{"id":366,"date":"2023-07-04T13:53:47","date_gmt":"2023-07-04T13:53:47","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d8%af%d8%a7%d9%84%d8%a9-%d8%a7%d9%84%d8%ac%d9%8a%d8%a8-%d8%a7%d9%84%d8%b2%d8%a7%d8%a6%d8%af%d9%8a%d8%a9\/"},"modified":"2023-07-04T13:53:47","modified_gmt":"2023-07-04T13:53:47","slug":"%d8%af%d8%a7%d9%84%d8%a9-%d8%a7%d9%84%d8%ac%d9%8a%d8%a8-%d8%a7%d9%84%d8%b2%d8%a7%d8%a6%d8%af%d9%8a%d8%a9","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d8%af%d8%a7%d9%84%d8%a9-%d8%a7%d9%84%d8%ac%d9%8a%d8%a8-%d8%a7%d9%84%d8%b2%d8%a7%d8%a6%d8%af%d9%8a%d8%a9\/","title":{"rendered":"\u062f\u0627\u0644\u0629 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0633\u062a\u062c\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629 \u0643\u0644 \u0634\u064a\u0621 \u0639\u0646 \u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0632\u0627\u0626\u062f\u064a: \u0645\u0627 \u0647\u064a \u0635\u064a\u063a\u062a\u0647\u060c \u062a\u0645\u062b\u064a\u0644\u0647 \u0627\u0644\u0628\u064a\u0627\u0646\u064a\u060c \u062c\u0645\u064a\u0639 \u062e\u0635\u0627\u0626\u0635\u0647\u060c \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0645\u0639 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0623\u062e\u0631\u0649\u060c&#8230; <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"formula-del-seno-hiperbolico\"><\/span> \u0635\u064a\u063a\u0629 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u062f\u0627\u0644\u0629 <strong>\u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629<\/strong> \u0647\u064a \u0625\u062d\u062f\u0649 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0642\u0637\u0639\u064a\u0629 \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 \u0648\u064a\u062a\u0645 \u062a\u0645\u062b\u064a\u0644\u0647\u0627 \u0628\u0627\u0644\u0631\u0645\u0632 <strong>sinh(x)<\/strong> \u0623\u0648 <strong>sinh(x)<\/strong> . \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u064a\u0633\u0627\u0648\u064a e <sup>x<\/sup> \u0646\u0627\u0642\u0635 e <sup>-x<\/sup> \u0645\u0642\u0633\u0648\u0645\u064b\u0627 \u0639\u0644\u0649 2.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0635\u064a\u063a\u0629 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0647\u064a \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-924551c3d4c8b1d68b0c9a7cf2115ca8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{senh}(x)=\\cfrac{e^{x}-e^{-x}}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"150\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0641\u0625\u0646 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u064a\u0631\u062a\u0628\u0637 \u0628\u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0627\u0646\u0638\u0631:<\/strong> <a href=\"https:\/\/mathority.org\/ar\/\u0648\u0638\u064a\u0641\u0629-\u0627\u0644\u0627\u0654\u0633\u064a\u0629\/\"><span style=\"text-decoration: underline;\">\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629<\/span><\/a> <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"representacion-grafica-del-seno-hiperbolico\"><\/span> \u062a\u0645\u062b\u064a\u0644 \u0631\u0633\u0648\u0645\u064a \u0644\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u064a \u0631\u0623\u064a\u0646\u0627\u0647\u0627 \u0641\u064a \u0627\u0644\u0642\u0633\u0645 \u0627\u0644\u0633\u0627\u0628\u0642\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0625\u0646\u0634\u0627\u0621 \u062c\u062f\u0648\u0644 \u0644\u0642\u064a\u0645 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u0648\u0631\u0633\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 \u0631\u0633\u0645\u064b\u0627 \u0628\u064a\u0627\u0646\u064a\u064b\u0627: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/sinus-hyperbolique.webp\" alt=\"\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\" class=\"wp-image-346\" width=\"281\" height=\"349\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u0646 \u0646\u0631\u0649 \u0623\u0646 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0647\u0648 \u062f\u0627\u0644\u0629 <strong>\u0641\u0631\u062f\u064a\u0629<\/strong> \u060c \u0644\u0623\u0646 x \u0627\u0644\u0645\u0639\u0627\u0643\u0633 \u0644\u0647 \u0635\u0648\u0631 \u0645\u062a\u0642\u0627\u0628\u0644\u0629\u060c \u0623\u0648 \u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631\u060c \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0627\u0644\u062c\u064a\u0628\u064a \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0645\u062a\u0645\u0627\u062b\u0644 \u062d\u0648\u0644 \u0623\u0635\u0644 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a (0\u060c 0).<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u062a\u0631\u0648\u0646\u060c \u0641\u0625\u0646 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0644\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u064a\u062e\u062a\u0644\u0641 \u062a\u0645\u0627\u0645\u064b\u0627 \u0639\u0646 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0644\u0644\u062c\u064a\u0628\u060c \u0648\u0647\u064a \u062f\u0627\u0644\u0629 \u062f\u0648\u0631\u064a\u0629. \u064a\u0645\u0643\u0646\u0643 \u0645\u0634\u0627\u0647\u062f\u0629 \u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0631\u0633\u0648\u0645\u064a \u0644\u0644\u062c\u064a\u0628 \u0648\u062c\u0645\u064a\u0639 \u0627\u0644\u0627\u062e\u062a\u0644\u0627\u0641\u0627\u062a \u0645\u0639 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0641\u064a \u0627\u0644\u0631\u0627\u0628\u0637 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0627\u0646\u0638\u0631:<\/strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ar\/\u0648\u0638\u064a\u0641\u0629-\u062c\u064a\u0628\u064a\u0629\/\">\u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0631\u0633\u0648\u0645\u064a \u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062c\u064a\u0628<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"caracteristicas-del-seno-hiperbolico\"><\/span> \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0644\u0647 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0645\u062c\u0627\u0644 \u062f\u0627\u0644\u0629 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u0647\u0648 \u0643\u0644 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062d\u0642\u064a\u0642\u064a\u0629:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0cd1539b66edeb38040ed80168e1fd9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0646\u0637\u0627\u0642 \u0623\u0648 \u0646\u0637\u0627\u0642 \u062f\u0627\u0644\u0629 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u0643\u0644\u0647\u0627 \u0623\u0631\u0642\u0627\u0645 \u062d\u0642\u064a\u0642\u064a\u0629 \u0623\u064a\u0636\u064b\u0627.<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5a954b5c192478c3b7b14428ac8d5cbc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Im } f= \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"74\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0647\u0648 \u062f\u0627\u0644\u0629 \u0645\u0633\u062a\u0645\u0631\u0629 \u0648\u063a\u0631\u064a\u0628\u0629.<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5b37f1a110d810d8dbf0b5a52a1175c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{senh}(-x) =- \\text{senh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"167\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u064a\u062a\u0642\u0627\u0637\u0639 \u0627\u0644\u0645\u062d\u0648\u0631 X \u0648\u0627\u0644\u0645\u062d\u0648\u0631 Y \u0639\u0646\u062f \u0646\u0641\u0633 \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0642\u0627\u0637\u0639\u060c \u0623\u0635\u0644 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9cf2000c782cfe94be6df5f499cd3e24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u062d\u062f \u062f\u0627\u0644\u0629 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 \u062a\u0645\u064a\u0644 x \u0625\u0644\u0649 \u0632\u0627\u0626\u062f\/\u0646\u0627\u0642\u0635 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629 \u064a\u0633\u0627\u0648\u064a \u0632\u0627\u0626\u062f\/\u0646\u0627\u0642\u0635 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-14c1cd1cfcf12880c94a1a992fca6636_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to+\\infty}\\text{senh}(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"162\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d3bad505c476b08f8494c9d4a558ca46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to-\\infty}\\text{senh}(x)=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"162\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u064a\u062a\u0632\u0627\u064a\u062f \u062c\u064a\u0628 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f \u0628\u0634\u0643\u0644 \u0635\u0627\u0631\u0645 \u0641\u064a \u062c\u0645\u064a\u0639 \u0623\u0646\u062d\u0627\u0621 \u0627\u0644\u0645\u062c\u0627\u0644\u060c \u0644\u0630\u0644\u0643 \u0644\u064a\u0633 \u0644\u0647 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0642\u0635\u0649 \u0623\u0648 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u062f\u0646\u0649.<\/li>\n<\/ul>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0641\u0625\u0646\u0647 \u064a\u063a\u064a\u0631 \u0627\u0646\u062d\u0646\u0627\u0621\u0647 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 x = 0\u060c \u0644\u0630\u0644\u0643 \u0641\u0647\u0648 \u0646\u0642\u0637\u0629 \u0627\u0646\u0642\u0644\u0627\u0628 \u0644\u0644\u062f\u0627\u0644\u0629. \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0623\u0642\u0644 \u0645\u0646 x=0 \u0641\u0647\u064a \u062f\u0627\u0644\u0629 \u0645\u0642\u0639\u0631\u0629\u060c \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0623\u0643\u0628\u0631 \u0645\u0646 x=0 \u0641\u0647\u064a \u062f\u0627\u0644\u0629 \u0645\u062d\u062f\u0628\u0629.<\/li>\n<\/ul>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0645\u0634\u062a\u0642 \u062f\u0627\u0644\u0629 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u0647\u0648 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c47c54bd2abef41b1660f7779cd51cc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(x) \\ \\longrightarrow \\ f'(x)=\\text{cosh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"286\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u0645\u062b\u0644\u060c \u0641\u0625\u0646 \u062a\u0643\u0627\u0645\u0644 \u062f\u0627\u0644\u0629 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u0647\u0648 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fb5ef4d6ad0649cda51f73b558814b45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\int \\text{senh}(x) \\ dx= \\text{cosh}(x) + C\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"221\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0633\u0644\u0633\u0644\u0629 \u062a\u0627\u064a\u0644\u0648\u0631 \u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u062a\u0639\u0627\u062f\u0644 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062a\u0627\u0644\u064a:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3db771459579b232c860bb1276f1d665_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{senh}(x)=x+\\cfrac{x^3}{3!}+\\cfrac{x^5}{5!}+\\cfrac{x^7}{7!}+\\dots=\\sum_{n=0}^\\infty\\cfrac{x^{2n+1}}{(2n+1)!}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"382\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u062a\u062d\u0648\u064a\u0644 \u0644\u0627\u0628\u0644\u0627\u0633 \u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u0647\u0648 \u0643\u0645\u0627 \u064a\u0644\u064a: <\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e3e6b1c1d82a639269c25218155f4019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathcal{L}\\bigl[\\text{senh}(at)\\bigr]=\\cfrac{a}{s^2-a^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"172\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"relaciones-matematicas-del-seno-hiperbolico\"><\/span> \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0644\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0631\u062a\u0628\u0637 \u062c\u064a\u0628 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f \u0628\u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0642\u0637\u0639\u064a\u0629 \u0627\u0644\u0623\u062e\u0631\u0649 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u062a\u0631\u0628\u0637 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0628\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4317a445a90e4d139b47db7cf4a49a1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}^2(x)-\\text{senh}^2(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"185\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643\u060c \u062a\u0631\u062a\u0628\u0637 \u062f\u0648\u0627\u0644 \u0627\u0644\u062c\u064a\u0628 \u0648\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u0628\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u060c \u0648\u0647\u064a x <sup>2<\/sup> -y <sup>2<\/sup> =1. \u0639\u0644\u0649 \u0639\u0643\u0633 \u062f\u0648\u0627\u0644 \u0627\u0644\u062c\u064a\u0628 \u0648\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0627\u0644\u0645\u0631\u062a\u0628\u0637\u0629 \u0628\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062f\u0627\u0626\u0631\u0629 (x <sup>2<\/sup> +y <sup>2<\/sup> =1).<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646 \u0631\u0628\u0637 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u0644\u0644\u062c\u064a\u0628 \u0648\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0648\u0627\u0644\u0638\u0644 \u0628\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-12f286528bc0635705aadbe510b6ceb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tanh}(x)=\\cfrac{\\text{senh}(x)}{\\text{cosh}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"144\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0644\u062c\u0645\u0639 \u0623\u0648 \u0637\u0631\u062d \u0631\u0642\u0645\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u064a\u0646 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0635\u064a\u063a \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d0b2492cbc95b27046485a6d7d9cd08c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{senh}(x+y)=\\text{senh}(x)\\text{cosh}(y)+\\text{senh}(y)\\text{cosh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"364\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a2205899042608a33bd61b158526026_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{senh}(x-y)=\\text{senh}(x)\\text{cosh}(y)-\\text{senh}(y)\\text{cosh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"364\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0644\u0639\u062f\u062f \u0645\u0632\u062f\u0648\u062c \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f0d5c63a53de957eac1f69a4fb209f96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{senh}(2x)=2\\text{senh}(x)\\text{cosh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"215\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646 \u0625\u064a\u062c\u0627\u062f \u0645\u062c\u0645\u0648\u0639 \u0623\u0648 \u0637\u0631\u062d \u062c\u064a\u0628\u064a\u0646 \u0632\u0627\u0626\u062f\u064a\u064a\u0646 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0635\u064a\u063a \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9d3598ef49dbf33b925a73edc773a85d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{senh}(x)+\\text{senh}(y)=2\\text{senh}\\left(\\frac{x+y}{2}\\right)\\text{cosh}\\left(\\frac{x-y}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"387\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-00ee545f4866d13406bc3d5de7de528a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{senh}(x)-\\text{senh}(y)=2\\text{senh}\\left(\\frac{x-y}{2}\\right)\\text{cosh}\\left(\\frac{x+y}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"387\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628 \u0645\u0631\u0628\u0639 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0628\u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e3e8284b95e317f876a4f8802ebf5fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{senh}^2(x)=\\cfrac{1}{2}\\Bigl(\\text{cosh}(2x)-1\\Bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"216\" style=\"vertical-align: -12px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0633\u062a\u062c\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629 \u0643\u0644 \u0634\u064a\u0621 \u0639\u0646 \u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0632\u0627\u0626\u062f\u064a: \u0645\u0627 \u0647\u064a \u0635\u064a\u063a\u062a\u0647\u060c \u062a\u0645\u062b\u064a\u0644\u0647 \u0627\u0644\u0628\u064a\u0627\u0646\u064a\u060c \u062c\u0645\u064a\u0639 \u062e\u0635\u0627\u0626\u0635\u0647\u060c \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0645\u0639 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0623\u062e\u0631\u0649\u060c&#8230; \u0635\u064a\u063a\u0629 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u062f\u0627\u0644\u0629 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u0647\u064a \u0625\u062d\u062f\u0649 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0642\u0637\u0639\u064a\u0629 \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 \u0648\u064a\u062a\u0645 \u062a\u0645\u062b\u064a\u0644\u0647\u0627 \u0628\u0627\u0644\u0631\u0645\u0632 sinh(x) \u0623\u0648 sinh(x) . \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u064a\u0633\u0627\u0648\u064a e x \u0646\u0627\u0642\u0635 e -x \u0645\u0642\u0633\u0648\u0645\u064b\u0627 \u0639\u0644\u0649 2. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0635\u064a\u063a\u0629 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d8%af%d8%a7%d9%84%d8%a9-%d8%a7%d9%84%d8%ac%d9%8a%d8%a8-%d8%a7%d9%84%d8%b2%d8%a7%d8%a6%d8%af%d9%8a%d8%a9\/\"> <span class=\"screen-reader-text\">\u062f\u0627\u0644\u0629 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629<\/span> \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f 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