{"id":8593,"date":"2024-01-22T19:37:32","date_gmt":"2024-01-22T11:37:32","guid":{"rendered":"http:\/\/www.aiersheng.cc\/?p=8593"},"modified":"2024-07-31T11:32:55","modified_gmt":"2024-07-31T03:32:55","slug":"%e4%b8%89%e8%a7%92%e5%87%bd%e6%95%b0","status":"publish","type":"post","link":"https:\/\/www.aiersheng.cc\/?p=8593","title":{"rendered":"\u4e09\u89d2\u51fd\u6570"},"content":{"rendered":"

\u4e09\u89d2\u51fd\u6570<\/p>\n

 <\/p>\n

\u89d2\u7684\u5206\u7c7b<\/p>\n

    \n
  1. \u6b63\u89d2\uff1a\u6309\u9006\u65f6\u9488\u65b9\u5411\u65cb\u8f6c\u5f62\u6210\u7684\u89d2<\/li>\n
  2. \u8d1f\u89d2\uff1a\u6309\u987a\u65f6\u9488\u65b9\u5411\u65cb\u8f6c\u5f62\u6210\u7684\u89d2<\/li>\n
  3. \u96f6\u89d2\uff1a\u6ca1\u6709\u65cb\u8f6c\u7684\u89d2<\/li>\n<\/ol>\n

    \u8c61\u9650\u89d2\u4e0e\u8f74\u7ebf\u89d2<\/p>\n

    \u8c61\u9650\u89d2\uff1a\u5728\u8c61\u9650\u5185\u7684\u89d2<\/p>\n

    \u8f74\u7ebf\u89d2\uff1a\u5728\u5750\u6807\u8f74\u4e0a\u7684\u89d2<\/p>\n

    \u7ec8\u8fb9\u76f8\u540c\u7684\u89d2<\/p>\n

    \u4e0e\u89d2a\u7ec8\u8fb9\u76f8\u540c\u7684\u89d2\uff1a{P<\/i><\/em>\u00a0<\/i><\/em>\u2223P<\/i><\/em>\u00a0<\/i><\/em>=\u00a0a <\/i><\/em>+\u00a0360\u00b0\u00a0\u2217\u00a0k<\/i><\/em>,k<\/i><\/em>\u00a0<\/i><\/em>\u2208\u00a0Z<\/i><\/em>}<\/p>\n

    \u7ec8\u8fb9\u5728x\u8f74\u4e0a\u7684\u89d2\u7684\u96c6\u5408\uff1a{a<\/i><\/em>\u2223a <\/i><\/em>=\u00a0k <\/i><\/em>\u2217\u00a0180\u00b0\u00a0,k<\/i><\/em>\u00a0<\/i><\/em>\u2208\u00a0Z<\/i><\/em>}<\/p>\n

    \u7ec8\u8fb9\u5728y\u8f74\u4e0a\u7684\u89d2\uff1a{a<\/i><\/em>\u2223a <\/i><\/em>=\u00a090\u00b0\u00a0+\u00a0180\u00b0\u00a0\u2217\u00a0k<\/i><\/em>,k<\/i><\/em>\u00a0<\/i><\/em>\u2208\u00a0Z<\/i><\/em>}<\/p>\n

    \u7ec8\u8fb9\u5728\u5750\u6807\u8f74\u4e0a\u7684\u89d2\uff1a{a<\/i><\/em>\u2223a <\/i><\/em>=\u00a0k <\/i><\/em>\u2217\u00a090\u00b0\u00a0,k<\/i><\/em>\u00a0<\/i><\/em>\u2208\u00a0Z<\/i><\/em>}<\/p>\n

    \u5f27\u5ea6\u4e0e\u89d2\u5ea6\u7684\u8f6c\u6362<\/p>\n

      \n
    1. \u00a02\u03a0=360\u00b0\u00a0,\u00a0\u00a0\u03a0\u00a0=\u00a0180\u00b0<\/li>\n
    2. 1\u00b0\u00a0=\u00a0\u00a00.01745\u00a0rad<\/i><\/em>.<\/li>\n
    3. 1rad<\/i><\/em>\u00a0<\/i><\/em>=\u00a0<\/li>\n<\/ol>\n

      \u5f27\u957f\u4e0e\u6247\u5f62\u9762\u79ef\u8ba1\u7b97\u516c\u5f0f<\/p>\n

       <\/p>\n

       <\/p>\n

      \u5f27\u957f\uff1al<\/i><\/em>\u00a0<\/i><\/em>=\u00a0\u2223a<\/i><\/em>\u2223\u00a0\u2217\u00a0r<\/i><\/em>\u00a0<\/i><\/em>;\u00a0\u6247\u5f62\u9762\u79ef\uff1aS<\/i><\/em>\u00a0<\/i><\/em>=<\/p>\n

      l <\/i><\/em>\u2217\u00a0r<\/i><\/em>\u00a0<\/i><\/em>=<\/p>\n

      \u2223a<\/i><\/em>\u2223\u00a0\u2217\u00a0r<\/i><\/em>2<\/p>\n

       <\/p>\n

      \u4e09\u89d2\u51fd\u6570\u7684\u5b9a\u4e49<\/p>\n

       <\/p>\n

       <\/p>\n\n\n\n
      \n

      sina <\/i><\/em>=<\/p>\n

      tana <\/i><\/em>=<\/p>\n<\/td>\n

      		\n

      y<\/i><\/u><\/em>\u00a0<\/i><\/em>\u00a0x<\/i><\/em><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \u5176\u4e2dr<\/i><\/em>\u00a0<\/i><\/em>=<\/p>\n

      ;cosa<\/i><\/em>\u00a0<\/i><\/em>=\u00a0x<\/i><\/u><\/em><\/p>\n

      ;cota<\/i><\/em>\u00a0<\/i><\/em>=\u00a0<\/p>\n

      x<\/i><\/em>2\u00a0+\u00a0y<\/i><\/em>2<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      \u7279\u6b8a\u89d2\u7684\u4e09\u89d2\u51fd\u6570\u503c<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      \u5404\u8c61\u9650\u7684\u4e09\u89d2\u51fd\u6570\u6570\u503c\u7684\u7b26\u53f7<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      \u540c\u89d2\u7684\u4e09\u89d2\u51fd\u6570\u57fa\u672c\u5173\u7cfb\u5f0f<\/p>\n

      \u5e73\u65b9\u5173\u7cfb\uff1asin<\/i><\/em>2a <\/i><\/em>+\u00a0cos<\/i><\/em>2a <\/i><\/em>=\u00a01\uff0c<\/p>\n

      \u5546\u6570\u5173\u7cfb\uff1atana<\/i><\/em>\u00a0<\/i><\/em>= cosa(sina)\u00a0<\/i><\/em>,<\/p>\n

      \u5012\u6570\u5173\u7cfb\uff1atana<\/i><\/em><\/p>\n

       <\/p>\n

      \u8bf1\u5bfc\u516c\u5f0f\uff1a<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      \u4e24\u89d2\u548c\u5dee\u516c\u5f0f<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      \u4e8c\u500d\u89d2\u516c\u5f0f<\/p>\n

       <\/p>\n

       <\/p>\n

      sin<\/i><\/em>(a <\/i><\/em>\u00b1\u00a0b<\/i><\/em>)\u00a0=\u00a0sina <\/i><\/em>\u2217\u00a0cosb <\/i><\/em>\u00b1\u00a0cosa <\/i><\/em>\u2217\u00a0sinb<\/i><\/em><\/p>\n

      cos<\/i><\/em>(a <\/i><\/em>+\u00a0b<\/i><\/em>)\u00a0=\u00a0cosa <\/i><\/em>\u2217\u00a0cosb <\/i><\/em>\u2212\u00a0sina <\/i><\/em>\u2217\u00a0sinb<\/i><\/em><\/p>\n

      cos<\/i><\/em>(a <\/i><\/em>\u2212\u00a0b<\/i><\/em>)\u00a0=\u00a0cosa <\/i><\/em>\u2217\u00a0cosb <\/i><\/em>+\u00a0sina <\/i><\/em>\u2217\u00a0sinb<\/i><\/em><\/p>\n

      tan<\/i><\/em>(a <\/i><\/em>+\u00a0b<\/i><\/em>)\u00a0= 1\u00a0\u2212\u00a0tana<\/i><\/em>\u00a0<\/i><\/em>\u2217\u00a0tanb<\/i><\/em><\/p>\n

      tan<\/i><\/em>(a <\/i><\/em>\u2212\u00a0b<\/i><\/em>)\u00a0= 1\u00a0tana(na \u2212)\u00a0<\/i><\/em>tan(anb)b<\/i><\/em><\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      2 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02<\/p>\n

       <\/p>\n

      \u4f59\u5f26\uff1acos<\/i><\/em>2a <\/i><\/em>=\u00a0cos<\/i><\/em>2a <\/i><\/em>\u2212\u00a0sin<\/i><\/em>2a <\/i><\/em>=\u00a02cos<\/i><\/em>2a <\/i><\/em>\u2212\u00a01\u00a0=\u00a01\u00a0\u2212\u00a02sin<\/i><\/em>2a<\/i><\/em>\u00a0<\/i><\/em>\u6b63\u5f26\uff1asin<\/i><\/em>2a <\/i><\/em>=\u00a02sinacosa<\/i><\/em>\u27a1\u00a0sinacosa<\/i><\/em>\u00a0<\/i><\/em>=\u00a0sin<\/i><\/em>2a<\/i><\/em><\/p>\n

      \u6b63\u5207\uff1atan<\/i><\/em>2a <\/i><\/em>= 1\u00a0t(a)an(na)2a<\/i><\/em>\u00a0<\/i><\/em>\u27a1\u00a01\u00a0ta(an)n(a)2a<\/i><\/em>\u00a0<\/i><\/em>= 2(1)tan<\/i><\/em>2a<\/i><\/em><\/p>\n

      \u4e8c\u500d\u89d2\u7684\u53d8\u5f62\u516c\u5f0f<\/p>\n

      sin<\/i><\/em>2a <\/i><\/em>=\u00a0\u00a0,cos<\/i><\/em>2a<\/i><\/em>\u00a0<\/i><\/em>=\u00a0<\/p>\n

      1\u00a0+\u00a0sin<\/i><\/em>2a <\/i><\/em>=\u00a0(sina <\/i><\/em>+\u00a0cosa<\/i><\/em>)2\u00a0,\u00a01\u00a0\u2212\u00a0sin<\/i><\/em>2a <\/i><\/em>=\u00a0(sina <\/i><\/em>\u2212\u00a0cosa<\/i><\/em>)2<\/p>\n

      \u8f85\u52a9\u89d2\u516c\u5f0f<\/p>\n

      asina <\/i><\/em>\u00b1\u00a0bcosa<\/i><\/em>\u00a0<\/i><\/em>=\u00a0\u00a0a<\/i><\/em>2 +\u00a0b<\/i><\/em>2\u00a0(sina <\/i><\/em>\u2217\u00a0\u00a0\u00b1\u00a0cosa <\/i><\/em>\u2217\u00a0)\u00a0==\u00a0\u00a0a<\/i><\/em>2 +\u00a0b<\/i><\/em>2\u00a0(sina <\/i><\/em>\u2217\u00a0cos\u03b8 <\/i><\/em>\u00b1\u00a0cosa <\/i><\/em>\u2217\u00a0sin\u03b8<\/i><\/em>)\u00a0=\u00a0\u00a0a<\/i><\/em>2 +\u00a0b<\/i><\/em>2sin<\/i><\/em>(ax <\/i><\/em>+\u00a0\u03b8<\/i><\/em>)<\/p>\n

      \u4e09\u89d2\u51fd\u6570\u7684\u56fe\u50cf\u53ca\u6027\u8d28<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      \u6b63\u5f26\u51fd\u6570\u7684\u56fe\u50cf\u53ca\u6027\u8d28<\/p>\n

      \u6b63\u5f26\u51fd\u6570\u89e3\u6790\u5f0f\uff1ay <\/i><\/em>=\u00a0Asin<\/i><\/em>(wx<\/i><\/em>\u00a0<\/i><\/em>+\u00a0\u03b8<\/i><\/em>)<\/p>\n

      \u6982\u5ff5\uff1aA<\/i><\/em>\u4e3a\u632f\u5e45\u00a0\uff0c\u03b8<\/i><\/em>\u4e3a\u521d\u9879\u00a0\uff0cwx <\/i><\/em>+\u00a0\u03b8<\/i><\/em>\u4e3a\u76f8\u4f4d<\/p>\n

      \u6027\u8d28\uff1a\u5b9a\u4e49\u57df\u4e3aR\u00a0\uff0c\u503c\u57df\u4e3a[\u2212A<\/i><\/em>,A<\/i><\/em>]\uff0c\u5468\u671f\u4e3aT <\/i><\/em>=\u00a0\u00a0\uff0c\u9891\u7387\u4e3a\uff1af<\/i><\/em>\u00a0<\/i><\/em>=\u00a0\u00a0\u4e09\u89d2\u5f62\u4e2d\u57fa\u672c\u7ed3\u8bba\u548c\u516c\u5f0f<\/p>\n

        \n
      1. \u00a0\u5185\u89d2\u548c\u5b9a\u7406\uff1a\u2220A <\/i><\/em>+\u2220B <\/i><\/em>+\u2220C<\/i><\/em>\u00a0<\/i><\/em>=\u00a0\u03a0\u00a0\u2194\u00a0\u2220C<\/i><\/em>\u00a0<\/i><\/em>=\u00a0\u03a0\u00a0\u2212\u00a0\uff08\u00a0\u2220A <\/i><\/em>+\u00a0\u2220B<\/i><\/em>\uff09 \u2194\u00a0\u00a0=\u00a0\u00a0<\/li>\n
      2. \u5927\u8fb9\u5bf9\u5927\u89d2\uff0c\u5c0f\u8fb9\u5bf9\u5c0f\u89d2\u00a0\uff0c\u7b49\u8fb9\u5bf9\u7b49\u89d2<\/li>\n
      3. sin<\/i><\/em>(A <\/i><\/em>+B<\/i><\/em>)\u00a0=\u00a0sinC<\/i><\/em>\u00a0<\/i><\/em>,cos<\/i><\/em>(A <\/i><\/em>+\u00a0B<\/i><\/em>)\u00a0=\u00a0\u2212cosC<\/i><\/em>\u00a0<\/i><\/em>,\u00a0\u00a0=\u00a0<\/li>\n<\/ol>\n

        \u6b63\u5f26\u5b9a\u7406\u548c\u4f59\u5f26\u5b9a\u7406<\/p>\n

        \u2b50\u6b63\u5f26\u5b9a\u7406\uff1a\u00a0\u00a0=\u00a0\u00a0=\u00a0\u00a0=\u00a02R<\/i><\/em><\/p>\n

        \u5e38\u7528\u53d8\u5f62\uff1a<\/p>\n

         <\/p>\n

          \n
        1. a <\/i><\/em>=2RsinA<\/i><\/em>;b <\/i><\/em>=\u00a02RsinB<\/i><\/em>;c <\/i><\/em>=\u00a02RsinC<\/i><\/em><\/li>\n
        2. sinA<\/i><\/em><\/i>=\u00a0\u00a0;sinB<\/i><\/em>\u00a0<\/i><\/em>=\u00a0;sinC<\/i><\/em>\u00a0<\/i><\/em>=\u00a0<\/li>\n
        3. a<\/i><\/em><\/i>:\u00a0b<\/i><\/em>\u00a0<\/i><\/em>:\u00a0c<\/i><\/em>\u00a0<\/i><\/em>=\u00a0sinA<\/i><\/em>\u00a0<\/i><\/em>:\u00a0sinB<\/i><\/em>\u00a0<\/i><\/em>:\u00a0sinC<\/i><\/em><\/li>\n
        4. b(a)<\/i>=\u00a0s(s)i(i)n(n)B(A)\u00a0<\/i><\/em>;\u00a0c(b)\u00a0<\/i><\/em>=\u00a0s(s)i(i)n(n)C(B)\u00a0<\/i><\/em>;\u00a0c(a)\u00a0<\/i><\/em>=\u00a0s(s)i(i)n(n)C(A)<\/li>\n
        5. =\u00a0\u00a0=\u00a0\u00a0=\u00a0\u00a0=\u00a0\u00a0=\u00a0<\/li>\n<\/ol>\n

          \u4e09\u89d2\u5f62\u9762\u79ef\u516c\u5f0f<\/p>\n

            \n
          1. S<\/i><\/em><\/i>\u25b2\u00a0\u00a0=\u00a0<\/li>\n<\/ol>\n

             <\/p>\n

             <\/p>\n

              \n
            1. S<\/i><\/em><\/i>\u25b2\u00a0\u00a0=\u00a0\u00a0=\u00a0\u00a0=<\/li>\n<\/ol>\n

              \u6e29\u99a8\u63d0\u793a<\/p>\n

              tanx<\/i><\/em>\u00a0<\/i><\/em>=\u00a0k<\/i><\/em>(k<\/i><\/em>\u4e3a\u2014\u6b21\u51fd\u6570\u7684\u659c\u7387)<\/p>\n

              absinC<\/i><\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

              \u4e09\u89d2\u51fd\u6570   \u89d2\u7684\u5206\u7c7b \u6b63\u89d2\uff1a\u6309\u9006\u65f6\u9488\u65b9\u5411\u65cb\u8f6c\u5f62\u6210\u7684\u89d2 \u8d1f\u89d2\uff1a\u6309\u987a\u65f6\u9488\u65b9\u5411\u65cb\u8f6c\u5f62\u6210\u7684\u89d2 \u96f6\u89d2\uff1a\u6ca1\u6709\u65cb […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[68],"tags":[],"content_type":[],"class_list":["post-8593","post","type-post","status-publish","format-standard","hentry","category-zzjy"],"_links":{"self":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/posts\/8593","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8593"}],"version-history":[{"count":0,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/posts\/8593\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8593"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8593"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8593"},{"taxonomy":"content_type","embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcontent_type&post=8593"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}