{"id":1766,"date":"2026-04-16T16:22:23","date_gmt":"2026-04-16T08:22:23","guid":{"rendered":"https:\/\/www.math.ntnu.edu.tw\/merc\/?page_id=1766"},"modified":"2026-04-21T12:10:18","modified_gmt":"2026-04-21T04:10:18","slug":"%e5%87%bd%e6%95%b8%e5%9c%96%e5%bd%a2%e7%9a%84%e4%bc%b8%e7%a7%bb%e5%b9%b3%e7%a7%bb%e6%ac%a1%e5%ba%8f","status":"publish","type":"page","link":"https:\/\/www.math.ntnu.edu.tw\/merc\/animated_math\/%e5%87%bd%e6%95%b8%e5%9c%96%e5%bd%a2%e7%9a%84%e4%bc%b8%e7%a7%bb%e5%b9%b3%e7%a7%bb%e6%ac%a1%e5%ba%8f\/","title":{"rendered":"\u51fd\u6578\u5716\u5f62\u7684\u4f38\u79fb\u5e73\u79fb\u6b21\u5e8f"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1766\" class=\"elementor elementor-1766\">\n\t\t\t\t<div class=\"elementor-element elementor-element-24fafdd3 e-flex e-con-boxed e-con e-parent\" data-id=\"24fafdd3\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1d925c2b elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"1d925c2b\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;bounceIn&quot;}\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">\u821e\u52d5\u6578\u5b78<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-612982ab e-flex e-con-boxed e-con e-parent\" data-id=\"612982ab\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-6710414 elementor-widget elementor-widget-heading\" data-id=\"6710414\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">\u51fd\u6578\u5716\u5f62\u7684\u4f38\u79fb\u5e73\u79fb\u6b21\u5e8f<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-3f4955ac e-flex e-con-boxed e-con e-parent\" data-id=\"3f4955ac\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5e910c42 elementor-widget elementor-widget-video\" data-id=\"5e910c42\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;video_type&quot;:&quot;hosted&quot;,&quot;autoplay&quot;:&quot;yes&quot;,&quot;loop&quot;:&quot;yes&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"e-hosted-video elementor-wrapper elementor-open-inline\">\n\t\t\t\t\t<video class=\"elementor-video\" src=\"https:\/\/cantor.math.ntnu.edu.tw\/workshop\/animated_math\/media\/\u51fd\u6578\u5716\u5f62\u7684\u4f38\u79fb\u5e73\u79fb\u6b21\u5e8f.mp4\" autoplay=\"\" loop=\"\" controls=\"\" controlsList=\"nodownload\"><\/video>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-1ae8751d e-flex e-con-boxed e-con e-parent\" data-id=\"1ae8751d\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5eaa28ff elementor-widget elementor-widget-text-editor\" data-id=\"5eaa28ff\" 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>\u8a31\u591a\u4eba\u5728\u8655\u7406\u51fd\u6578\u5716\u5f62\u7684\u4f38\u5c55\u3001\u58d3\u7e2e\u8207\u5e73\u79fb\u6642\uff0c\u5e38\u6703\u8aa4\u4ee5\u70ba\u9806\u5e8f\u4e26\u4e0d\u91cd\u8981\uff0c\u4f46\u5f71\u7247\u900f\u904e\u5be6\u969b\u7684\u6578\u5b78\u63a8\u5c0e\u8207\u8996\u89ba\u5316\u5716\u5f62\u8b49\u660e\uff0c**\u300c\u5148\u58d3\u7e2e\u518d\u5e73\u79fb\u300d\u8207\u300c\u5148\u5e73\u79fb\u518d\u58d3\u7e2e\u300d**\u6703\u5c0e\u81f4\u5b8c\u5168\u4e0d\u540c\u7684\u7d50\u679c \u3002<\/p>\n<ul>\n    <li>\u5169\u5927\u8b8a\u63db\u8def\u5f91\u7684\u5c0d\u6bd4\uff1a\u5f71\u7247\u4ee5\u6b63\u5f26\u51fd\u6578 $y = \\sin x$ \u70ba\u4f8b\uff0c\u5c55\u793a\u4e86\u5169\u7a2e\u4e0d\u540c\u7684\u8b8a\u63db\u908f\u8f2f \uff1a\n        <ol>\n            <li>\u8def\u5f91\u4e00\uff08\u5148\u58d3\u7e2e\u5f8c\u5e73\u79fb\uff09\uff1a\u5148\u5c07 $x$ \u8b8a\u70ba $2x$\uff08\u6c34\u5e73\u58d3\u7e2e\u4e00\u500d\uff09\uff0c\u518d\u5411\u53f3\u5e73\u79fb $\\frac{\\pi}{6}$ \u55ae\u4f4d\uff0c\u6700\u7d42\u51fd\u6578\u70ba $y = \\sin 2(x &#8211; \\frac{\\pi}{6})$ \u3002<\/li>\n            <li>\u8def\u5f91\u4e8c\uff08\u5148\u5e73\u79fb\u5f8c\u58d3\u7e2e\uff09\uff1a\u5148\u5411\u53f3\u5e73\u79fb $\\frac{\\pi}{6}$ \u55ae\u4f4d\uff0c\u518d\u5c07 $x$ \u8b8a\u70ba $2x$\uff0c\u6700\u7d42\u51fd\u6578\u8b8a\u70ba $y = \\sin (2x &#8211; \\frac{\\pi}{6})$ \u3002<\/li>\n        <\/ol>\n    <\/li>\n    <li>\u95dc\u9375\u9ede\u7684\u4f4d\u79fb\u5dee\u7570\uff1a\u900f\u904e\u8ffd\u8e64\u539f\u9ede $(0,0)$ \u7684\u8b8a\u5316\uff0c\u6211\u5011\u53ef\u4ee5\u6e05\u695a\u770b\u5230\u6b21\u5e8f\u7684\u5f71\u97ff \uff1a\n        <ol>\n            <li>\u5148\u58d3\u7e2e\u518d\u5e73\u79fb\u6642\uff0c\u57fa\u6e96\u9ede\u6700\u7d42\u5230\u9054 $(\\frac{\\pi}{6}, 0)$ \u3002<\/li>\n            <li>\u5148\u5e73\u79fb\u518d\u58d3\u7e2e\u6642\uff0c\u57fa\u6e96\u9ede\u5247\u6703\u56e0\u70ba\u5f8c\u7e8c\u7684\u58d3\u7e2e\u800c\u7e2e\u6e1b\u4e00\u534a\uff0c\u6700\u7d42\u505c\u5728 $(\\frac{\\pi}{12}, 0)$ \u3002<\/li>\n        <\/ol>\n    <\/li>\n    <li>\u7d50\u8ad6\u8207\u63d0\u9192\uff1a\u5f71\u7247\u5f37\u8abf $\\sin 2(x &#8211; \\frac{\\pi}{6})$ \u4e26\u4e0d\u7b49\u65bc $\\sin (2x &#8211; \\frac{\\pi}{6})$ \u3002\u5728\u8655\u7406\u51fd\u6578\u8b8a\u63db\u6642\uff0c\u5fc5\u9808\u8a18\u4f4f\u6bcf\u4e00\u6b21\u8b8a\u63db\u90fd\u6703\u5f71\u97ff\u5f8c\u7e8c\u64cd\u4f5c\u7684\u57fa\u6e96\u9ede\uff0c\u56e0\u6b64\u6e96\u78ba\u638c\u63e1\u904b\u7b97\u9806\u5e8f\u81f3\u95dc\u91cd\u8981 \u3002<\/li>\n<\/ul>\n<p>\u9019\u662f\u4e00\u90e8\u975e\u5e38\u9069\u5408\u7528\u4f86\u91d0\u6e05\u51fd\u6578\u5e73\u79fb\u4f38\u7e2e\u89c0\u5ff5\u7684\u77ed\u7247\uff0c\u80fd\u5e6b\u52a9\u4f60\u5728\u9762\u5c0d\u8907\u96dc\u51fd\u6578\u8b8a\u63db\u6642\uff0c\u4e0d\u518d\u6389\u9032\u9806\u5e8f\u6df7\u6dc6\u7684\u9677\u9631\u88e1\uff01<\/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\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-5e6d21d7 e-flex e-con-boxed e-con e-parent\" data-id=\"5e6d21d7\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5b603b8c elementor-widget elementor-widget-text-editor\" data-id=\"5b603b8c\" 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<hr style=\"margin-bottom: 10px;\" \/>\n\n<a style=\"font-size: 32; color: red;\" href=\"https:\/\/www.math.ntnu.edu.tw\/workshop\/animated_math\/media\/\u51fd\u6578\u5716\u5f62\u7684\u4f38\u79fb\u5e73\u79fb\u6b21\u5e8f\u5b78\u7fd2\u55ae.pdf\" target=\"_blank\" rel=\"noopener\">\u5b78\u7fd2\u55ae\uff1a\u51fd\u6578\u5716\u5f62\u7684\u4f38\u79fb\u5e73\u79fb\u6b21\u5e8f<\/a>\n\n<hr style=\"margin-bottom: 10px;\" \/>\n<p style=\"color: #306f7f;\">\n\u5f71\u7247\u69cb\u60f3\uff1a\u8607\u9e97\u654f<br>\n\u88fd\u4f5c\u4eba\uff1a\u6797\u5b87\u661f<br>\n\u5b78\u7fd2\u55ae\uff1a\u8607\u9e97\u654f<\/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\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>\u821e\u52d5\u6578\u5b78 \u51fd\u6578\u5716\u5f62\u7684\u4f38\u79fb\u5e73\u79fb\u6b21\u5e8f https:\/\/cantor.math.ntnu.edu.tw\/worksh [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":193,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"ocean_post_layout":"full-width","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"0","ocean_second_sidebar":"0","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"0","ocean_custom_header_template":"0","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"0","ocean_menu_typo_font_family":"0","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"0","footnotes":""},"class_list":["post-1766","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages\/1766","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/comments?post=1766"}],"version-history":[{"count":7,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages\/1766\/revisions"}],"predecessor-version":[{"id":1795,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages\/1766\/revisions\/1795"}],"up":[{"embeddable":true,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages\/193"}],"wp:attachment":[{"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/media?parent=1766"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}