{"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":"2022-03-06T19:49:15","modified_gmt":"2022-03-06T10:49:15","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\\[180^\\circ = \\pi \\,\\text{radians}\\]<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 \u2018\ub77c\ub514\uc548\u2019\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. \uc989 \ubc18\uc2dc\uacc4\ubc29\ud5a5\uc73c\ub85c \ud68c\uc804\ud55c \uc815\ub3c4\ub97c \uac01\uc73c\ub85c \ud45c\ud604\ud560 \ub550 \uac01\uc758 \ud06c\uae30\ub97c \uc591\uc218\ub85c \ub098\ud0c0\ub0b4\uace0 \uc2dc\uacc4\ubc29\ud5a5\uc73c\ub85c \ud68c\uc804\ud55c \uc815\ub3c4\ub97c \uac01\uc73c\ub85c \ud45c\ud604\ud560 \ub550 \uac01\uc758 \ud06c\uae30\ub97c \uc74c\uc218\ub85c \ub098\ud0c0\ub0b8\ub2e4. \ud55c \ubc14\ud034\ub97c \ucd08\uacfc\ud558\ub294 \ud68c\uc804\uc744 \uac01\uc73c\ub85c \ub098\ud0c0\ub0bc \ub550 \uc808\ub313\uac12\uc774 \\(2\\pi\\)\ubcf4\ub2e4 \ud070 \uac12\uc744 \uc0ac\uc6a9\ud55c\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. \uadf8\ub9ac\uace0 \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 \uc810 \\(\\mathrm{P}\\)\ub97c \uc0dd\uac01\ud558\uc790. (\uc5ec\uae30\uc11c \uc810 \\(\\mathrm{P}\\)\ub294 \uc6d0\uc810\uc774 \uc544\ub2cc \uc810\uc744 \uc0dd\uac01\ud55c\ub2e4.)<\/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>\uadf8\ub9bc\uacfc \uac19\uc774 \uc810 \\(\\mathrm{P}\\)\uc758 \uc88c\ud45c\ub97c \\(\\mathrm{P}(x,\\,y)\\)\ub77c\uace0 \ud558\uc790. \uadf8\ub9ac\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\\[\\sin\\theta = \\frac{y}{r} ,\\quad \\cos\\theta = \\frac{x}{y} .\\]<br \/>\n\ub2e4\ub978 \uc0bc\uac01\ud568\uc218\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<br \/>\n\\[\\begin{gather}<br \/>\n\\tan\\theta = \\frac{\\sin\\theta}{\\cos\\theta} ,\\quad<br \/>\n\\sec\\theta = \\frac{1}{\\cos\\theta} ,\\\\[5pt]<br \/>\n\\operatorname{cosec}\\theta = \\frac{1}{\\sin\\theta} ,\\quad<br \/>\n\\cot\\theta = \\frac{\\cos\\theta}{\\sin\\theta}.<br \/>\n\\end{gather}\\]<br \/>\n\uac01 \uc0bc\uac01\ud568\uc218\ub294 \ub2f9\uc5f0\ud788 \ubd84\uc218\uc2dd\uc758 \ubd84\ubaa8\uac00 \\(0\\)\uc774 \ub418\ub3c4\ub85d \ud558\uc9c0 \uc54a\ub294 \\(\\theta\\)\uc5d0 \ub300\ud574\uc11c\ub9cc \uc815\uc758\ub41c\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 \ub550 \uad00\uc2b5\uc801\uc73c\ub85c \uc9c0\uc218\ub97c \ud568\uc218\uc758 \uc606\uc5d0 \ubd99\uc5ec \uc4f4\ub2e4. \uc608\ucee8\ub300 \ub2e4\uc74c\uacfc \uac19\uc774 \uc4f4\ub2e4.<br \/>\n\\[\\sin^2 \\theta = (\\sin \\theta )^2 ,\\,\\, \\cos^3 \\theta = (\\cos\\theta )^3 ,\\,\\, \\cdots\\]<br \/>\n\uc0bc\uac01\ud568\uc218\uc758 \uc815\uc758\ub97c \uc774\uc6a9\ud558\uba74 \ub2e4\uc74c \ub4f1\uc2dd\uc744 \uc720\ub3c4\ud560 \uc218 \uc788\ub2e4.<\/p>\n<ul>\n<li>\\( \\sin^2 \\theta + \\cos^2 \\theta = 1 . \\)<\/li>\n<li>\\( \\sin(\\theta + 2\\pi ) = \\sin\\theta ,\\,\\, \\cos(\\theta + 2\\pi ) = \\cos\\theta . \\)<\/li>\n<li>\\( \\sin(-\\theta ) = &#8211; \\sin\\theta ,\\,\\, \\cos(-\\theta ) = \\cos\\theta . \\)<\/li>\n<li>\\( \\sin\\left(\\frac{\\pi}{2} &#8211; \\theta \\right) = \\cos\\theta ,\\,\\, \\cos\\left(\\frac{\\pi}{2} &#8211; \\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:<br \/>\n\\[\\sin^2 \\theta + \\cos^2 \\theta = \\frac{y^2}{r^2} + \\frac{x^2}{r^2} = \\frac{x^2 +y^2}{r^2} = \\frac{r^2}{r^2} = 1.\\]<br \/>\n\ub450 \ubc88\uc9f8 \ub4f1\uc2dd\uc740 \uc0bc\uac01\ud568\uc218\uac00 \uc8fc\uae30\ud568\uc218\uc784\uc744 \ub098\ud0c0\ub0b8\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) \uc81c 1 \ucf54\uc0ac\uc778 \ubc95\uce59:<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(\u2171) \uc81c 2 \ucf54\uc0ac\uc778 \ubc95\uce59:<br \/>\n\\[\\begin{align}<br \/>\na^2 &#038;= b^2 + c^2 &#8211; 2bc \\cos A , \\\\[6pt]<br \/>\nb^2 &#038;= a^2 + c^2 &#8211; 2ac \\cos B , \\\\[6pt]<br \/>\nc^2 &#038;= a^2 + b^2 &#8211; 2ab \\cos C .<br \/>\n\\end{align}\\]<br \/>\n\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.\n<\/p>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n<p>\uc81c 1 \ucf54\uc0ac\uc778 \ubc95\uce59\uc740 \ub2e4\uc74c \uadf8\ub9bc\uc744 \uc774\uc6a9\ud558\uba74 \uc27d\uac8c \uc99d\uba85\ub41c\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_tri06.png\" alt=\"\" width=\"285\" height=\"179\" class=\"aligncenter size-full wp-image-7069\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri06.png 1423w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri06-300x188.png 300w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri06-1024x643.png 1024w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri06-768x482.png 768w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri06-1170x734.png 1170w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/calculus_00-06_tri06-585x367.png 585w\" sizes=\"(max-width: 285px) 100vw, 285px\" \/>\n<\/div>\n<p>\uc81c 2 \ucf54\uc0ac\uc778 \ubc95\uce59\uc740 \uc81c 1 \ucf54\uc0ac\uc778 \ubc95\uce59\uc744 \uacb0\ud569\ud558\uba74 \uc99d\uba85\ub41c\ub2e4. \uc989 \uc81c 1 \ucf54\uc0ac\uc778 \ubc95\uce59\uc758 \uc138 \ub4f1\uc2dd\uc5d0 \uc21c\uc11c\ub300\ub85c \uc591\ubcc0\uc5d0 \\(a,\\) \\(b,\\) \\(c\\)\ub97c \uacf1\ud558\uba74 \ub2e4\uc74c\uc744 \uc5bb\ub294\ub2e4.<br \/>\n\\[\\begin{align}<br \/>\na^2 &#038;= ab \\cos C + ac \\cos B , \\\\[6pt]<br \/>\nb^2 &#038;= ab \\cos C + bc \\cos C , \\\\[6pt]<br \/>\nc^2 &#038;= ac \\cos B + bc \\cos A .<br \/>\n\\end{align}\\]<br \/>\n\uc774 \uc2dd\uc744 \uacb0\ud569\ud558\uba74 \uc81c 2 \ucf54\uc0ac\uc778 \ubc95\uce59\uc758 \uc138 \ub4f1\uc2dd\uc744 \uc5bb\ub294\ub2e4.<br \/>\n<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 \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<br \/>\n\\[\\frac{a}{\\sin A} = \\frac{b}{\\sin B} = \\frac{c}{\\sin C} = 2R.\\]\n<\/p>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n<p>\ub2e4\uc74c \uadf8\ub9bc\uc744 \uc0b4\ud3b4\ubcf4\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_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>\uc810 \\(\\mathrm{B}\\)\uc640 \\(\\mathrm{C}\\)\ub97c \uace0\uc815\ud558\uace0, \uc120\ubd84 \\(\\mathrm{DC}\\)\uac00 \uc6d0\uc758 \uc9c0\ub984\uc774 \ub418\ub3c4\ub85d \uc810 \\(\\mathrm{D}\\)\ub97c \uc7a1\ub294\ub2e4. \uadf8\ub7ec\uba74 \uc120\ubd84 \\(\\mathrm{DC}\\)\uc758 \uae38\uc774\uac00 \\(2R\\)\uc774\uace0 \\(\\angle \\mathrm{A} = \\angle \\mathrm{D}\\)\uc774\ubbc0\ub85c<br \/>\n\\[2R \\sin A = 2R \\sin D = a\\]<br \/>\n\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c<br \/>\n\\[\\frac{a}{\\sin A} = 2R\\]<br \/>\n\ub97c \uc5bb\ub294\ub2e4. \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \ub2e4\ub978 \ub450 \ubd84\uc218\uc2dd\uc758 \uac12\uc774 \\(2R\\)\ub77c\ub294 \uc0ac\uc2e4\uc744 \uc720\ub3c4\ud560 \uc218 \uc788\ub2e4.<br \/>\n<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 &#8211; \\beta ) = \\sin \\alpha \\cos \\beta &#8211; \\cos \\alpha \\sin \\beta \\)<\/li>\n<li>\\( \\cos ( \\alpha + \\beta ) = \\cos \\alpha \\cos \\beta &#8211; \\sin \\alpha \\sin \\beta \\)<\/li>\n<li>\\( \\cos ( \\alpha &#8211; \\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>\ub2e4\uc74c \uadf8\ub9bc\uc744 \uc0b4\ud3b4\ubcf4\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>\uc0bc\uac01\ud615 \\(\\mathrm{POQ}\\)\uc5d0 \ucf54\uc0ac\uc778 \ubc95\uce59\uc744 \uc801\uc6a9\ud558\uba74 \ub2e4\uc74c \ub4f1\uc2dd\uc744 \uc5bb\ub294\ub2e4.<br \/>\n\\[\\overline{\\mathrm{PQ}}^2 = \\overline{\\mathrm{OP}}^2 + \\overline{\\mathrm{OQ}}^2 &#8211; 2 \\cdot \\overline{\\mathrm{OP}} \\cdot \\overline{\\mathrm{OQ}} \\cdot \\cos ( \\alpha &#8211; \\beta ).\\]<br \/>\n\uadf8\ub7f0\ub370 \\(\\overline{\\mathrm{OP}} = \\overline{\\mathrm{OQ}} = 1\\)\uc774\ubbc0\ub85c, \uc704 \uc2dd\uc73c\ub85c\ubd80\ud130 \ub2e4\uc74c \ub4f1\uc2dd\uc744 \uc5bb\ub294\ub2e4.<br \/>\n\\[ ( \\cos \\alpha &#8211; \\cos \\beta )^2 + ( \\sin \\alpha &#8211; \\sin \\beta )^2 = 1^2 + 1^2 &#8211; 2 \\times 1 \\times 1 \\times \\cos ( \\alpha &#8211; \\beta ).\\]<br \/>\n\uc774 \uc2dd\uacfc<br \/>\n\\[ \\sin^2 \\alpha + \\cos^2 \\alpha = 1 , \\,\\, \\sin^2 \\beta + \\cos^2 \\beta = 1 \\]<br \/>\n\uc744 \uacb0\ud569\ud558\uba74 \ub2e4\uc74c \ub4f1\uc2dd\uc744 \uc5bb\ub294\ub2e4.<br \/>\n\\[\\cos(\\alpha &#8211; \\beta ) = \\cos \\alpha \\cos \\beta + \\sin \\alpha \\sin \\beta .\\]<br \/>\n\uc774 \uc2dd\uc5d0\uc11c \\(\\beta\\)\ub97c \\(-\\beta\\)\ub85c \ubc14\uafb8\uba74 \ub2e4\uc74c \ub4f1\uc2dd\uc744 \uc5bb\ub294\ub2e4.<br \/>\n\\[\\cos ( \\alpha + \\beta ) = \\cos \\alpha \\cos \\beta &#8211; \\sin \\alpha \\sin \\beta .\\]<br \/>\n\uc774 \uc2dd\uc5d0\uc11c \\(\\alpha\\)\ub97c \\(\\frac{\\pi}{2} &#8211; \\alpha\\)\ub85c \ubc14\uafb8\uba74<br \/>\n\\[\\cos\\left\\{ \\left( \\frac{\\pi}{2} &#8211; \\alpha \\right) + \\beta \\right\\}<br \/>\n= \\cos \\left( \\frac{\\pi}{2} &#8211; \\alpha \\right) \\cos\\beta &#8211; \\sin\\left(\\frac{\\pi}{2} &#8211; \\alpha\\right) \\sin\\beta\\]<br \/>\n\uc774\ubbc0\ub85c \ub2e4\uc74c\uc744 \uc5bb\ub294\ub2e4.<br \/>\n\\[\\sin ( \\alpha &#8211; \\beta ) = \\sin \\alpha \\cos \\beta &#8211; \\cos \\alpha \\sin \\beta .\\]<br \/>\n\uc774 \uc2dd\uc5d0\uc11c \\(\\beta\\)\ub97c \\(-\\beta\\)\ub85c \ubc14\uafb8\uba74 \ub2e4\uc74c \ub4f1\uc2dd\uc744 \uc5bb\ub294\ub2e4.<br \/>\n\\[ \\sin ( \\alpha + \\beta ) = \\sin \\alpha \\cos \\beta + \\cos \\alpha \\sin \\beta . \\]<br \/>\n\uc774\ub85c\uc368 \uc815\ub9ac\uc758 \ub4f1\uc2dd [4], [3], [2], [1]\uc744 \uc5bb\uc5c8\ub2e4.<br \/>\n<span class=\"qed\"><\/span><\/p>\n<\/div>\n<p>\uc0ac\uc2e4 \uc815\ub9ac 0.6.3\uc758 \uc99d\uba85\uc740 \\(\\alpha\\)\uc640 \\(\\beta\\)\uac00 \\(2\\pi\\) \ubbf8\ub9cc \uc591\uc218\uc774\uace0, \ub450 \uac01\uc758 \ucc28\uc774\uac00 \\(\\pi\\) \ubbf8\ub9cc\uc778 \uacbd\uc6b0\ub9cc \uc99d\uba85\ud55c \uac83\uc774\ub2e4. \ud558\uc9c0\ub9cc \uc0ac\uc778\uacfc \ucf54\uc0ac\uc778\uc758 \uc8fc\uae30\uc131\uacfc \uc55e\uc5d0\uc11c \uc0b4\ud3b4\ubcf8 \uc0bc\uac01\ud568\uc218\uc758 \ub4f1\uc2dd\uc744 \uc774\uc6a9\ud558\uba74 \uc784\uc758\uc758 \uac01 \\(\\alpha\\)\uc640 \\(\\beta\\)\uc5d0 \ub300\ud558\uc5ec \ub124 \uac1c\uc758 \ub4f1\uc2dd\uc774 \uc131\ub9bd\ud568\uc744 \ud655\uc778\ud560 \uc218 \uc788\ub2e4.<\/p>\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&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":"","_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":35,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6984\/revisions"}],"predecessor-version":[{"id":8380,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6984\/revisions\/8380"}],"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}]}}