB2stx-6.17<\/a><\/td>\n        <\/tr>\n        <tr>\n            <td><a href=\"https:\/\/matstxab2opgaver.systime.dk\/?id=c2782\" target=\"_blank\" rel=\"noopener noreferrer\">MatAB2stx-6.15<\/a><\/td>\n            <td><a href=\"https:\/\/matstxab2opgaver.systime.dk\/?id=c1374\" target=\"_blank\" rel=\"noopener noreferrer\">MatAB2stx-6.20<\/a><\/td>\n            <td><a href=\"https:\/\/matbhtx.systime.dk\/?id=c13774\" target=\"_blank\" rel=\"noopener noreferrer\">MatBhtx-8.64<\/a><\/td>\n        <\/tr>\n        <tr>\n            <td><a href=\"https:\/\/matstxab2opgaver.systime.dk\/?id=c1371\" target=\"_blank\" rel=\"noopener noreferrer\">MatAB2stx-6.18<\/a><\/td>\n            <td><\/td>\n            <td><a href=\"https:\/\/matbhtx.systime.dk\/?id=c13775\" target=\"_blank\" rel=\"noopener noreferrer\">MatBhtx-8.65<\/a><\/td>\n        <\/tr>\n        <tr>\n            <td><a href=\"https:\/\/matstxab2opgaver.systime.dk\/?id=c1372\" target=\"_blank\" rel=\"noopener noreferrer\">MatAB2stx-6.19<\/a><\/td>\n            <td><\/td>\n            <td><\/td>\n        <\/tr>\n        <tr>\n            <td><a href=\"https:\/\/matbhtx.systime.dk\/?id=c13773\" target=\"_blank\" rel=\"noopener noreferrer\">MatBhtx-8.63<\/a><\/td>\n            <td><\/td>\n            <td><\/td>\n        <\/tr>\n        <tr>\n            <td><a href=\"https:\/\/sites.google.com\/view\/matematikopgaverpmtekmatr4\/11-trigonometriske-funktioner\/trigonometriske-grundligninger\/opgave-286\" target=\"_blank\" rel=\"noopener noreferrer\">PM286<\/a><\/td>\n            <td><\/td>\n            <td><\/td>\n        <\/tr>\n        <tr>\n            <td><a href=\"https:\/\/sites.google.com\/view\/matematikopgaverpmtekmatr4\/11-trigonometriske-funktioner\/trigonometriske-grundligninger\/opgave-287\" target=\"_blank\" rel=\"noopener noreferrer\">PM287<\/a><\/td>\n            <td><\/td>\n            <td><\/td>\n        <\/tr>\n    <\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Der er her 4 eksempler hvor der gennemg\u00e5es hvorledes trigonometriske ligninger l\u00f8ses. De er alle med sinusfunktionen, men tilsvarende g\u00f8r sig g\u00e6ldende for cosinusfunktionen. Eksempel 1 Vi ser her p\u00e5 en simpel trigonometrisk ligning nemlig . Eksempel 2 Vi ser her p\u00e5 en igen simpel trigonometrisk ligning,nemlig , men ser p\u00e5 et interval der ligger [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","editor_plus_copied_stylings":"{}","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[3,8],"tags":[17,19,20],"class_list":["post-496","post","type-post","status-publish","format-standard","hentry","category-matematik","category-trigonometriske-funktioner","tag-ligninger","tag-trigonometri","tag-trigonometriske-ligninger"],"featured_image_src":null,"author_info":{"display_name":"Henriksen","author_link":"https:\/\/mxth.dk\/?author=1"},"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/496","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=496"}],"version-history":[{"count":4,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/496\/revisions"}],"predecessor-version":[{"id":3059,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/496\/revisions\/3059"}],"wp:attachment":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=496"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=496"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=496"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}