{"id":4534,"date":"2025-11-02T15:45:59","date_gmt":"2025-11-02T07:45:59","guid":{"rendered":"http:\/\/jhwk.online\/?p=4534"},"modified":"2025-11-04T17:07:09","modified_gmt":"2025-11-04T09:07:09","slug":"%e4%b8%89%e8%a7%92%e5%87%bd%e6%95%b0%e9%a2%98%e7%9b%ae1-2-2-2","status":"publish","type":"post","link":"http:\/\/jhwk.online\/?p=4534","title":{"rendered":"\u4e09\u89d2\u51fd\u6570\u9898\u76ee2-2"},"content":{"rendered":"\n<div class=\"wp-block-stackable-subtitle stk-block-subtitle stk-block stk-8afe3d6\" data-block-id=\"8afe3d6\"><style>.stk-8afe3d6 .stk-block-subtitle__text{font-size:var(--stk--preset--font-size--medium, 20px) !important;color:#0693e3 !important;}@media screen and (max-width:999px){.stk-8afe3d6 .stk-block-subtitle__text{font-size:var(--stk--preset--font-size--medium, 20px) !important;}}<\/style><p class=\"stk-block-subtitle__text stk-subtitle has-text-color\">\u672c\u9898\u75312023\u7ea725\u73ed\u674e\u6dd1\u6674\u8bb2\u89e3\uff01<\/p><\/div>\n\n\n\n<figure class=\"wp-block-video\"><video height=\"1080\" style=\"aspect-ratio: 1554 \/ 1080;\" width=\"1554\" controls src=\"http:\/\/jhwk.online\/wp-content\/uploads\/2025\/11\/\u4e09\u89d2\u9898\u76ee2-2.1.mp4\"><\/video><\/figure>\n\n\n\n<p>[ratemypost]<\/p>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-vivid-cyan-blue-color has-alpha-channel-opacity has-vivid-cyan-blue-background-color has-background is-style-wide\"\/>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-8a052dbd5caa870510f1e594e9e095cf\">\u9898\u76ee\u5c55\u793a\u2014\u2014\u5148\u63a2\u7a76\u3001\u518d\u542c\u8bb2<\/h5>\n\n\n\n<h5>\u9898\u76ee2<\/h5>\n\n\u5728\u9510\u89d2$\\triangle ABC$\u4e2d\uff0c\u89d2$A$\uff0c$B$\uff0c$C$\u6240\u5bf9\u7684\u8fb9\u4e3a$a$\uff0c$b$\uff0c$c$\uff0c\u82e5$\\displaystyle\\frac{\\sin B\\sin C}{3\\sin A} = \\frac{\\cos A}{a} + \\frac{\\cos C}{c}$\u4e14$\\sin^2 A + \\sin^2 B &#8211; \\sin^2 C = \\sin A \\cdot \\sin B$\uff0c\u6c42$\\displaystyle\\frac{c^2}{a + b}$\u7684\u53d6\u503c\u8303\u56f4\u3002\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-text-color has-background has-link-color has-medium-font-size wp-elements-9d0540021c94136dca84d09cf7cfb04a\" style=\"color:#1e4b69;background:linear-gradient(0deg,rgb(230,242,255) 0%,rgb(230,242,255) 16%,rgb(92,175,230) 100%)\">\u89e3\u9898\u63a2\u7a76\u2014\u2014\u70b9\u51fb\u76f4\u8fbe<\/h4>\n\n\n\n<style>\n  .video-jump-btn {\n    cursor: pointer;\n    text-align: left;\n    background-color: #e6f2ff; \/* \u6de1\u84dd\u8272\u80cc\u666f *\/\n    border: none;\n    padding: 8px 12px;\n    border-radius: 4px;\n    transition: all 0.3s ease; \/* \u5e73\u6ed1\u8fc7\u6e21\u52a8\u753b *\/\n    font-size: 16px;\n  }\n  \n  .video-jump-btn:hover {\n    background-color: #cce0ff; \/* \u7565\u6df1\u7684\u84dd\u8272\u80cc\u666f *\/\n    transform: scale(1.02); \/* \u8f7b\u5fae\u653e\u5927\u6548\u679c *\/\n    box-shadow: 0 2px 4px rgba(0,0,0,0.1); \/* \u589e\u52a0\u8f7b\u5fae\u9634\u5f71 *\/\n  }\n<\/style>\n\n<button class=\"video-jump-btn\" onclick=\"document.querySelector('video').currentTime = 0; document.querySelector('video').play();\">\n\u7b2c\u4e00\u6b65\uff1a\u6c42\u51fa\\( C= \\displaystyle\\frac{\\pi}{3} \\)\uff1b\n<\/button>\n\n\n\n<br>\n\n<style>\n  .video-jump-btn {\n    cursor: pointer;\n    text-align: left; \/* \u5de6\u5bf9\u9f50\u6587\u672c *\/\n   \n  }\n<\/style>\n\n<button class=\"video-jump-btn\" onclick=\"document.querySelector('video').currentTime =32; document.querySelector('video').play();\">\n    \u7b2c\u4e8c\u6b65\uff1a\u5f97\u51fa\\( c=2\\sqrt{3} \\);\n\n<\/button>\n\n\n\n<br>\n<style>\n  .video-jump-btn {\n    cursor: pointer;\n    text-align: left; \/* \u5de6\u5bf9\u9f50\u6587\u672c *\/\n   \n  }\n<\/style>\n\n<button class=\"video-jump-btn\" onclick=\"document.querySelector('video').currentTime =114; document.querySelector('video').play();\">\n\n\u7b2c\u4e09\u6b65\uff1a\\( a+b=\\sin (A+\\displaystyle\\frac{\\pi}{6}) \\)\u4e14\\( \\displaystyle\\frac{\\pi}{6} < A <\\displaystyle\\frac{\\pi}{2} \\).\n\n<\/button>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848\u89e3\u6790<\/summary>\n<p>\u89e3: \u2235 $\\sin^2 A + \\sin^2 B &#8211; \\sin^2 C = \\sin A \\sin B$<\/p> <p>\u2234 $a^2 + b^2 &#8211; c^2 = ab,\u2234 \\cos C = \\displaystyle \\frac{a^2 + b^2 &#8211; c^2}{2ab} = \\displaystyle \\frac{1}{2}$<\/p> <p>\u2235 $0 < C < \\displaystyle \\frac{\\pi}{2},\u2234 C = \\displaystyle \\frac{\\pi}{3} \u2234 \\sin C = \\displaystyle \\frac{\\sqrt{3}}{2}$<\/p> <p>\u2235 $\\displaystyle \\frac{\\sin B\\sin C}{3\\sin A} = \\displaystyle \\frac{\\cos A}{a} + \\displaystyle \\frac{\\cos C}{c}$<\/p> <p>\u2234 $\\displaystyle \\frac{\\sqrt{3}}{2} \\cdot \\displaystyle \\frac{b}{3a} = \\displaystyle \\frac{\\sin C\\cos A+\\sin A\\cos C}{\\sin A\\sin C}$<\/p> <p>$= \\displaystyle \\frac{\\sin(A+C)}{\\sin A\\sin C} = \\displaystyle \\frac{\\sin B}{\\sin A\\sin C} = \\displaystyle \\frac{b}{ac}$<\/p> <p>\u2234 $c = 2\\sqrt{3}$<\/p> <p>\u2235 $\\displaystyle \\frac{a}{\\sin A} = \\displaystyle \\frac{b}{\\sin B} = \\displaystyle \\frac{c}{\\sin C} = 4$<\/p> <p>\u2234 $a = 4\\sin A, b = 4\\sin B$<\/p> <p>\u2234 $a + b = 4(\\sin A + \\sin B)$<\/p> <p>$= 4\\left[\\sin A + \\sin\\left(\\displaystyle \\frac{2\\pi}{3} &#8211; A\\right)\\right] = 4\\sqrt{3}\\sin\\left(A + \\displaystyle \\frac{\\pi}{6}\\right)$<\/p> <p>\u2235 $\\begin{cases} 0 < A < \\displaystyle \\frac{\\pi}{2} \\\\ 0 < B = \\displaystyle \\frac{2\\pi}{3} - A < \\displaystyle \\frac{\\pi}{2} \\end{cases} \\Rightarrow \\displaystyle \\frac{\\pi}{6} < A < \\displaystyle \\frac{\\pi}{2}$<\/p> <p>\u2234 $A + \\displaystyle \\frac{\\pi}{6} \\in \\left(\\displaystyle \\frac{\\pi}{3}, \\displaystyle \\frac{2\\pi}{3}\\right)$<\/p> <p>\u2234 $\\sin\\left(A + \\displaystyle \\frac{\\pi}{6}\\right) \\in \\left(\\displaystyle \\frac{\\sqrt{3}}{2}, 1\\right]$<\/p> <p>\u2234 $a + b \\in (6, 4\\sqrt{3}]$<\/p> <p>\u2234 $\\displaystyle \\frac{c^2}{a+b} \\in [\\sqrt{3}, 2)$<\/p>\n<\/details>\n\n\n\n \n","protected":false},"excerpt":{"rendered":"<p>\u672c\u9898\u75312023\u7ea725\u73ed\u674e\u6dd1\u6674\u8bb2\u89e3\uff01 [ratemypost] \u9898\u76ee\u5c55\u793a\u2014\u2014\u5148\u63a2\u7a76\u3001\u518d\u542c\u8bb2 \u9898\u76ee2 \u5728\u9510\u89d2$\\t [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-4534","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/4534","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4534"}],"version-history":[{"count":8,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/4534\/revisions"}],"predecessor-version":[{"id":4602,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/4534\/revisions\/4602"}],"wp:attachment":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4534"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4534"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4534"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}