{"id":8606,"date":"2022-07-10T12:20:24","date_gmt":"2022-07-10T04:20:24","guid":{"rendered":"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental-shape_n_space\/more_about_trigonometry\/sine_and_cosine_formulae-2\/"},"modified":"2023-03-28T13:51:23","modified_gmt":"2023-03-28T05:51:23","slug":"sine_and_cosine_formulae","status":"publish","type":"page","link":"https:\/\/www.study-together.com\/edu\/dse-maths-core\/non_fundamental-shape_n_space\/more_about_trigonometry\/sine_and_cosine_formulae\/","title":{"rendered":"\u6b63\u5f26\u548c\u9918\u5f26\u516c\u5f0f"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"8606\" class=\"elementor elementor-8606\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6e6d9785 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6e6d9785\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-41dc1ba6\" data-id=\"41dc1ba6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-aa1ecbd elementor-widget elementor-widget-text-editor\" data-id=\"aa1ecbd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>14.4 \u7406\u89e3 \u6b63\u5f26\u548c\u9918\u5f26\u516c\u5f0f (Understand the Sine Formula and Cosine Formula)<\/h2><p>\u6b63\u5f26\u548c\u9918\u5f26\u516c\u5f0f (Sine Formula and Cosine Formula) \u53ef\u4ee5\u8a71\u4fc2\u55baDSE\u8ab2\u7a0b\u5605\u4e09\u89d2\u5b78\u5165\u9762\u6700\u4e3b\u8981\u5605\u65b0\u77e5\u8b58\uff0c\u4ea6\u53ef\u4ee5\u8b1b\u8003\u5f97\u6700\u591a\u3002\u53c8\u6216\u8005\u5481\u8a71\uff0c\u5982\u679c\u5514\u8b58\u904b\u7528 \u6b63\u5f26\u548c\u9918\u5f26\u516c\u5f0f \uff0c\u4e09\u89d2\u6bd4\u5605\u61c9\u7528\u984c\u57fa\u672c\u4e0a\u53ef\u4ee5\u9023\u984c\u76ee\u90fd\u5514\u7747\u3002\u6240\u4ee5\u5927\u5bb6\u6700\u597d\u5b78\u8b58\u4f62\u3002<\/p><h3>14.4.1 \u6b63\u5f26\u516c\u5f0f (Sine formula)<\/h3><p>\u5c0d\u65bc\u4efb\u4f55\u4e00\u500b\u4e09\u500b\u5f62\uff0c\u6bcf\u96bb\u89d2\u540c\u4f62\u5c0d\u908a\u5605\u9577\u5ea6\u6bd4\u4fc2\u76f8\u7b49\u5605\uff0c\u5373\uff1a<\/p><p style=\"padding-left: 40px;\">\\(\\dfrac{a}{sin\\angle A}=\\dfrac{b}{sin\\angle B}\\)<\/p><p>\u7559\u610f\uff1a<\/p><ul><li>\u5982\u4e09\u89d2\u5f62\u5605\u4e09\u500b\u9802\u9ede\u70baA\u3001B\u540cC\uff1a<ul><li>\u6211\u54cb\u6703\u53eb\u9802\u9ede\u55f0\u96bb\u89d2\u505a\u00a0 \u2220A\u3001\u2220B \u540c \u2220C<\/li><li>\u9802\u9ede\u5c0d\u4f4f\u689d\u908a\u5605\u9577\u5ea6\u5c31\u53eba\u3001b\u540cc<\/li><\/ul><\/li><li>\u6559\u79d1\u66f8\u6703\u5beb\u57cb \uff0c\u4f46\u5be6\u969b\u8a08\u6578\u6642\uff0c\u6211\u54cb\u53ea\u6703\u7528<br \/>\\(\\dfrac{a}{sin\\angle A}=\\dfrac{b}{sin\\angle B}\\)<br \/>\u569f\u5beb\u51fa\u4e00\u689d\u65b9\u7a0b\u3002\u7136\u5f8c\u53bb\u89e3\u65b9\u8a08\u4e2d\u5605\u672a\u77e5\u6578\u3002<\/li><\/ul><h3>14.4.2 \u9918\u5f26\u516c\u5f0f (Cosine formula)<\/h3><p>\u5c0d\u65bc\u4efb\u4f55\u4e00\u500b\u4e09\u500b\u5f62\uff1a<\/p><p style=\"padding-left: 40px;\">\\(c^{2} = a^{2}+b^{2}-2abcos\\angle C\\)<\/p><p>\u7559\u610f\uff1a<\/p><ul><li>\u5982\u679c\u89ba\u5f97\u689d\u5f0f\u597d\u96e3\u8a18\uff0c\u53ef\u4ee5\u8a66\u5413\u5481\u8a18\uff1a<br \/>c\u908a\u4e8c\u6b21 (\u5373 c<sup>2<\/sup> ) \uff1d\u53e6\u5916\u5169\u689d\u908a\u5605\u4e8c\u6b21\u76f8\u52a0 \uff0d 2 x\u53e6\u5916\u5169\u689d\u908ax cos \u2220C<\/li><li>\u53ea\u8981\u8a18\u5f97\u201c\u908a\u4e00\u689d\u908a\u4fc2\u5de6\u908a\uff0ccos\u5605\u5c31\u4fc2\u76f8\u5c0d\u5605\u89d2\u201d\u5c31\u6703\u6613\u8a18\u5c11\u5c11\u3002<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-490866a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"490866a\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-0379c0c\" data-id=\"0379c0c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-eed70b4 elementor-widget elementor-widget-text-editor\" data-id=\"eed70b4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><i class=\"far fa-arrow-alt-circle-left\" aria-hidden=\"true\"><\/i>\u00a0<a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/non_fundamental-shape_n_space\/more_about_trigonometry\/formula_for_areas_of_trainagles\/\">\u4e09\u89d2\u5f62\u9762\u7a4d\u516c\u5f0f<\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-c578045\" data-id=\"c578045\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-43bf54d\" data-id=\"43bf54d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e2b472c elementor-widget elementor-widget-text-editor\" data-id=\"e2b472c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: right;\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/non_fundamental-shape_n_space\/more_about_trigonometry\/the_herons_formula\/\">\u5e0c\u7f85\u516c\u5f0f<\/a>\u00a0<i class=\"far fa-arrow-alt-circle-right\" aria-hidden=\"true\"><\/i><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-4bfd21bc\" data-id=\"4bfd21bc\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-20775dbc elementor-widget elementor-widget-sidebar\" data-id=\"20775dbc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"sidebar.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"sidebar-box widget-oceanwp-custom-menu custom-menu-widget clr\"><style type=\"text\/css\">.ocean_custom_menu-5 > ul > li > a, .custom-menu-widget .ocean_custom_menu-5 .dropdown-menu .sub-menu li a.menu-link{font-size:16px;line-height:17px;}.custom-menu-widget .ocean_custom_menu-5.oceanwp-custom-menu > ul.click-menu .open-this{font-size:16px;}<\/style><h4 class=\"widget-title\">DSE\u6578\u5b78 &#8211; \u5fc5\u4fee\u90e8\u5206\u3010\u76ee\u9304\u3011<\/h4><div class=\"oceanwp-custom-menu clr ocean_custom_menu-5 left dropdown-hover\"><ul id=\"menu-dsemaths_core\" class=\"dropdown-menu sf-menu\"><li  id=\"menu-item-1744\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1744\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/course-analysis\/\" class=\"menu-link\">\u8ab2\u7a0b\u5206\u6790 (Core)<\/a><\/li>\n<li  id=\"menu-item-1745\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children dropdown menu-item-1745\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/\" class=\"menu-link\">\u5514\u597d\u4ee5\u70ba\u5514\u99db\u8003 &#8211; \u76ee\u9304 <span class=\"nav-arrow fa fa-angle-down\"><\/span><\/a>\n<ul class=\"sub-menu\">\n\t<li  id=\"menu-item-4067\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4067\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/solving-equation\/\" class=\"menu-link\">1. \u89e3\u65b9\u7a0b<\/a><\/li>\n\t<li  id=\"menu-item-4068\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4068\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/polynomials\/\" class=\"menu-link\">2. \u591a\u9805\u5f0f<\/a><\/li>\n\t<li  id=\"menu-item-4069\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4069\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/laws-of-indices\/\" class=\"menu-link\">3. \u6307\u6578\u5b9a\u5f8b<\/a><\/li>\n\t<li  id=\"menu-item-4070\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4070\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/factorization\/\" class=\"menu-link\">4. \u56e0\u5f0f\u5206\u89e3<\/a><\/li>\n\t<li  id=\"menu-item-4071\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4071\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/formulae\/\" class=\"menu-link\">5. \u516c\u5f0f<\/a><\/li>\n\t<li  id=\"menu-item-4072\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4072\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/percentage\/\" class=\"menu-link\">6. \u767e\u5206\u6cd5<\/a><\/li>\n\t<li  id=\"menu-item-4073\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4073\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/rate-and-ratio\/\" class=\"menu-link\">7. \u7387\u53ca\u6bd4<\/a><\/li>\n\t<li  id=\"menu-item-4074\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4074\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/functions\/\" class=\"menu-link\">8. \u51fd\u6578<\/a><\/li>\n\t<li  id=\"menu-item-4075\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4075\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/estimation\/\" class=\"menu-link\">9. \u4f30\u7b97<\/a><\/li>\n\t<li  id=\"menu-item-4076\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4076\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/inequalities\/\" class=\"menu-link\">10. \u4e0d\u7b49\u5f0f<\/a><\/li>\n\t<li  id=\"menu-item-4077\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4077\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/coordinates\/\" class=\"menu-link\">11. \u5750\u6a19<\/a><\/li>\n\t<li  id=\"menu-item-4079\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4079\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/geometry\/\" class=\"menu-link\">12. \u6f14\u7e79\u63a8\u7406\u5e7e\u4f55<\/a><\/li>\n\t<li  id=\"menu-item-4080\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4080\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/trigonometry\/\" class=\"menu-link\">13. \u4e09\u89d2\u6bd4<\/a><\/li>\n\t<li  id=\"menu-item-4081\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4081\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/shapes\/\" class=\"menu-link\">14. \u5e73\u9762\u53ca\u7acb\u9ad4\u5716\u5f62<\/a><\/li>\n\t<li  id=\"menu-item-4082\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4082\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/15-probability\/\" class=\"menu-link\">15. \u6982\u7387<\/a><\/li>\n\t<li  id=\"menu-item-4083\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4083\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/16-statistics\/\" class=\"menu-link\">16. \u7d71\u8a08<\/a><\/li>\n<\/ul>\n<\/li>\n<li  id=\"menu-item-3231\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3231\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental_algebra\/\" class=\"menu-link\">\u57fa\u790e &#8211; \u6578\u8207\u4ee3\u6578<\/a><\/li>\n<li  id=\"menu-item-3241\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3241\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental-shape_n_space\/\" class=\"menu-link\">\u57fa\u790e &#8211; \u5ea6\u91cf\u3001\u5716\u5f62\u8207\u7a7a\u9593<\/a><\/li>\n<li  id=\"menu-item-3246\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3246\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental_data_handling\/\" class=\"menu-link\">\u57fa\u790e &#8211; \u6578\u64da\u8655\u7406<\/a><\/li>\n<li  id=\"menu-item-3290\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3290\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/non_fundamental_algebra\/\" class=\"menu-link\">\u975e\u57fa\u790e &#8211; \u6578\u8207\u4ee3\u6578<\/a><\/li>\n<li  id=\"menu-item-3288\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3288\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/non_fundamental-shape_n_space\/\" class=\"menu-link\">\u975e\u57fa\u790e &#8211; \u5ea6\u91cf\u3001\u5716\u5f62\u8207\u7a7a\u9593<\/a><\/li>\n<li  id=\"menu-item-3289\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3289\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/non_fundamental_data_handling\/\" class=\"menu-link\">\u975e\u57fa\u790e &#8211; \u6578\u64da\u8655\u7406<\/a><\/li>\n<\/ul><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>14.4 \u7406\u89e3 \u6b63\u5f26\u548c\u9918\u5f26\u516c\u5f0f (Understand the Sine Formula and Cosine 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