{"id":6984,"date":"2021-07-23T23:21:46","date_gmt":"2021-07-23T14:21:46","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=6984"},"modified":"2026-09-27T16:58:02","modified_gmt":"2026-09-27T07:58:02","slug":"trigonometric-functions","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-calculus\/trigonometric-functions\/","title":{"rendered":"\uc0bc\uac01\ud568\uc218"},"content":{"rendered":"<div style=\"display: none; visibility: hidden;\">\n<style type=\"text\/css\">\n\timg.mfp-img { background-color: white; }\n<\/style>\n<p><!--\n\\[\n\\newcommand{\\vecf}{{\\mathbf{f}}}\n\\newcommand{\\vecL}{{\\mathbf{L}}}\n\\newcommand{\\vecR}{{\\mathbb{R}}}\n\\newcommand{\\imI}{\\boldsymbol{i}}\n\\]\n-->\n<\/div>\n<div class=\"box itc_intro\">\n<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 0\uc7a5 6\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; <span class=\"itc_viewcontents\">(<a href=\"..\/\">\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30<\/a>)<\/span><\/p>\n<\/div>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\ud638\ub3c4\ubc95<\/h2>\n<p>\uadf8\ub9bc\uacfc \uac19\uc774 \ubc18\uc9c0\ub984\uc758 \uae38\uc774\uac00 \\(1\\)\uc778 \uc6d0\uc744 \uc0dd\uac01\ud558\uc790.<\/p>\n<div style=\"margin-top: 2em; margin-bottom: 2em;\">\n<img decoding=\"async\" src=\"\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri01.png\" alt=\"\" width=\"168\" height=\"153\" class=\"aligncenter size-full wp-image-7064\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri01.png 842w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri01-300x273.png 300w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri01-768x700.png 768w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri01-585x533.png 585w\" sizes=\"(max-width: 168px) 100vw, 168px\" \/>\n<\/div>\n<p>\ud638\uc758 \uae38\uc774\uac00 \\(1\\)\uc778 \ubd80\ucc44\uaf34\uc758 \uc911\uc2ec\uac01\uc758 \ud06c\uae30\ub97c <span class=\"defined\">\\(\\boldsymbol{1}\\)\ub77c\ub514\uc548<\/span>(radian)\uc73c\ub85c \uc815\uc758\ud55c\ub2e4. \ubc18\uc9c0\ub984\uc758 \uae38\uc774\uac00 \\(1\\)\uc778 \uc6d0\uc758 \ub458\ub808\uc758 \uae38\uc774\uac00 \\(2\\pi\\)\uc774\ubbc0\ub85c<br \/>\n\\[<br \/>\n180^\\circ=\\pi\\,\\text{radians}<br \/>\n\\]<br \/>\n\uc774\ub2e4. \uc774\uc640 \uac19\uc774 \ub77c\ub514\uc548\uc744 \ub2e8\uc704\ub85c \uac01\uc758 \ud06c\uae30\ub97c \ub098\ud0c0\ub0b4\ub294 \ubc29\ubc95\uc744 <span class=\"defined\">\ud638\ub3c4\ubc95<\/span>(circular measure)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<p>\ud638\ub3c4\ubc95\uc73c\ub85c \uac01\uc758 \ud06c\uae30\ub97c \ub098\ud0c0\ub0bc \ub54c \ub2e8\uc704 \u2018\ub77c\ub514\uc548\u2019\uc744 \uc0dd\ub7b5\ud558\ub294 \uacbd\uc6b0\uac00 \ub9ce\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \uac01\uc758 \ud06c\uae30\ub97c \ub2e8\uc704 \uc5c6\uc774 \ub098\ud0c0\ub0b4\uba74 \ubcc4\ub2e4\ub978 \uc5b8\uae09\uc774 \uc5c6\ub294 \ud55c \ub2e8\uc704\uac00 \ub77c\ub514\uc548\uc778 \uac83\uc73c\ub85c \uc57d\uc18d\ud55c\ub2e4.<\/p>\n<p>\ud68c\uc804 \ubc29\ud5a5\uc5d0 \ub530\ub77c \uac01\uc758 \ud06c\uae30\ub97c \uc591\uc218\uc640 \uc74c\uc218\ub85c \ub098\ud0c0\ub0b4\uba74 \ud3b8\ub9ac\ud558\ub2e4. \ubc18\uc2dc\uacc4\ubc29\ud5a5\uc73c\ub85c \ud68c\uc804\ud55c \uc815\ub3c4\ub294 \uc591\uc218\ub85c \ub098\ud0c0\ub0b4\uace0, \uc2dc\uacc4\ubc29\ud5a5\uc73c\ub85c \ud68c\uc804\ud55c \uc815\ub3c4\ub294 \uc74c\uc218\ub85c \ub098\ud0c0\ub0b8\ub2e4. \ud55c \ubc14\ud034\ub97c \ucd08\uacfc\ud558\ub294 \ud68c\uc804\uc744 \ub098\ud0c0\ub0bc \ub54c\uc5d0\ub294 \uc808\ub313\uac12\uc774 \\(2\\pi\\)\ubcf4\ub2e4 \ud070 \uac12\uc744 \uc0ac\uc6a9\ud560 \uc218 \uc788\ub2e4. \uc544\ub798 \uadf8\ub9bc\uc740 \ub2e4\uc591\ud55c \uac01\uc758 \ud06c\uae30\ub97c \ub098\ud0c0\ub0b8 \uac83\uc774\ub2e4.<\/p>\n<div style=\"margin-top: 2em; margin-bottom: 2em;\">\n<img fetchpriority=\"high\" decoding=\"async\" src=\"\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri02-04.png\" alt=\"\" width=\"465\" height=\"149\" class=\"aligncenter size-full wp-image-7072\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri02-04.png 2326w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri02-04-300x96.png 300w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri02-04-1024x329.png 1024w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri02-04-768x247.png 768w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri02-04-1536x493.png 1536w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri02-04-2048x658.png 2048w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri02-04-1920x617.png 1920w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri02-04-1170x376.png 1170w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri02-04-585x188.png 585w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/>\n<\/div>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\uc0bc\uac01\ud568\uc218\uc758 \uc815\uc758<\/h2>\n<p>\uc2e4\uc218 \\(\\theta\\)\uac00 \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790. \uc88c\ud45c\ud3c9\uba74\uc5d0\uc11c \uc6d0\uc810\uc744 \uc911\uc2ec\uc73c\ub85c \\(x\\)\ucd95\uc758 \uc591\uc758 \ubc29\ud5a5\uc5d0\uc11c \ucd9c\ubc1c\ud558\uc5ec \\(\\theta\\)\ub9cc\ud07c \ud68c\uc804\ud55c \ubc18\uc9c1\uc120 \uc704\uc5d0 \ub193\uc778, \uc6d0\uc810\uc774 \uc544\ub2cc \uc810 \\(\\mathrm{P}\\)\ub97c \uc0dd\uac01\ud558\uc790.<\/p>\n<div style=\"margin-top: 2em; margin-bottom: 2em;\">\n<img decoding=\"async\" src=\"\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri05.png\" alt=\"\" width=\"295\" height=\"203\" class=\"aligncenter size-full wp-image-7068\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri05.png 1475w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri05-300x207.png 300w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri05-1024x706.png 1024w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri05-768x530.png 768w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri05-1170x807.png 1170w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri05-585x403.png 585w\" sizes=\"(max-width: 295px) 100vw, 295px\" \/>\n<\/div>\n<p>\uc810 \\(\\mathrm{P}\\)\uc758 \uc88c\ud45c\ub97c \\(\\mathrm{P}(x,\\,y)\\)\ub77c\uace0 \ud558\uace0, \uc120\ubd84 \\(\\mathrm{OP}\\)\uc758 \uae38\uc774\ub97c \\(r\\)\ub77c\uace0 \ud558\uc790. \uc774\ub54c \\(\\theta\\)\uc758 <span class=\"defined\">\uc0ac\uc778<\/span>(sine)\uacfc <span class=\"defined\">\ucf54\uc0ac\uc778<\/span>(cosine)\uc744 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<br \/>\n\\[<br \/>\n\\sin\\theta=\\frac{y}{r},<br \/>\n\\qquad<br \/>\n\\cos\\theta=\\frac{x}{r}.<br \/>\n\\]<br \/>\n\uac19\uc740 \ubc18\uc9c1\uc120 \uc704\uc5d0\uc11c \uc810 \\(\\mathrm{P}\\)\ub97c \ub2e4\ub978 \uc810\uc73c\ub85c \ubc14\uafb8\uba74 \\(x,\\) \\(y,\\) \\(r\\)\uac00 \ubaa8\ub450 \uac19\uc740 \uc591\uc758 \ube44\uc728\ub85c \ubcc0\ud558\ubbc0\ub85c \uc704 \ub450 \uac12\uc740 \ubcc0\ud558\uc9c0 \uc54a\ub294\ub2e4. \ub530\ub77c\uc11c \uc0ac\uc778\uacfc \ucf54\uc0ac\uc778\uc740 \uc810 \\(\\mathrm{P}\\)\uc758 \uc120\ud0dd\uacfc \uad00\uacc4\uc5c6\uc774 \\(\\theta\\)\uc5d0 \uc758\ud558\uc5ec \uacb0\uc815\ub41c\ub2e4.<\/p>\n<p>\ub2e4\ub978 \uc0bc\uac01\ud568\uc218\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<br \/>\n\\[<br \/>\n\\begin{gather}<br \/>\n\\tan\\theta=\\frac{\\sin\\theta}{\\cos\\theta},<br \/>\n\\qquad<br \/>\n\\sec\\theta=\\frac{1}{\\cos\\theta},<br \/>\n\\\\[5pt]<br \/>\n\\operatorname{cosec}\\theta=\\frac{1}{\\sin\\theta},<br \/>\n\\qquad<br \/>\n\\cot\\theta=\\frac{\\cos\\theta}{\\sin\\theta}.<br \/>\n\\end{gather}<br \/>\n\\]<br \/>\n\uc0ac\uc778\uacfc \ucf54\uc0ac\uc778\uc740 \ubaa8\ub4e0 \uc2e4\uc218 \\(\\theta\\)\uc5d0 \ub300\ud558\uc5ec \uc815\uc758\ub41c\ub2e4. \ud0c4\uc820\ud2b8\uc640 \uc2dc\ucee8\ud2b8\ub294 \\(\\cos\\theta\\ne0\\)\uc778 \uacbd\uc6b0\uc5d0\ub9cc \uc815\uc758\ub418\uace0, \ucf54\uc2dc\ucee8\ud2b8\uc640 \ucf54\ud0c4\uc820\ud2b8\ub294 \\(\\sin\\theta\\ne0\\)\uc778 \uacbd\uc6b0\uc5d0\ub9cc \uc815\uc758\ub41c\ub2e4.<\/p>\n<p>\ud2b9\ud788 \\(r=1\\)\uc778 \ub2e8\uc704\uc6d0 \uc704\uc758 \uc810\uc744 \ud0dd\ud558\uba74 \uadf8 \uc810\uc758 \uc88c\ud45c\ub294<br \/>\n\\[<br \/>\n(\\cos\\theta,\\,\\sin\\theta)<br \/>\n\\]<br \/>\n\uc774\ub2e4. \ub530\ub77c\uc11c \uc0ac\uc778\uacfc \ucf54\uc0ac\uc778\uc740 \ub2e8\uc704\uc6d0 \uc704\uc758 \uc810\uc758 \uc88c\ud45c\ub85c \uc774\ud574\ud560 \uc218 \uc788\ub2e4.<\/p>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\uc720\uc6a9\ud55c \uacf5\uc2dd<\/h2>\n<p>\uc0bc\uac01\ud568\uc218\uc758 \uac70\ub4ed\uc81c\uacf1\uc744 \ub098\ud0c0\ub0bc \ub54c\uc5d0\ub294 \uad00\uc2b5\uc801\uc73c\ub85c \uc9c0\uc218\ub97c \ud568\uc218\uc758 \uc606\uc5d0 \ubd99\uc5ec \uc4f4\ub2e4. \uc608\ub97c \ub4e4\uc5b4<br \/>\n\\[<br \/>\n\\sin^2\\theta=(\\sin\\theta)^2,<br \/>\n\\qquad<br \/>\n\\cos^3\\theta=(\\cos\\theta)^3,<br \/>\n\\qquad<br \/>\n\\cdots<br \/>\n\\]<br \/>\n\uc640 \uac19\uc774 \uc4f4\ub2e4.<\/p>\n<p>\uc0bc\uac01\ud568\uc218\uc758 \uc815\uc758\ub85c\ubd80\ud130 \ub2e4\uc74c \ub4f1\uc2dd\uc744 \uc5bb\uc744 \uc218 \uc788\ub2e4.<\/p>\n<ul>\n<li>\\(\\sin^2\\theta+\\cos^2\\theta=1.\\)<\/li>\n<li>\\(\\sin(\\theta+2\\pi)=\\sin\\theta,\\quad \\cos(\\theta+2\\pi)=\\cos\\theta.\\)<\/li>\n<li>\\(\\sin(-\\theta)=-\\sin\\theta,\\quad \\cos(-\\theta)=\\cos\\theta.\\)<\/li>\n<li>\\(\\sin\\left(\\frac{\\pi}{2}-\\theta\\right)=\\cos\\theta,\\quad \\cos\\left(\\frac{\\pi}{2}-\\theta\\right)=\\sin\\theta.\\)<\/li>\n<\/ul>\n<p>\uccab\uc9f8 \ub4f1\uc2dd\uc740 \ud53c\ud0c0\uace0\ub77c\uc2a4 \uc815\ub9ac\ub85c\ubd80\ud130 \uc5bb\uc5b4\uc9c4\ub2e4. \uc2e4\uc81c\ub85c<br \/>\n\\[<br \/>\n\\sin^2\\theta+\\cos^2\\theta<br \/>\n=<br \/>\n\\frac{y^2}{r^2}+\\frac{x^2}{r^2}<br \/>\n=<br \/>\n\\frac{x^2+y^2}{r^2}<br \/>\n=<br \/>\n\\frac{r^2}{r^2}<br \/>\n=<br \/>\n1.<br \/>\n\\]\n<\/p>\n<p>\\(\\theta\\)\uc640 \\(\\theta+2\\pi\\)\ub294 \uac19\uc740 \ubc18\uc9c1\uc120\uc744 \ub098\ud0c0\ub0b4\ubbc0\ub85c \ub450 \ubc88\uc9f8 \ub4f1\uc2dd\uc744 \uc5bb\ub294\ub2e4. \ub610\ud55c \uac01 \\(\\theta\\)\uc5d0 \ub300\uc751\ud558\ub294 \ub2e8\uc704\uc6d0 \uc704\uc758 \uc810\uc744 \\(x\\)\ucd95\uc5d0 \ub300\ud558\uc5ec \ub300\uce6d\uc774\ub3d9\ud558\uba74 \uac01 \\(-\\theta\\)\uc5d0 \ub300\uc751\ud558\ub294 \uc810\uc774 \ub418\ubbc0\ub85c \uc138 \ubc88\uc9f8 \ub4f1\uc2dd\uc744 \uc5bb\ub294\ub2e4. \ub9c8\uc9c0\ub9c9\uc73c\ub85c \uc9c1\uc120 \\(y=x\\)\uc5d0 \ub300\ud558\uc5ec \ub300\uce6d\uc774\ub3d9\ud558\uba74 \ub450 \uc88c\ud45c\uac00 \uc11c\ub85c \ubc14\ub00c\uace0 \uac01 \\(\\theta\\)\uac00 \\(\\frac{\\pi}{2}-\\theta\\)\ub85c \ubc14\ub00c\ubbc0\ub85c \ub124 \ubc88\uc9f8 \ub4f1\uc2dd\uc744 \uc5bb\ub294\ub2e4.<\/p>\n<p>\uc774\uc81c \uc790\uc8fc \uc0ac\uc6a9\ub418\ub294 \uacf5\uc2dd \uc138 \uac00\uc9c0\ub97c \uc0b4\ud3b4\ubcf4\uc790.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 0.6.1. (\ucf54\uc0ac\uc778 \ubc95\uce59)<\/span><\/p>\n<p>\uc0bc\uac01\ud615 \\(\\mathrm{ABC}\\)\uc5d0\uc11c \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<p>(\u2170) \uc81c1 \ucf54\uc0ac\uc778 \ubc95\uce59:<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\na&#038;=b\\cos C+c\\cos B,\\\\[6pt]<br \/>\nb&#038;=a\\cos C+c\\cos A,\\\\[6pt]<br \/>\nc&#038;=a\\cos B+b\\cos A.<br \/>\n\\end{align}<br \/>\n\\]<\/p>\n<p>(\u2171) \uc81c2 \ucf54\uc0ac\uc778 \ubc95\uce59:<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\na^2&#038;=b^2+c^2-2bc\\cos A,\\\\[6pt]<br \/>\nb^2&#038;=a^2+c^2-2ac\\cos B,\\\\[6pt]<br \/>\nc^2&#038;=a^2+b^2-2ab\\cos C.<br \/>\n\\end{align}<br \/>\n\\]<\/p>\n<p>\uc5ec\uae30\uc11c \\(A,\\) \\(B,\\) \\(C\\)\ub294 \uac01\uac01 \uaf2d\uc9d3\uc810 \\(\\mathrm{A},\\) \\(\\mathrm{B},\\) \\(\\mathrm{C}\\)\uc758 \ub0b4\uac01\uc774\uba70, \\(a,\\) \\(b,\\) \\(c\\)\ub294 \uac01\uac01 \uaf2d\uc9d3\uc810 \\(\\mathrm{A},\\) \\(\\mathrm{B},\\) \\(\\mathrm{C}\\)\uc758 \ub300\ubcc0\uc758 \uae38\uc774\uc774\ub2e4.<\/p>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n<p>\uba3c\uc800 \uc81c2 \ucf54\uc0ac\uc778 \ubc95\uce59\uc744 \uc99d\uba85\ud558\uc790. \uc88c\ud45c\ud3c9\uba74\uc5d0\uc11c<br \/>\n\\[<br \/>\n\\mathrm{B}=(0,0),<br \/>\n\\qquad<br \/>\n\\mathrm{C}=(a,0)<br \/>\n\\]<br \/>\n\uc73c\ub85c \ub193\uace0, \uc810 \\(\\mathrm{A}\\)\uac00 \\(x\\)\ucd95\uc758 \uc704\ucabd\uc5d0 \ub193\uc774\ub3c4\ub85d \uc88c\ud45c\ucd95\uc744 \uc7a1\uc790. \\(\\overline{\\mathrm{AB}}=c\\)\uc774\uace0 \\(\\angle\\mathrm{ABC}=B\\)\uc774\ubbc0\ub85c<br \/>\n\\[<br \/>\n\\mathrm{A}=(c\\cos B,\\,c\\sin B).<br \/>\n\\]<br \/>\n\ub530\ub77c\uc11c \ud53c\ud0c0\uace0\ub77c\uc2a4 \uc815\ub9ac\uc5d0 \uc758\ud558\uc5ec<br \/>\n\\[<br \/>\n\\begin{aligned}<br \/>\nb^2<br \/>\n&#038;=<br \/>\n(a-c\\cos B)^2+(c\\sin B)^2\\\\<br \/>\n&#038;=<br \/>\na^2-2ac\\cos B+c^2(\\cos^2B+\\sin^2B)\\\\<br \/>\n&#038;=<br \/>\na^2+c^2-2ac\\cos B.<br \/>\n\\end{aligned}<br \/>\n\\]<br \/>\n\uaf2d\uc9d3\uc810\uc758 \uc5ed\ud560\uc744 \ucc28\ub840\ub85c \ubc14\uafb8\uba74<br \/>\n\\[<br \/>\na^2=b^2+c^2-2bc\\cos A<br \/>\n\\]<br \/>\n\uc640<br \/>\n\\[<br \/>\nc^2=a^2+b^2-2ab\\cos C<br \/>\n\\]<br \/>\n\ub3c4 \uc5bb\ub294\ub2e4. \ub530\ub77c\uc11c \uc81c2 \ucf54\uc0ac\uc778 \ubc95\uce59\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<p>\uc774\uc81c \uc81c1 \ucf54\uc0ac\uc778 \ubc95\uce59\uc744 \uc99d\uba85\ud558\uc790. \uc81c2 \ucf54\uc0ac\uc778 \ubc95\uce59\uc73c\ub85c\ubd80\ud130<br \/>\n\\[<br \/>\n2ab\\cos C=a^2+b^2-c^2<br \/>\n\\]<br \/>\n\uc774\uace0<br \/>\n\\[<br \/>\n2ac\\cos B=a^2+c^2-b^2<br \/>\n\\]<br \/>\n\uc774\ubbc0\ub85c<br \/>\n\\[<br \/>\n\\begin{aligned}<br \/>\nb\\cos C+c\\cos B<br \/>\n&#038;=<br \/>\n\\frac{a^2+b^2-c^2}{2a}<br \/>\n+<br \/>\n\\frac{a^2+c^2-b^2}{2a}\\\\<br \/>\n&#038;=a.<br \/>\n\\end{aligned}<br \/>\n\\]<br \/>\n\ub530\ub77c\uc11c<br \/>\n\\[<br \/>\na=b\\cos C+c\\cos B.<br \/>\n\\]<br \/>\n\ub098\uba38\uc9c0 \ub450 \ub4f1\uc2dd\ub3c4 \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \uc5bb\ub294\ub2e4. <span class=\"qed\"><\/span><\/p>\n<\/div>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 0.6.2. (\uc0ac\uc778 \ubc95\uce59)<\/span><\/p>\n<p>\ubc18\uc9c0\ub984\uc758 \uae38\uc774\uac00 \\(R\\)\uc778 \uc6d0 \\(\\mathrm{O}\\) \uc704\uc5d0 \uc11c\ub85c \ub2e4\ub978 \uc138 \uc810 \\(\\mathrm{A},\\) \\(\\mathrm{B},\\) \\(\\mathrm{C}\\)\uac00 \uc788\ub2e4\uace0 \ud558\uc790. \uc774\ub54c \uc0bc\uac01\ud615 \\(\\mathrm{ABC}\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[<br \/>\n\\frac{a}{\\sin A}<br \/>\n=<br \/>\n\\frac{b}{\\sin B}<br \/>\n=<br \/>\n\\frac{c}{\\sin C}<br \/>\n=<br \/>\n2R<br \/>\n\\]<br \/>\n\uac00 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n<p>\uba3c\uc800 \ubcc0 \\(\\mathrm{BC}\\)\ub97c \uc0dd\uac01\ud558\uc790. \ub9cc\uc57d \\(\\mathrm{BC}\\)\uac00 \uc6d0\uc758 \uc9c0\ub984\uc774\uba74<br \/>\n\\[<br \/>\na=2R,<br \/>\n\\qquad<br \/>\nA=\\frac{\\pi}{2}<br \/>\n\\]<br \/>\n\uc774\ubbc0\ub85c<br \/>\n\\[<br \/>\na=2R\\sin A<br \/>\n\\]<br \/>\n\uc774\ub2e4.<\/p>\n<p>\uc774\uc81c \\(\\mathrm{BC}\\)\uac00 \uc9c0\ub984\uc774 \uc544\ub2c8\ub77c\uace0 \ud558\uc790. \uc120\ubd84 \\(\\mathrm{DC}\\)\uac00 \uc6d0\uc758 \uc9c0\ub984\uc774 \ub418\ub3c4\ub85d \uc6d0 \uc704\uc5d0 \uc810 \\(\\mathrm{D}\\)\ub97c \uc7a1\ub294\ub2e4.<\/p>\n<div style=\"margin-top: 2em; margin-bottom: 2em;\">\n<img loading=\"lazy\" decoding=\"async\" src=\"\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri07.png\" alt=\"\" width=\"212\" height=\"198\" class=\"aligncenter size-full wp-image-7070\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri07.png 1058w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri07-300x281.png 300w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri07-1024x960.png 1024w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri07-768x720.png 768w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri07-585x549.png 585w\" sizes=\"(max-width: 212px) 100vw, 212px\" \/>\n<\/div>\n<p>\ud0c8\ub808\uc2a4\uc758 \uc815\ub9ac\uc5d0 \uc758\ud558\uc5ec<br \/>\n\\[<br \/>\n\\angle\\mathrm{DBC}=\\frac{\\pi}{2}.<br \/>\n\\]<br \/>\n\ub530\ub77c\uc11c \uc9c1\uac01\uc0bc\uac01\ud615 \\(\\mathrm{DBC}\\)\uc5d0\uc11c<br \/>\n\\[<br \/>\n\\sin\\angle\\mathrm{BDC}<br \/>\n=<br \/>\n\\frac{a}{2R}.<br \/>\n\\]<br \/>\n\ud55c\ud3b8 \\(\\angle\\mathrm{BDC}\\)\uc640 \\(A=\\angle\\mathrm{BAC}\\)\ub294 \uac19\uc740 \ud604 \\(\\mathrm{BC}\\)\ub97c \ubc14\ub77c\ubcf4\ub294 \uc6d0\uc8fc\uac01\uc774\ubbc0\ub85c \uc11c\ub85c \uac19\uac70\ub098 \uc11c\ub85c \ubcf4\uac01\uc774\ub2e4. \uc5b4\ub290 \uacbd\uc6b0\uc5d0\ub3c4 \ub450 \uac01\uc758 \uc0ac\uc778\uc740 \uac19\uc73c\ubbc0\ub85c<br \/>\n\\[<br \/>\n\\sin A=\\sin\\angle\\mathrm{BDC}.<br \/>\n\\]<br \/>\n\ub530\ub77c\uc11c<br \/>\n\\[<br \/>\na=2R\\sin A,<br \/>\n\\]<br \/>\n\uc989<br \/>\n\\[<br \/>\n\\frac{a}{\\sin A}=2R<br \/>\n\\]<br \/>\n\uc774\ub2e4. \uac19\uc740 \ubc29\ubc95\uc744 \ub2e4\ub978 \ub450 \ubcc0\uc5d0 \uc801\uc6a9\ud558\uba74<br \/>\n\\[<br \/>\n\\frac{b}{\\sin B}=2R,<br \/>\n\\qquad<br \/>\n\\frac{c}{\\sin C}=2R<br \/>\n\\]<br \/>\n\ub97c \uc5bb\ub294\ub2e4. <span class=\"qed\"><\/span><\/p>\n<\/div>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 0.6.3. (\uc0bc\uac01\ud568\uc218\uc758 \ub367\uc148 \uc815\ub9ac)<\/span><\/p>\n<p>\\(\\alpha\\)\uc640 \\(\\beta\\)\uac00 \uc2e4\uc218\uc77c \ub54c \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ol class=\"bracket\">\n<li>\\(\\sin(\\alpha+\\beta)=\\sin\\alpha\\cos\\beta+\\cos\\alpha\\sin\\beta\\).<\/li>\n<li>\\(\\sin(\\alpha-\\beta)=\\sin\\alpha\\cos\\beta-\\cos\\alpha\\sin\\beta\\).<\/li>\n<li>\\(\\cos(\\alpha+\\beta)=\\cos\\alpha\\cos\\beta-\\sin\\alpha\\sin\\beta\\).<\/li>\n<li>\\(\\cos(\\alpha-\\beta)=\\cos\\alpha\\cos\\beta+\\sin\\alpha\\sin\\beta\\).<\/li>\n<\/ol>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n<p>\ub2e8\uc704\uc6d0 \uc704\uc5d0\uc11c \uac01 \\(\\alpha,\\beta\\)\uc5d0 \ub300\uc751\ud558\ub294 \ub450 \uc810\uc744 \uac01\uac01<br \/>\n\\[<br \/>\n\\mathrm{P}=(\\cos\\alpha,\\,\\sin\\alpha),<br \/>\n\\qquad<br \/>\n\\mathrm{Q}=(\\cos\\beta,\\,\\sin\\beta)<br \/>\n\\]<br \/>\n\ub77c\uace0 \ud558\uc790.<\/p>\n<div style=\"margin-top: 2em; margin-bottom: 2em;\">\n<img loading=\"lazy\" decoding=\"async\" src=\"\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri08.png\" alt=\"\" width=\"245\" height=\"250\" class=\"aligncenter size-full wp-image-7071\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri08.png 1225w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri08-294x300.png 294w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri08-1004x1024.png 1004w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri08-768x784.png 768w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri08-1170x1194.png 1170w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri08-585x597.png 585w\" sizes=\"(max-width: 245px) 100vw, 245px\" \/>\n<\/div>\n<p>\ub450 \ubc18\uc9c1\uc120 \\(\\mathrm{OP}\\)\uc640 \\(\\mathrm{OQ}\\) \uc0ac\uc774\uc758 \uc791\uc740 \uac01\uc744 \\(\\gamma\\)\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(\\gamma\\)\ub294 \\(\\alpha-\\beta\\) \ub610\ub294 \\(\\beta-\\alpha\\)\uc640 \\(2\\pi\\)\uc758 \uc815\uc218\ubc30\ub9cc\ud07c \ucc28\uc774\uac00 \ub098\ub294 \uac01\uc774\ubbc0\ub85c, \uc0ac\uc778\uacfc \ucf54\uc0ac\uc778\uc758 \uc8fc\uae30\uc131\uacfc \ucf54\uc0ac\uc778\uc774 \uc9dd\ud568\uc218\ub77c\ub294 \uc0ac\uc2e4\uc5d0 \uc758\ud558\uc5ec<br \/>\n\\[<br \/>\n\\cos\\gamma=\\cos(\\alpha-\\beta)<br \/>\n\\]<br \/>\n\uc774\ub2e4.<\/p>\n<p>\uc0bc\uac01\ud615 \\(\\mathrm{POQ}\\)\uc5d0 \ucf54\uc0ac\uc778 \ubc95\uce59\uc744 \uc801\uc6a9\ud558\uba74 \\(\\overline{\\mathrm{OP}}=\\overline{\\mathrm{OQ}}=1\\)\uc774\ubbc0\ub85c<br \/>\n\\[<br \/>\n\\overline{\\mathrm{PQ}}^2<br \/>\n=<br \/>\n2-2\\cos(\\alpha-\\beta).<br \/>\n\\]<br \/>\n\ud55c\ud3b8 \ub450 \uc810\uc758 \uc88c\ud45c\ub97c \uc774\uc6a9\ud558\uba74<br \/>\n\\[<br \/>\n\\overline{\\mathrm{PQ}}^2<br \/>\n=<br \/>\n(\\cos\\alpha-\\cos\\beta)^2<br \/>\n+<br \/>\n(\\sin\\alpha-\\sin\\beta)^2.<br \/>\n\\]<br \/>\n\ub530\ub77c\uc11c<br \/>\n\\[<br \/>\n\\begin{aligned}<br \/>\n2-2\\cos(\\alpha-\\beta)<br \/>\n&#038;=<br \/>\n(\\cos\\alpha-\\cos\\beta)^2<br \/>\n+<br \/>\n(\\sin\\alpha-\\sin\\beta)^2\\\\<br \/>\n&#038;=<br \/>\n2<br \/>\n&#8211;<br \/>\n2\\cos\\alpha\\cos\\beta<br \/>\n&#8211;<br \/>\n2\\sin\\alpha\\sin\\beta.<br \/>\n\\end{aligned}<br \/>\n\\]<br \/>\n\uadf8\ub7ec\ubbc0\ub85c<br \/>\n\\[<br \/>\n\\cos(\\alpha-\\beta)<br \/>\n=<br \/>\n\\cos\\alpha\\cos\\beta+\\sin\\alpha\\sin\\beta.<br \/>\n\\]<br \/>\n\uc774\ub85c\uc368 (4)\ub97c \uc5bb\uc5c8\ub2e4.<\/p>\n<p>(4)\uc5d0\uc11c \\(\\beta\\)\ub97c \\(-\\beta\\)\ub85c \ubc14\uafb8\uace0<br \/>\n\\[<br \/>\n\\cos(-\\beta)=\\cos\\beta,<br \/>\n\\qquad<br \/>\n\\sin(-\\beta)=-\\sin\\beta<br \/>\n\\]<br \/>\n\ub97c \uc0ac\uc6a9\ud558\uba74<br \/>\n\\[<br \/>\n\\cos(\\alpha+\\beta)<br \/>\n=<br \/>\n\\cos\\alpha\\cos\\beta-\\sin\\alpha\\sin\\beta<br \/>\n\\]<br \/>\n\ub97c \uc5bb\ub294\ub2e4. \ub530\ub77c\uc11c (3)\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<p>\uc774\uc81c (3)\uc5d0\uc11c \\(\\alpha\\)\ub97c \\(\\frac{\\pi}{2}-\\alpha\\)\ub85c \ubc14\uafb8\uba74<br \/>\n\\[<br \/>\n\\begin{aligned}<br \/>\n\\cos\\left(<br \/>\n\\frac{\\pi}{2}-\\alpha+\\beta<br \/>\n\\right)<br \/>\n&#038;=<br \/>\n\\cos\\left(\\frac{\\pi}{2}-\\alpha\\right)\\cos\\beta<br \/>\n&#8211;<br \/>\n\\sin\\left(\\frac{\\pi}{2}-\\alpha\\right)\\sin\\beta.<br \/>\n\\end{aligned}<br \/>\n\\]<br \/>\n\uc55e\uc5d0\uc11c \uc5bb\uc740 \uad00\uacc4\ub97c \uc0ac\uc6a9\ud558\uba74<br \/>\n\\[<br \/>\n\\sin(\\alpha-\\beta)<br \/>\n=<br \/>\n\\sin\\alpha\\cos\\beta-\\cos\\alpha\\sin\\beta.<br \/>\n\\]<br \/>\n\ub530\ub77c\uc11c (2)\uac00 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<p>\ub9c8\uc9c0\ub9c9\uc73c\ub85c (2)\uc5d0\uc11c \\(\\beta\\)\ub97c \\(-\\beta\\)\ub85c \ubc14\uafb8\uba74<br \/>\n\\[<br \/>\n\\sin(\\alpha+\\beta)<br \/>\n=<br \/>\n\\sin\\alpha\\cos\\beta+\\cos\\alpha\\sin\\beta<br \/>\n\\]<br \/>\n\ub97c \uc5bb\ub294\ub2e4. \ub530\ub77c\uc11c (1)\ub3c4 \uc131\ub9bd\ud55c\ub2e4. <span class=\"qed\"><\/span><\/p>\n<\/div>\n<p><!-- ##################################################################### --><br \/>\n<!--\n\n\n<h2 class=\"itc_h2\">\uc81c\ubaa9<\/h2>\n\n\n--><\/p>\n<p><!--\n\n\n\n<div class=\"theorem margintop2\">\n\n\n<p><span class=\"theorem\">\uc815\ub9ac 1.<\/span>\n\n\n<\/p>\n\n<\/div>\n\n\n\n\n\n<div class=\"proof\">\n\n\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n\n\n\n\n<p>\n\n<span class=\"qed\"><\/span><\/p>\n\n<\/div>\n\n\n\n\n########\n\n\u201c\u201d\n\u2018\u2019\n\n\n\n<div class=\"example\">\n\n\n<p><span class=\"example\">\ubcf4\uae30 1.<\/span>\n\n<\/p>\n\n<\/div>\n\n\n\n\n\n<h2 class=\"itc_h2\"><\/h2>\n\n\n\n--><\/p>\n<p><!--\n\n\n<div style=\"display: none; visibility: hidden;\">\n\\[\n\\newcommand{\\Hom}{{\\operatorname{Hom}}}\n\\newcommand{\\Mat}{{\\operatorname{Mat}}}\n\\newcommand{\\proj}{{\\operatorname{proj}}}\n\\newcommand{\\adj}{{\\operatorname{adj}}}\n\\]\n<\/div>\n\n\n--><\/p>\n<div class=\"box itc_prev_next_box\">\n<ul class=\"itc_ul\">\n<li class=\"itc_li_prev\">\uc55e\uc758 \uae00 : <a href=\"..\/complex-numbers\">\ud589\ub82c\uacfc \ubcf5\uc18c\uc218<\/a><\/li>\n<li class=\"itc_li_next\">\ub2e4\uc74c \uae00 : <a href=\"..\/exponential-and-logarithmic-functions\">\uc9c0\uc218\ud568\uc218\uc640 \ub85c\uadf8\ud568\uc218<\/a><\/li>\n<\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 0\uc7a5 6\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; (\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30) \ud638\ub3c4\ubc95 \uadf8\ub9bc\uacfc \uac19\uc774 \ubc18\uc9c0\ub984\uc758 \uae38\uc774\uac00 \\(1\\)\uc778 \uc6d0\uc744 \uc0dd\uac01\ud558\uc790. \ud638\uc758 \uae38\uc774\uac00 \\(1\\)\uc778 \ubd80\ucc44\uaf34\uc758 \uc911\uc2ec\uac01\uc758 \ud06c\uae30\ub97c \\(\\boldsymbol{1}\\)\ub77c\ub514\uc548(radian)\uc73c\ub85c \uc815\uc758\ud55c\ub2e4. \ubc18\uc9c0\ub984\uc758 \uae38\uc774\uac00 \\(1\\)\uc778 \uc6d0\uc758 \ub458\ub808\uc758 \uae38\uc774\uac00 \\(2\\pi\\)\uc774\ubbc0\ub85c \\( 180^\\circ=\\pi\\,\\text{radians} \\) \uc774\ub2e4. \uc774\uc640 \uac19\uc774 \ub77c\ub514\uc548\uc744 \ub2e8\uc704\ub85c \uac01\uc758 \ud06c\uae30\ub97c \ub098\ud0c0\ub0b4\ub294 \ubc29\ubc95\uc744 \ud638\ub3c4\ubc95(circular measure)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \ud638\ub3c4\ubc95\uc73c\ub85c \uac01\uc758 \ud06c\uae30\ub97c \ub098\ud0c0\ub0bc \ub54c \ub2e8\uc704 \u2018\ub77c\ub514\uc548\u2019\uc744 \uc0dd\ub7b5\ud558\ub294 \uacbd\uc6b0\uac00 \ub9ce\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \uac01\uc758 \ud06c\uae30\ub97c \ub2e8\uc704 \uc5c6\uc774&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":6620,"menu_order":16,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"class_list":["post-6984","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6984","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=6984"}],"version-history":[{"count":36,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6984\/revisions"}],"predecessor-version":[{"id":10128,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6984\/revisions\/10128"}],"up":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6620"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=6984"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}