{"id":2123,"date":"2023-04-02T09:44:37","date_gmt":"2023-04-02T01:44:37","guid":{"rendered":"https:\/\/www.appblog.cn\/?p=2123"},"modified":"2023-04-05T20:42:22","modified_gmt":"2023-04-05T12:42:22","slug":"fundamentals-of-high-school-mathematics-the-concept-of-angles-and-common-trigonometric-formulas","status":"publish","type":"post","link":"https:\/\/www.appblog.cn\/index.php\/2023\/04\/02\/fundamentals-of-high-school-mathematics-the-concept-of-angles-and-common-trigonometric-formulas\/","title":{"rendered":"\u9ad8\u4e2d\u6570\u5b66\u57fa\u7840\uff1a\u89d2\u7684\u6982\u5ff5\u4e0e\u4e09\u89d2\u5e38\u7528\u516c\u5f0f"},"content":{"rendered":"<h2>\u89d2\u7684\u6982\u5ff5<\/h2>\n<p>\u5728\u6570\u5b66\u548c\u7269\u7406\u4e2d\uff0c\u5f27\u5ea6\u662f\u89d2\u7684\u5ea6\u91cf\u5355\u4f4d\u3002\u5b83\u662f\u7531\u56fd\u9645\u5355\u4f4d\u5236\u5bfc\u51fa\u7684\u5355\u4f4d<\/p>\n<p><!-- more --><\/p>\n<ul>\n<li>\u540c\u4e00\u4e09\u89d2\u5f62\u4e2d\uff0c\u7b49\u8fb9\u5bf9\u7b49\u89d2\uff0c\u7b49\u89d2\u5bf9\u7b49\u8fb9<\/li>\n<li>\u76f4\u89d2\u4e09\u89d2\u5f62\u4e2d\uff0c30\u5ea6\u89d2\u6240\u5bf9\u8fb9\u7b49\u4e8e\u659c\u8fb9\u4e00\u534a<\/li>\n<li>\u76f4\u89d2\u4e09\u89d2\u5f62\u4e2d\uff0c\u659c\u8fb9\u4e2d\u7ebf\u7b49\u4e8e\u659c\u8fb9\u4e00\u534a<\/li>\n<li>\u76f4\u89d2\u4e09\u89d2\u5f62\u4e2d\uff0c\u4e24\u76f4\u89d2\u8fb9\u7684\u5e73\u65b9\u548c\u7b49\u4e8e\u659c\u8fb9\u7684\u5e73\u65b9\uff08\u52fe\u80a1\u5b9a\u7406\uff09<\/li>\n<li>\u7b49\u8170\u4e09\u89d2\u5f62\u4e2d\uff0c\u4e24\u8170\u76f8\u7b49<\/li>\n<li>\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62\u4e2d\uff0c\u4e24\u76f4\u89d2\u8fb9\u76f8\u7b49<\/li>\n<\/ul>\n<h3>\u4efb\u610f\u89d2<\/h3>\n<p>1\u3001\u6b63\u89d2\u3001\u7236\u89d2\u3001\u96f6\u89d2\u3001\u8c61\u9650\u89d2\u7684\u6982\u5ff5<\/p>\n<p>2\u3001\u4e0e\u89d2$\\alpha$\u7ec8\u8fb9\u76f8\u540c\u7684\u89d2\u7684\u96c6\u5408\uff1a$\\{ \\beta | \\beta=\\alpha + 2k\\pi, \\, k \\in Z \\}$<\/p>\n<h3>\u5f27\u5ea6\u5236<\/h3>\n<p>1\u3001\u628a\u957f\u5ea6\u7b49\u4e8e\u534a\u5f84\u957f\u7684\u5f27\u6240\u5bf9\u7684\u5706\u5fc3\u89d2\u53eb\u505a1\u5f27\u5ea6\u7684\u89d2<\/p>\n<p>2\u3001$|\\alpha|=\\frac{l}{r}$<\/p>\n<p>3\u3001\u5f27\u957f\u516c\u5f0f\uff1a$l=\\frac{n\\pi r}{180}=|\\alpha|r$<\/p>\n<p>4\u3001\u6247\u5f62\u9762\u79ef\u516c\u5f0f\uff1a$S=\\frac{n\\pi r^2}{360}=\\frac{1}{2}lr$<\/p>\n<h3>\u4efb\u610f\u89d2\u7684\u4e09\u89d2\u51fd\u6570<\/h3>\n<p>1\u3001\u8bbe$\\alpha$\u662f\u4e00\u4e2a\u4efb\u610f\u89d2\uff0c\u5b83\u7684\u7ec8\u8fb9\u4e0e\u5355\u4f4d\u5706\u4ea4\u4e8e\u70b9$P(x,y)$\uff0c\u90a3\u4e48<\/p>\n<p>$\\sin \\alpha = y$\uff0c$\\cos \\alpha = x$\uff0c$\\tan \\alpha = \\frac{y}{x}$<\/p>\n<p>2\u3001\u8bbe\u70b9$A(x,y)$\u4e3a\u89d2$\\alpha$\u7ec8\u8fb9\u4e0a\u4efb\u610f\u4e00\u70b9\uff0c\u90a3\u4e48\uff1a\uff08\u8bbe$r=\\sqrt{(x^2+y^2)}$\uff09<\/p>\n<p>$\\sin \\alpha = \\frac{y}{r}$\uff0c$\\cos \\alpha = \\frac{x}{r}$\uff0c$\\tan \\alpha = \\frac{y}{x}$\uff0c$\\cot \\alpha = \\frac{x}{y}$<\/p>\n<p>3\u3001\u7279\u6b8a\u89d2\u7684\u4e09\u89d2\u51fd\u6570\u503c<\/p>\n<table>\n<thead>\n<tr>\n<th style=\"text-align: center;\">$\\alpha$<\/th>\n<th style=\"text-align: center;\">0<\/th>\n<th style=\"text-align: center;\">$\\frac{\\pi}{6}$<\/th>\n<th style=\"text-align: center;\">$\\frac{\\pi}{4}$<\/th>\n<th style=\"text-align: center;\">$\\frac{\\pi}{3}$<\/th>\n<th style=\"text-align: center;\">$\\frac{\\pi}{2}$<\/th>\n<th style=\"text-align: center;\">$\\frac{2\\pi}{3}$<\/th>\n<th style=\"text-align: center;\">$\\frac{3\\pi}{4}$<\/th>\n<th style=\"text-align: center;\">$\\frac{5\\pi}{6}$<\/th>\n<th style=\"text-align: center;\">$\\pi$<\/th>\n<th style=\"text-align: center;\">$\\frac{3\\pi}{2}$<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">$\\sin \\alpha$<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">$\\frac{1}{2}$<\/td>\n<td style=\"text-align: center;\">$\\frac{\\sqrt{2}}{2}$<\/td>\n<td style=\"text-align: center;\">$\\frac{\\sqrt{3}}{2}$<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">$\\frac{\\sqrt{3}}{2}$<\/td>\n<td style=\"text-align: center;\">$\\frac{\\sqrt{2}}{2}$<\/td>\n<td style=\"text-align: center;\">$\\frac{1}{2}$<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">-1<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$\\cos \\alpha$<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">$\\frac{\\sqrt{3}}{2}$<\/td>\n<td style=\"text-align: center;\">$\\frac{\\sqrt{2}}{2}$<\/td>\n<td style=\"text-align: center;\">$\\frac{1}{2}$<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">$\\frac{1}{2}$<\/td>\n<td style=\"text-align: center;\">$-\\frac{\\sqrt{2}}{2}$<\/td>\n<td style=\"text-align: center;\">$-\\frac{\\sqrt{3}}{2}$<\/td>\n<td style=\"text-align: center;\">-1<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$\\tan \\alpha$<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">$\\frac{\\sqrt{3}}{3}$<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">$\\sqrt{3}$<\/td>\n<td style=\"text-align: center;\">$+\u221e$<\/td>\n<td style=\"text-align: center;\">$-\\sqrt{3}$<\/td>\n<td style=\"text-align: center;\">-1<\/td>\n<td style=\"text-align: center;\">$-\\frac{\\sqrt{3}}{3}$<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">$-\u221e$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>\u4e09\u89d2\u51fd\u6570\u56fe\u50cf\u4e0e\u6027\u8d28<\/h3>\n<table>\n<thead>\n<tr>\n<th style=\"text-align: left;\">\u6027\u8d28<\/th>\n<th style=\"text-align: left;\">$\\sin x$<\/th>\n<th style=\"text-align: left;\">$\\cos x$<\/th>\n<th style=\"text-align: left;\">$\\tan x$<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: left;\">\u5468\u671f\u6027<\/td>\n<td style=\"text-align: left;\">$T=2\\pi$<\/td>\n<td style=\"text-align: left;\">$T=2\\pi$<\/td>\n<td style=\"text-align: left;\">$T=\\pi$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: left;\">\u5947\u5076\u6027<\/td>\n<td style=\"text-align: left;\">\u5947<\/td>\n<td style=\"text-align: left;\">\u5076<\/td>\n<td style=\"text-align: left;\">\u5947<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: left;\">\u5355\u8c03\u6027<\/td>\n<td style=\"text-align: left;\">\u5728$[2k\\pi-\\pi\/2,2k\\pi+\\pi\/2]$\u4e0a\u5355\u8c03\u9012\u589e <br \/> \u5728$[2k\\pi+\\pi\/2,2k\\pi+3\\pi\/2]$\u4e0a\u5355\u8c03\u9012\u51cf<\/td>\n<td style=\"text-align: left;\">\u5728$[2k\\pi-\\pi,2k\\pi]$\u4e0a\u5355\u8c03\u9012\u589e <br \/> \u5728$[2k\\pi,2k\\pi+\\pi]$\u4e0a\u5355\u8c03\u9012\u51cf<\/td>\n<td style=\"text-align: left;\">\u5728$[k\\pi-\\pi\/2,k\\pi+\\pi\/2]$\u4e0a\u5355\u8c03\u9012\u589e<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: left;\">\u5bf9\u79f0\u6027<\/td>\n<td style=\"text-align: left;\">\u5bf9\u79f0\u8f74\u65b9\u7a0b\uff1a$x=k\\pi+\\pi\/2$ <br \/> \u5bf9\u79f0\u4e2d\u5fc3\uff1a$(k\\pi,0)$<\/td>\n<td style=\"text-align: left;\">\u5bf9\u79f0\u8f74\u65b9\u7a0b\uff1a$x=k\\pi$ <br \/> \u5bf9\u79f0\u4e2d\u5fc3\uff1a$(k\\pi+\\pi\/2,0)$<\/td>\n<td style=\"text-align: left;\">\u65e0\u5bf9\u79f0\u8f74 <br \/> \u5bf9\u79f0\u4e2d\u5fc3\uff1a$(k\\pi\/2,0)$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u4e09\u89d2\u51fd\u6570\u5e38\u7528\u516c\u5f0f<\/h2>\n<h3>\u540c\u89d2\u4e09\u89d2\u51fd\u6570\u7684\u57fa\u672c\u5173\u7cfb<\/h3>\n<p>1\u3001\u5e73\u65b9\u5173\u7cfb\uff1a$\\sin^2 \\alpha + \\cos^2 \\alpha = 1$<\/p>\n<p>2\u3001\u5546\u6570\u5173\u7cfb\uff1a$\\tan \\alpha = \\frac{\\sin \\alpha}{\\cos \\alpha}$<\/p>\n<p>3\u3001\u5012\u6570\u5173\u7cfb\uff1a$\\tan \\alpha \\cot \\alpha = 1$<\/p>\n<h3>\u4e09\u89d2\u51fd\u6570\u8bf1\u5bfc\u516c\u5f0f<\/h3>\n<p>$\\sin (\\alpha + 2k \\pi) = \\sin \\alpha$<br \/>\n$\\cos (\\alpha + 2k \\pi) = \\cos \\alpha$<br \/>\n$\\tan (\\alpha + 2k \\pi) = \\tan \\alpha$<\/p>\n<p>$\\sin (\\pi + \\alpha) = -\\sin \\alpha$<br \/>\n$\\cos (\\pi + \\alpha) = -\\cos \\alpha$<br \/>\n$\\tan (\\pi + \\alpha) = \\tan \\alpha$<\/p>\n<p>$\\sin (\\pi &#8211; \\alpha) = \\sin \\alpha$<br \/>\n$\\cos (\\pi &#8211; \\alpha) = -\\cos \\alpha$<br \/>\n$\\tan (\\pi &#8211; \\alpha) = -\\tan \\alpha$<\/p>\n<p>$\\sin (-\\alpha) = -\\sin \\alpha$<br \/>\n$\\cos (-\\alpha) = \\cos \\alpha$<br \/>\n$\\tan (-\\alpha) = -\\tan \\alpha$<\/p>\n<p>$\\sin (\\frac{\\pi}{2}-\\alpha) = \\cos \\alpha$<br \/>\n$\\cos (\\frac{\\pi}{2}-\\alpha) = \\sin \\alpha$<\/p>\n<p>$\\sin (\\frac{\\pi}{2}+\\alpha) = \\cos \\alpha$<br \/>\n$\\cos (\\frac{\\pi}{2}+\\alpha) = -\\sin \\alpha$<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u89d2\u7684\u6982\u5ff5 \u5728\u6570\u5b66\u548c\u7269\u7406\u4e2d\uff0c\u5f27\u5ea6\u662f\u89d2\u7684\u5ea6\u91cf\u5355\u4f4d\u3002\u5b83\u662f\u7531\u56fd\u9645\u5355\u4f4d\u5236\u5bfc\u51fa\u7684\u5355\u4f4d \u540c\u4e00\u4e09\u89d2\u5f62\u4e2d\uff0c\u7b49\u8fb9\u5bf9\u7b49\u89d2\uff0c\u7b49\u89d2\u5bf9\u7b49\u8fb9 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[509],"tags":[],"class_list":["post-2123","post","type-post","status-publish","format-standard","hentry","category-mathematics-fundamentals"],"_links":{"self":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts\/2123","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/comments?post=2123"}],"version-history":[{"count":0,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts\/2123\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/media?parent=2123"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/categories?post=2123"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/tags?post=2123"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}