{"id":2122,"date":"2022-02-22T14:08:52","date_gmt":"2022-02-22T05:08:52","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=2122"},"modified":"2024-07-11T10:10:04","modified_gmt":"2024-07-11T01:10:04","slug":"%e5%8f%82%e8%80%83%ef%bc%9a%e4%b8%89%e8%a7%92%e9%96%a2%e6%95%b0%e3%81%ae%e5%8a%a0%e6%b3%95%e5%ae%9a%e7%90%86%e3%81%ae%e8%a8%bc%e6%98%8e","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6b\/%e4%b8%89%e8%a7%92%e9%96%a2%e6%95%b0%e3%81%ae%e5%be%ae%e5%88%86\/%e5%8f%82%e8%80%83%ef%bc%9a%e4%b8%89%e8%a7%92%e9%96%a2%e6%95%b0%e3%81%ae%e5%8a%a0%e6%b3%95%e5%ae%9a%e7%90%86%e3%81%ae%e8%a8%bc%e6%98%8e\/","title":{"rendered":"\u53c2\u8003\uff1a\u4e09\u89d2\u95a2\u6570\u306e\u52a0\u6cd5\u5b9a\u7406\u306e\u8a3c\u660e"},"content":{"rendered":"<p dir=\"ltr\">2\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u304b\u3089\uff0c\u4e09\u89d2\u95a2\u6570\u306e\u52a0\u6cd5\u5b9a\u7406<br \/>\n$$\\cos(\\alpha + \\beta) = \\cos\\alpha \\cos\\beta -\\sin\\alpha\\sin\\beta$$ \u3092\u8a3c\u660e\u3059\u308b\u3002\u4ed6\u306e\u52a0\u6cd5\u5b9a\u7406 \\(\\sin(\\alpha + \\beta)\\) \u3084 \\(\\tan (\\alpha + \\beta)\\) \u306f\uff0c\u3053\u308c\u3092\u4f7f\u3063\u3066\u793a\u305b\u308b\u3002<\/p>\n<p><!--more--><\/p>\n<hr \/>\n<p dir=\"ltr\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-8504\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Kahoufig1.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<h3 id=\"yui_3_17_2_1_1645506405543_1625\">\u30b3\u30b5\u30a4\u30f3\u306e\u52a0\u6cd5\u5b9a\u7406\u306e\u8a3c\u660e<\/h3>\n<p>\u4e0a\u306e\u56f3\u306e\u3088\u3046\u306b\uff0c\u534a\u5f84 \\(1\\) \u306e\u5186\u5468\u4e0a\u306b\u70b9 \\(A, B\\) \u3092\u7f6e\u304f\u3068\uff0c<\/p>\n<p id=\"yui_3_17_2_1_1645506405543_1690\">$$\\color{blue}\\overrightarrow{OA} \\equiv \\boldsymbol{a} = (a_x, a_y) = (\\cos\\alpha, \\sin\\alpha)$$<\/p>\n<p id=\"yui_3_17_2_1_1645506405543_1691\">$$\\color{red}\\overrightarrow{OB} \\equiv \\boldsymbol{b} = (b_x, b_y) = (\\cos\\beta, -\\sin\\beta)$$<\/p>\n<p id=\"yui_3_17_2_1_1645506405543_1693\" dir=\"ltr\">2\u3064\u306e\u30d9\u30af\u30c8\u30eb \\({\\color{blue}{\\boldsymbol{a}}}, {\\color{red}{\\boldsymbol{b}}}\\) \u306e\u5185\u7a4d\u306f<br id=\"yui_3_17_2_1_1645506405543_1694\" \/>\\begin{eqnarray}<br id=\"yui_3_17_2_1_1645506405543_1695\" \/>{\\color{blue}{\\boldsymbol{a}}}\\cdot {\\color{red}{\\boldsymbol{b}}}&amp;=&amp;<br \/>\n{\\color{blue}{a_x}} \\ {\\color{red}{b_x}} + {\\color{blue}{a_y}} \\ {\\color{red}{b_y}} \\\\<br id=\"yui_3_17_2_1_1645506405543_1696\" \/>&amp;=&amp; {\\color{blue}{\\cos\\alpha}} \\ {\\color{red}{\\cos\\beta}} -{\\color{blue}{\\sin\\alpha}}\\ {\\color{red}{\\sin\\beta}}<br id=\"yui_3_17_2_1_1645506405543_1697\" \/>\\end{eqnarray}<br id=\"yui_3_17_2_1_1645506405543_1698\" \/>\u4e00\u65b9\u3067\u3053\u306e\u5185\u7a4d\u306f2\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u306a\u3059\u89d2 \\(\\theta \\equiv \\alpha+\\beta\\) \u3092\u4f7f\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3082\u66f8\u3051\u308b\u3002 \uff08\u534a\u5f84 \\(1\\) \u306e\u5186\u5468\u4e0a\u3060\u304b\u3089 \\(|{\\color{blue}{\\boldsymbol{a}}}| = |{\\color{red}{\\boldsymbol{b}}}| =1\\) \u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3002\uff09<br id=\"yui_3_17_2_1_1645506405543_1699\" \/>\\begin{eqnarray}<br id=\"yui_3_17_2_1_1645506405543_1700\" \/>{\\color{blue}{\\boldsymbol{a}}}\\cdot {\\color{red}{\\boldsymbol{b}}}&amp;=&amp; |{\\color{blue}{\\boldsymbol{a}}}| |{\\color{red}{\\boldsymbol{b}}}| \\cos\\theta \\\\<br id=\"yui_3_17_2_1_1645506405543_1701\" \/>&amp;=&amp; \\cos(\\alpha + \\beta)<br id=\"yui_3_17_2_1_1645506405543_1702\" \/>\\end{eqnarray}<br id=\"yui_3_17_2_1_1645506405543_1703\" \/>\u3057\u305f\u304c\u3063\u3066<br id=\"yui_3_17_2_1_1645506405543_1704\" \/>$$\\cos(\\alpha + \\beta) = {\\color{blue}{\\cos\\alpha}} \\ {\\color{red}{\\cos\\beta}} -{\\color{blue}{\\sin\\alpha}}\\ {\\color{red}{\\sin\\beta}}$$<\/p>\n<h3 id=\"yui_3_17_2_1_1645506405543_1705\">\u30b5\u30a4\u30f3\u306e\u52a0\u6cd5\u5b9a\u7406\u306e\u8a3c\u660e<\/h3>\n<p id=\"yui_3_17_2_1_1645506405543_1706\" dir=\"ltr\">\\(\\displaystyle \\sin x = \\cos\\left(\\frac{\\pi}{2}-x\\right) \\) \u3092\u4f7f\u3063\u3066\u30b3\u30b5\u30a4\u30f3\u306e\u52a0\u6cd5\u5b9a\u7406\u306b\u306a\u304a\u3059\u3002<\/p>\n<p id=\"yui_3_17_2_1_1645506405543_1708\" dir=\"ltr\">\\begin{eqnarray}<br id=\"yui_3_17_2_1_1645506405543_1709\" \/>\\sin(\\alpha + \\beta) &amp;=&amp; \\cos\\left(\\frac{\\pi}{2} -(\\alpha+\\beta)\\right) \\\\<br id=\"yui_3_17_2_1_1645506405543_1710\" \/>&amp;=&amp; \\cos\\left(\\frac{\\pi}{2}-\\alpha -\\beta\\right) \\\\<br id=\"yui_3_17_2_1_1645506405543_1711\" \/>&amp;=&amp; \\cos\\left(\\frac{\\pi}{2} -\\alpha\\right) \\cos(-\\beta) -\\sin\\left(\\frac{\\pi}{2} -\\alpha\\right) \\sin(-\\beta)\\\\<br id=\"yui_3_17_2_1_1645506405543_1712\" \/>&amp;=&amp; \\sin\\alpha\\cos\\beta + \\cos\\alpha\\sin\\beta<br id=\"yui_3_17_2_1_1645506405543_1713\" \/>\\end{eqnarray}<\/p>\n<h3 id=\"yui_3_17_2_1_1645506405543_1714\">\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u52a0\u6cd5\u5b9a\u7406<\/h3>\n<p>\\(\\displaystyle \\tan(\\alpha + \\beta) = \\frac{\\sin(\\alpha + \\beta)}{\\cos(\\alpha + \\beta)}\\) \u3060\u304b\u3089&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p dir=\"ltr\">2\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u304b\u3089\uff0c\u4e09\u89d2\u95a2\u6570\u306e\u52a0\u6cd5\u5b9a\u7406 $$\\cos(\\alpha + \\beta) = \\cos\\alpha \\cos\\beta -\\sin\\alpha\\sin\\beta$$ \u3092\u8a3c\u660e\u3059\u308b\u3002\u4ed6\u306e\u52a0\u6cd5\u5b9a\u7406 \\(\\sin(\\alpha + \\beta)\\) \u3084 \\(\\tan (\\alpha + \\beta)\\) \u306f\uff0c\u3053\u308c\u3092\u4f7f\u3063\u3066\u793a\u305b\u308b\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6b\/%e4%b8%89%e8%a7%92%e9%96%a2%e6%95%b0%e3%81%ae%e5%be%ae%e5%88%86\/%e5%8f%82%e8%80%83%ef%bc%9a%e4%b8%89%e8%a7%92%e9%96%a2%e6%95%b0%e3%81%ae%e5%8a%a0%e6%b3%95%e5%ae%9a%e7%90%86%e3%81%ae%e8%a8%bc%e6%98%8e\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":2096,"menu_order":40,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-2122","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.10 - aioseo.com -->\n\t<meta name=\"description\" content=\"2\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u304b\u3089\uff0c\u4e09\u89d2\u95a2\u6570\u306e\u52a0\u6cd5\u5b9a\u7406 $$\\cos(\\alpha + \\beta) = \\cos\\al\" \/>\n\t<meta name=\"robots\" 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