{"id":1286,"date":"2022-03-29T10:37:26","date_gmt":"2022-03-29T08:37:26","guid":{"rendered":"https:\/\/mxth.dk\/?p=1286"},"modified":"2022-04-09T01:06:57","modified_gmt":"2022-04-08T23:06:57","slug":"cosinusrelationerne","status":"publish","type":"post","link":"https:\/\/mxth.dk\/?p=1286","title":{"rendered":"Cosinusrelationerne"},"content":{"rendered":"\n<p class=\" eplus-wrapper\">Der vil v\u00e6re tilf\u00e6lde, hvor vi ikke kan benytte sinusrelationerne. Vi har derfor brug for endnu en relation og dette er cosinusrelationerne. I mods\u00e6tningen til sinusrelationerne som kan gives som en enkelt formel s\u00e5 er cosinusrelationerne et s\u00e6t af tre formler, som ser s\u00e5ledes ud.<\/p>\n\n\n\n<p class=\"has-text-align-center eplus-wrapper\">$\\small a^2=b^2+c^2-2\\cdot b\\cdot c\\cdot \\cos(A)$<\/p>\n\n\n\n<p class=\"has-text-align-center eplus-wrapper\">$\\small b^2=a^2+c^2-2\\cdot a\\cdot c\\cdot \\cos(B)$<\/p>\n\n\n\n<p class=\"has-text-align-center eplus-wrapper\">$\\small c^2=a^2+b^2-2\\cdot a\\cdot b\\cdot \\cos(C)$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">I videoen herunder gennemg\u00e5es <strong>beviset for cosinusrelationerne<\/strong>.<\/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\/39c-UsVgsyA?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<style>\n    table, th, td {\n      border: 1px solid black;\n      border-collapse: collapse;\n    }\n    <\/style>\n    <table width=\"100%\" border=\"1\">\n        <thead>\n            <tr>\n                <th scope=\"col\" width=\"33%\" bgcolor=\"#3CB371\">Gr\u00f8n<\/th>\n                <th scope=\"col\" width=\"33%\" bgcolor=\"#FFA500\">Gul<\/th>\n                <th scope=\"col\" width=\"33%\" bgcolor=\"#DC143C\">R\u00f8d<\/th>\n            <\/tr>\n        <\/thead>\n            <tbody>\n            <tr>\n                <td>\n                    <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-hf-mat-c\/trigonometri-2?authuser=0#h.4jylpvz6hth\" target=\"_blank\" rel=\"noopener\"><\/a>HF-C 661<\/p>\n                <\/td>\n                <td>\n                    <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-hf-mat-c\/trigonometri-2?authuser=0#h.glkmlnqgh1el\" target=\"_blank\" rel=\"noopener\">HF-C 662<\/a><\/p>\n                <\/td>\n                <td>\n                    <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-hf-mat-c\/trigonometri-2?authuser=0#h.f97fgcgq4ylp\" target=\"_blank\" rel=\"noopener\">HF-C 667<\/a><\/p>\n                <\/td>\n            <\/tr>\n            \n            <tr>\n                <td>\n                    <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-hf-mat-c\/trigonometri-2?authuser=0#h.4jylpvz6hth\" target=\"_blank\" rel=\"noopener\"><\/a>HF-C 663<\/p>\n                <\/td>\n                <td>\n                    <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-hf-mat-c\/trigonometri-2?authuser=0#h.vxpqzb7gvvg1\" target=\"_blank\" rel=\"noopener\">HF-C 668<\/a><\/p>\n                <\/td>\n                <td>\n                    <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-mat-ab1-stx\/klassisk-geometri?authuser=0#h.idaip69xh7et\" target=\"_blank\" rel=\"noopener\">StxAB1 10.03<\/a><\/p>\n                <\/td>\n            <\/tr>\n            \n            <tr>\n                <td>\n                    <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaverpmtekmatr4\/4-trigonometri\/cosinusrelationen\/opgave-106\" target=\"_blank\" rel=\"noopener\"><\/a>PM-106<\/p>\n                <\/td>\n                <td>\n                    <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-hf-mat-c\/trigonometri-2?authuser=0#h.bjprqcavwzcj\" target=\"_blank\" rel=\"noopener\">HF-C 669<\/a><\/p>\n                <\/td>\n                <td>\n                    <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-mat-ab1-stx\/klassisk-geometri?authuser=0#h.b0laqy4e8lyi\" target=\"_blank\" rel=\"noopener\">StxAB1 10.04<\/a><\/p>\n                <\/td>\n            <\/tr>\n            \n            <tr>\n                <td>\n                    <p><a href=\"https:\/\/mxth.dk\/?page_id=331#TCR001\" target=\"_blank\" rel=\"noopener\">TCR001<\/a><\/p>\n                <\/td>\n                <td>\n                    <p><a href=\"https:\/\/mxth.dk\/?page_id=331#TCR007\" target=\"_blank\" rel=\"noopener\">TCR007<\/a><\/p>\n                <\/td>\n                <td>\n                    <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-mat-ab1-stx\/klassisk-geometri?authuser=0#h.ovn1dxsjjtyc\" target=\"_blank\" rel=\"noopener\">StxAB1 10.05<\/a><\/p>\n                <\/td>\n            <\/tr>\n            \n            <tr>\n                <td>\n                    <p><a href=\"https:\/\/mxth.dk\/?page_id=331#TCR002\" target=\"_blank\" rel=\"noopener\">TCR002<\/a><\/p>\n                <\/td>\n                <td>\n                    <p><a href=\"https:\/\/mxth.dk\/?page_id=331#TCR008\" target=\"_blank\" rel=\"noopener\">TCR008<\/a><\/p>\n                <\/td>\n                <td>\n                    <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-mat-ab1-stx\/klassisk-geometri?authuser=0#h.gpdwzzuxteqh\" target=\"_blank\" rel=\"noopener\">StxAB1 10.09<\/a><\/p>\n                <\/td>\n            <\/tr>\n            \n            <tr>\n                <td>\n                    <p><a href=\"https:\/\/mxth.dk\/?page_id=331#TCR003\" target=\"_blank\" rel=\"noopener\">TCR003<\/a><\/p>\n                <\/td>\n                <td>\n                    <p><a href=\"https:\/\/mxth.dk\/?page_id=331#TCR009\" target=\"_blank\" rel=\"noopener\">TCR009<\/a><\/p>\n                <\/td>\n                <td>\n                    <p><a href=\"https:\/\/mxth.dk\/?page_id=331#TCR014\" target=\"_blank\" rel=\"noopener\">TCR014<\/a><\/p>\n                <\/td>\n            <\/tr>\n            \n            <tr>\n                <td>\n                    <p><a href=\"https:\/\/mxth.dk\/?page_id=331#TCR004\" target=\"_blank\" rel=\"noopener\">TCR004<\/a><\/p>\n                <\/td>\n                <td>\n                    <p><a href=\"https:\/\/mxth.dk\/?page_id=331#TCR010\" target=\"_blank\" rel=\"noopener\">TCR010<\/a><\/p>\n                <\/td>\n                <td>\n                    <p><a href=\"https:\/\/mxth.dk\/?page_id=331#TCR015\" target=\"_blank\" rel=\"noopener\">TCR015<\/a><\/p>\n                <\/td>\n            <\/tr>\n            \n            <tr>\n                <td>\n                    <p><a href=\"https:\/\/mxth.dk\/?page_id=331#TCR005\" target=\"_blank\" rel=\"noopener\">TCR005<\/a><\/p>\n                <\/td>\n                <td>\n                    <p><a href=\"https:\/\/mxth.dk\/?page_id=331#TCR011\" target=\"_blank\" rel=\"noopener\">TCR011<\/a><\/p>\n                <\/td>\n                <td><\/td>\n            <\/tr>\n            \n            <tr>\n                <td>\n                    <p><a href=\"https:\/\/mxth.dk\/?page_id=331#TCR006\" target=\"_blank\" rel=\"noopener\">TCR006<\/a><\/p>\n                <\/td>\n                <td>\n                    <p><a href=\"https:\/\/mxth.dk\/?page_id=331#TCR012\" target=\"_blank\" rel=\"noopener\">TCR012<\/a><\/p>\n                <\/td>\n                <td><\/td>\n            <\/tr>\n            \n            <tr>\n                <td><\/td>\n                <td>\n                    <p><a href=\"https:\/\/mxth.dk\/?page_id=331#TCR013\" target=\"_blank\" rel=\"noopener\">TCR013<\/a><\/p>\n                <\/td>\n                <td><\/td>\n            <\/tr>\n        <\/tbody>\n    <\/table>\n","protected":false},"excerpt":{"rendered":"<p>Der vil v\u00e6re tilf\u00e6lde, hvor vi ikke kan benytte sinusrelationerne. Vi har derfor brug for endnu en relation og dette er cosinusrelationerne, hvilke vi ser p\u00e5 her.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","editor_plus_copied_stylings":"{}","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[3,32],"tags":[],"class_list":["post-1286","post","type-post","status-publish","format-standard","hentry","category-matematik","category-trigonometri"],"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\/1286","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=1286"}],"version-history":[{"count":5,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/1286\/revisions"}],"predecessor-version":[{"id":1616,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/1286\/revisions\/1616"}],"wp:attachment":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1286"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1286"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1286"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}