{"id":153,"date":"2025-09-15T12:52:23","date_gmt":"2025-09-15T03:52:23","guid":{"rendered":"https:\/\/www.masmath.online\/?p=153"},"modified":"2025-09-15T12:52:24","modified_gmt":"2025-09-15T03:52:24","slug":"%e9%80%86%e9%96%a2%e6%95%b0%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0","status":"publish","type":"post","link":"https:\/\/www.masmath.online\/?p=153","title":{"rendered":"\u9006\u95a2\u6570\u306e\u5c0e\u95a2\u6570"},"content":{"rendered":"\n<div class=\"wp-block-jin-gb-block-box simple-box3\">\n<p>\u3000\\( y = \\sin x \\) \\( \\left( -\\dfrac{\\pi}{2} &lt; x &lt; \\dfrac{\\pi}{2} \\right) \\) \u306e\u9006\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u3088\uff0e<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-jin-gb-block-box simple-box9\">\n<p>\uff0a\u9006\u95a2\u6570\u306e\u5c0e\u95a2\u6570\uff0a<br>\u3000\u6c42\u3081\u65b9\u306f\u6b21\u306e \\( 2 \\) \u3064\uff0e<br>\\( 1^\\circ \\)\u3000\\( x = f(y) \\) \u3092 \\( y \\) \u306b\u3064\u3044\u3066\u89e3\u304d\uff0c \\( x \\) \u306e\u95a2\u6570 \\( y \\) \u3092 \\( x \\) \u3067\u5fae\u5206\u3059\u308b\uff0e<br><br>\\( 2^\\circ \\)\u3000\\( \\dfrac{dx}{dy} \\neq 0 \\) \u306e\u3068\u304d\uff0c \\( \\dfrac{dy}{dx} = \\dfrac{1}{\\ \\dfrac{dx}{dy}\\ } \\) \u3068\u306a\u308b\u3053\u3068\u3092\u5229\u7528\u3059\u308b\uff0e<\/p>\n<\/div>\n\n\n\n<p>\u3000\\( x = \\sin y \\) \\( \\left( -\\dfrac{\\pi}{2} &lt; y &lt; \\dfrac{\\pi}{2} \\right) \\) \u306e\u4e21\u8fba\u3092 \\( y \\) \u3067\u5fae\u5206\u3057\u3066<br><br>\u3000\u3000\u3000\\( \\dfrac{dx}{dy} = \\cos y \\)<br><br>\u3053\u308c\u3088\u308a<br><br>\u3000\u3000\u3000\\( \\dfrac{dy}{dx} = \\dfrac{1}{\\ \\dfrac{dx}{dy}\\ } \\)<br><br>\u3000\u3000\u3000\\( = \\dfrac{1}{\\cos y} \\)<br><br>\u3000\u3000\u3000\\( = \\dfrac{1}{\\sqrt{1 &#8211; \\sin^2 y}} \\)<br><br>\u3000\u3000\u3000\\( = \\dfrac{1}{\\sqrt{1-x^2}} \\cdots \\) \u7b54<\/p>\n\n\n\n<div class=\"wp-block-jin-gb-block-box simple-box6\">\n<p>\\( 1^\\circ \\)<br>\u3000\u4e09\u89d2\u95a2\u6570\u306e\u9006\u95a2\u6570\u306e\u3088\u3046\u306b\uff0c \\( f^{-1}(x) \\) \u3092 \\( x \\) \u306e\u7c21\u5358\u306a\u5f0f\u3067\u8868\u305b\u306a\u3044\u5834\u5408\u306f\uff0c\u672c\u554f\u306e\u3088\u3046\u306b\uff0c\u5192\u982d\u306b\u8ff0\u3079\u305f\u65b9\u6cd5\u306e\u3046\u3061 \\( 2 \\) \u3064\u76ee\u3092\u63a1\u7528\u3059\u308b\uff0e<\/p>\n\n\n\n<p>\\( 2^\\circ \\)<br>\u3000\\( \\sin x \\) \\( \\left( -\\dfrac{\\pi}{2} \\leqq x \\leqq \\dfrac{\\pi}{2} \\right) \\) \u306e\u9006\u95a2\u6570\u306f \\( \\arcsin x \\) \u3068\u8868\u3055\u308c\u308b\uff0e\u672c\u554f\u306e\u7d50\u679c\u304b\u3089<br><br>\u3000\u3000\u3000\\( (\\arcsin x)&#8217; = \\dfrac{1}{\\sqrt{1-x^2}} \\)<br><br>\u3068\u306a\u308b\uff0e\u540c\u69d8\u306b\uff0c \\( \\cos x \\) \\( ( 0 \\leqq x \\leqq \\pi ) \\) \u306e\u9006\u95a2\u6570\u306f \\( \\arccos x \\) \uff0c \\( \\tan x \\) \\( \\left( -\\dfrac{\\pi}{2} &lt; x &lt; \\dfrac{\\pi}{2} \\right) \\) \u306e\u9006\u95a2\u6570\u306f \\( \\arctan x \\) \u3068\u8868\u3055\u308c\uff0c\u5c0e\u95a2\u6570\u306f\u305d\u308c\u305e\u308c<br><br>\u3000\u3000\u3000\\( (\\arccos x)&#8217; = -\\dfrac{1}{\\sqrt{1-x^2}} \\)<br><br>\u3000\u3000\u3000\\( (\\arctan x)&#8217; = \\dfrac{1}{x^2 + 1} \\)<br><br>\u3068\u306a\u308b\uff0e<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u3000\\( x = \\sin y \\) \\( \\left( -\\dfrac{\\pi}{2} lt; y lt; \\dfrac{\\pi}{2} \\right) \\) \u306e\u4e21\u8fba\u3092 \\( y \\) \u3067\u5fae\u5206\u3057\u3066 \u3000\u3000\u3000\\( \\df<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jin_ogp_image_url":"","_jin_last_featured_id":0,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-153","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.masmath.online\/index.php?rest_route=\/wp\/v2\/posts\/153","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.masmath.online\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.masmath.online\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.masmath.online\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.masmath.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=153"}],"version-history":[{"count":12,"href":"https:\/\/www.masmath.online\/index.php?rest_route=\/wp\/v2\/posts\/153\/revisions"}],"predecessor-version":[{"id":181,"href":"https:\/\/www.masmath.online\/index.php?rest_route=\/wp\/v2\/posts\/153\/revisions\/181"}],"wp:attachment":[{"href":"https:\/\/www.masmath.online\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=153"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.masmath.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=153"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.masmath.online\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=153"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}