{"id":360,"date":"2023-07-04T16:06:25","date_gmt":"2023-07-04T16:06:25","guid":{"rendered":"https:\/\/mathority.org\/pt\/funcao-tangente\/"},"modified":"2023-07-04T16:06:25","modified_gmt":"2023-07-04T16:06:25","slug":"funcao-tangente","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/funcao-tangente\/","title":{"rendered":"Fun\u00e7\u00e3o tangente"},"content":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 tudo sobre a fun\u00e7\u00e3o tangente: o que \u00e9, qual a sua f\u00f3rmula, como represent\u00e1-la em um gr\u00e1fico, as caracter\u00edsticas da fun\u00e7\u00e3o, seu per\u00edodo, etc. Al\u00e9m disso, voc\u00ea poder\u00e1 ver exemplos de fun\u00e7\u00f5es tangentes para compreender totalmente o conceito. Ele ainda explica o teorema da tangente e as rela\u00e7\u00f5es que a fun\u00e7\u00e3o tangente tem com outras rela\u00e7\u00f5es trigonom\u00e9tricas. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-funcion-tangente\"><\/span> F\u00f3rmula da fun\u00e7\u00e3o tangente <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div style=\"background:linear-gradient(to bottom, #FFFFFF 0%, #FFE0B2 100%); padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px;\">\n<p style=\"text-align:left\"> A <strong>fun\u00e7\u00e3o tangente<\/strong> de um \u00e2ngulo \u03b1 \u00e9 uma fun\u00e7\u00e3o trigonom\u00e9trica cuja f\u00f3rmula \u00e9 definida como a raz\u00e3o entre o ramo oposto e o ramo cont\u00edguo (ou adjacente) de um tri\u00e2ngulo ret\u00e2ngulo (tri\u00e2ngulo com \u00e2ngulo reto). <\/p>\n<\/div>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-153\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-de-la-fonction-tangente.webp\" alt=\"Qual \u00e9 a f\u00f3rmula da fun\u00e7\u00e3o tangente?\" class=\"wp-image-299\" width=\"291\" height=\"71\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/fonctions-trigonometriques.webp\" alt=\"tangente \u00e9 uma fun\u00e7\u00e3o trigonom\u00e9trica\" class=\"wp-image-277\" width=\"233\" height=\"159\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<p> Este tipo de fun\u00e7\u00e3o matem\u00e1tica tamb\u00e9m \u00e9 chamada de fun\u00e7\u00e3o tangent\u00f3ide, tangen\u00f3ide ou tangencial. E pode ser expresso com a abreviatura \u201ctg\u201d ou mesmo \u201ctan\u201d.<\/p>\n<p> A fun\u00e7\u00e3o tangente \u00e9 uma das tr\u00eas raz\u00f5es trigonom\u00e9tricas mais conhecidas, junto com o seno e o cosseno de um \u00e2ngulo. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"valores-caracteristicos-de-la-funcion-tangente\"><\/span> Valores caracter\u00edsticos da fun\u00e7\u00e3o tangente<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Existem certos \u00e2ngulos que se repetem frequentemente e, portanto, \u00e9 conveniente saber o valor da fun\u00e7\u00e3o tangente nestes \u00e2ngulos: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/valeurs-caracteristiques-fonction-tangente.webp\" alt=\"valores caracter\u00edsticos da fun\u00e7\u00e3o tangente\" class=\"wp-image-300\" width=\"740\" height=\"195\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Por outro lado, a fun\u00e7\u00e3o tangente pode ser ligada \u00e0s fun\u00e7\u00f5es seno e cosseno pela seguinte identidade trigonom\u00e9trica fundamental:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97ecd1e5d04b9e0aa9aab914a5ef9fe4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tg } \\alpha = \\cfrac{\\text{sen }\\alpha}{\\text{cos }\\alpha}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"102\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Assim, o sinal da fun\u00e7\u00e3o tangente depende do quadrante em que o \u00e2ngulo est\u00e1 localizado:<\/p>\n<ul>\n<li> Se o \u00e2ngulo pertencer ao primeiro quadrante, sua tangente ser\u00e1 positiva, pois neste quadrante o seno e o cosseno tamb\u00e9m s\u00e3o positivos.<\/li>\n<li> Se o \u00e2ngulo cair no segundo quadrante, sua tangente ser\u00e1 negativa, pois neste quadrante o seno \u00e9 positivo mas o cosseno \u00e9 negativo.<\/li>\n<li> Se o \u00e2ngulo estiver no terceiro quadrante, sua tangente ser\u00e1 positiva, pois neste quadrante o seno e o cosseno s\u00e3o negativos.<\/li>\n<li> Se o \u00e2ngulo estiver no quarto quadrante, sua tangente ser\u00e1 negativa, pois neste quadrante o seno \u00e9 negativo e ao inv\u00e9s o cosseno \u00e9 positivo. <\/li>\n<\/ul>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/fonction-signe-de-la-tangente.webp\" alt=\"sinal da fun\u00e7\u00e3o tangente\" class=\"wp-image-301\" width=\"305\" height=\"295\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"representacion-grafica-de-la-funcion-tangente\"><\/span> Representa\u00e7\u00e3o gr\u00e1fica da fun\u00e7\u00e3o tangente<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Com a tabela de valores que vimos na se\u00e7\u00e3o anterior, podemos representar graficamente a fun\u00e7\u00e3o tangente. E fazendo o gr\u00e1fico da fun\u00e7\u00e3o tangente, obtemos: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/representation-graphique-fonction-tangente.webp\" alt=\"representa\u00e7\u00e3o gr\u00e1fica da fun\u00e7\u00e3o tangente\" class=\"wp-image-298\" width=\"779\" height=\"451\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Como pode ser visto no gr\u00e1fico, os valores das imagens da fun\u00e7\u00e3o tangente n\u00e3o s\u00e3o limitados, ao contr\u00e1rio das fun\u00e7\u00f5es seno e cosseno. Al\u00e9m disso, os valores se repetem a cada 180 graus (\u03c0 radianos), portanto \u00e9 uma <strong>fun\u00e7\u00e3o peri\u00f3dica<\/strong> cujo per\u00edodo \u00e9 180\u00ba.<\/p>\n<p> Por outro lado, neste gr\u00e1fico podemos ver que a fun\u00e7\u00e3o tangente \u00e9 <strong>\u00edmpar<\/strong> , pois seus elementos opostos possuem imagens opostas, ou seja, \u00e9 sim\u00e9trica em rela\u00e7\u00e3o \u00e0 origem (0,0). Por exemplo, a tangente de 45\u00b0 vale 1 e a de -45\u00b0 vale -1.<\/p>\n<p> Finalmente, tamb\u00e9m podemos ver que a fun\u00e7\u00e3o tangente possui <strong>ass\u00edntotas verticais<\/strong> . Por exemplo, chega muito perto da linha x=90\u00ba, mas nunca a toca, e a mesma coisa acontece a cada 180 graus. Isso significa que o limite da fun\u00e7\u00e3o nesses pontos tende ao infinito. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-funcion-tangente\"><\/span> Propriedades da fun\u00e7\u00e3o tangente<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A fun\u00e7\u00e3o tangente possui as seguintes caracter\u00edsticas:<\/p>\n<ul>\n<li> O dom\u00ednio da fun\u00e7\u00e3o tangente s\u00e3o todos os n\u00fameros reais, exceto os pontos onde h\u00e1 uma ass\u00edntota vertical:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-29b8cf7eff7870df6c68bac95de5bdaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{Dom } f = \\mathbb{R} - \\left\\{(2k+1)\\cdot \\frac{\\pi}{2} \\right\\} \\qquad k \\in \\mathbb{Z}\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"308\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e82581257a3efb00f920674c5318bc85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{Dom } f = \\mathbb{R} - \\left\\{\\ldots \\ , \\ -\\frac{\\pi}{2} \\ , \\ \\frac{\\pi}{2} \\ , \\ \\frac{3\\pi}{2} \\ , \\ \\ldots \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"326\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> O contradom\u00ednio ou contradom\u00ednio da fun\u00e7\u00e3o tangente s\u00e3o todos n\u00fameros reais.<\/li>\n<\/ul>\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>\n<li> \u00c9 uma fun\u00e7\u00e3o cont\u00ednua e \u00edmpar com periodicidade \u03c0.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4338f2dfc213a0dbac8aba420dd33179_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg}(-x) =- \\text{tg }x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Este tipo de fun\u00e7\u00e3o trigonom\u00e9trica possui um \u00fanico ponto de intersec\u00e7\u00e3o com o eixo y (eixo Y) no ponto (0,0).<\/li>\n<\/ul>\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>\n<li> Em vez disso, ele intercepta periodicamente a abcissa (eixo X) em v\u00e1rias coordenadas de pi.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eab7b9b3afd7706a5a1aea4aca69413c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (k\\pi ,0) \\qquad k \\in \\mathbb{Z}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> A fun\u00e7\u00e3o \u00e9 estritamente crescente em todo o dom\u00ednio, portanto n\u00e3o tem m\u00e1ximo nem m\u00ednimo.<\/li>\n<\/ul>\n<ul>\n<li> A derivada da tangente \u00e9:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ad6c6fdefd907c51ac1e7b85e59260e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tg } x \\ \\longrightarrow \\ f'(x)= 1+\\text{tg}^2 x=\\cfrac{1}{\\text{cos}^2 x} =\\text{sec}^2 x\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"398\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> Finalmente, a integral da fun\u00e7\u00e3o tangente \u00e9: <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8c7736fa3869dbff86797b1ff879cc43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\int \\text{tg } x \\ dx= -\\ln \\lvert \\text{cos }x \\rvert + C\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"218\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"periodo-de-la-funcion-tangente\"><\/span> Per\u00edodo da fun\u00e7\u00e3o tangente<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ao contr\u00e1rio de outras fun\u00e7\u00f5es trigonom\u00e9tricas, como seno e cosseno, a fun\u00e7\u00e3o tangente n\u00e3o tem magnitude, pois n\u00e3o tem valor m\u00e1ximo nem m\u00ednimo. Por\u00e9m, \u00e9 uma fun\u00e7\u00e3o peri\u00f3dica, ou seja, seus valores se repetem com uma frequ\u00eancia como vimos em seu gr\u00e1fico.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e5e2cc1f194f1a7fee12fa1156ad3fa6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\text{tg}(wx)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> O <strong>per\u00edodo<\/strong> da fun\u00e7\u00e3o tangente \u00e9 a dist\u00e2ncia entre dois pontos nos quais o gr\u00e1fico se repete e \u00e9 calculado com a seguinte f\u00f3rmula: <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3018883cc7bcf87eaf5d39ca88d719c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{Periodo}=T=\\cfrac{\\pi}{w}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"135\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"teorema-de-la-tangente\"><\/span> teorema da tangente<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Embora a f\u00f3rmula da tangente seja normalmente usada em tri\u00e2ngulos ret\u00e2ngulos, existe tamb\u00e9m um teorema que pode ser aplicado a qualquer tipo de tri\u00e2ngulo: o teorema da tangente.<\/p>\n<p> O <strong>teorema da tangente<\/strong> relaciona os lados e \u00e2ngulos de qualquer tri\u00e2ngulo da seguinte forma: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/theoreme-des-sinus-ou-des-sinus.webp\" alt=\"\" class=\"wp-image-281\" width=\"188\" height=\"136\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-261e505be252193e417e40524dc7fec7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{a+b}{a-b} = \\cfrac{ \\text{tg}\\left(\\frac{\\alpha+\\beta}{2}\\right)}{\\text{tg}\\left(\\frac{\\alpha-\\beta}{2}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"136\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3e330dd1d596b748ac4f24b84a0a41e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{a+c}{a-c} = \\cfrac{ \\text{tg}\\left(\\frac{\\alpha+\\gamma \\vphantom{\\beta}}{2}\\right)}{\\text{tg}\\left(\\frac{\\alpha-\\gamma\\vphantom{\\beta}}{2}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"136\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-267dc10c3b0e77cd0d01c8f1194c48e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{b+c}{b-c} = \\cfrac{ \\text{tg}\\left(\\frac{\\beta+\\gamma}{2}\\right)}{\\text{tg}\\left(\\frac{\\beta-\\gamma}{2}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"133\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"relaciones-de-la-funcion-tangente-con-otras-razones-trigonometricas\"><\/span> Rela\u00e7\u00f5es da fun\u00e7\u00e3o tangente com outras raz\u00f5es trigonom\u00e9tricas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Abaixo voc\u00ea encontra as rela\u00e7\u00f5es da tangente com as raz\u00f5es trigonom\u00e9tricas mais importantes da trigonometria.<\/p>\n<h3 class=\"wp-block-heading\"> Rela\u00e7\u00e3o com o seio<\/h3>\n<ul>\n<li> A tangente e o seno de um \u00e2ngulo est\u00e3o relacionados da seguinte forma:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7a86df77c498819d8ea98595aeae1e78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg }\\alpha = \\pm \\cfrac{\\text{sen }\\alpha }{\\sqrt{1-\\text{sen}^2\\alpha \\vphantom{\\bigl( }}}\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"165\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Raz\u00e3o cosseno<\/h3>\n<ul>\n<li> Da mesma forma, a tangente e o cosseno de um \u00e2ngulo est\u00e3o relacionados \u00e0 seguinte igualdade:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4cd911a6fe6c9f7a24fc1da0f14253cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg }\\alpha = \\pm \\cfrac{\\sqrt{1-\\text{cos}^2\\alpha \\vphantom{\\bigl( }} }{\\text{cos }\\alpha}\" title=\"Rendered by QuickLaTeX.com\" height=\"51\" width=\"164\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Rela\u00e7\u00e3o com a cossecante<\/h3>\n<ul>\n<li> Embora seja dif\u00edcil de provar, a tangente pode ser resolvida de modo que dependa apenas da cossecante:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1d5565a2114d02ca91e1f40c48a768e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg }\\alpha = \\pm \\cfrac{1}{\\sqrt{\\text{csc}^2\\alpha -1 \\vphantom{\\bigl( }}}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"163\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Rela\u00e7\u00e3o com a secante<\/h3>\n<ul>\n<li> A tangente e a secante de um \u00e2ngulo est\u00e3o relacionadas pela seguinte equa\u00e7\u00e3o:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-da24bf5121188e8b3822a780b7ceeda4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg }\\alpha =  \\pm\\sqrt{\\text{sec}^2\\alpha -1\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"161\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Rela\u00e7\u00e3o com a cotangente<\/h3>\n<ul>\n<li> Tangente e cotangente s\u00e3o inversos multiplicativos:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-19dad2de61693ec3497a367b9ca36871_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg }\\alpha =\\pm \\cfrac{1}{\\text{cot }\\alpha}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"113\" style=\"vertical-align: -12px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 tudo sobre a fun\u00e7\u00e3o tangente: o que \u00e9, qual a sua f\u00f3rmula, como represent\u00e1-la em um gr\u00e1fico, as caracter\u00edsticas da fun\u00e7\u00e3o, seu per\u00edodo, etc. Al\u00e9m disso, voc\u00ea poder\u00e1 ver exemplos de fun\u00e7\u00f5es tangentes para compreender totalmente o conceito. Ele ainda explica o teorema da tangente e as rela\u00e7\u00f5es que a fun\u00e7\u00e3o &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/funcao-tangente\/\"> <span class=\"screen-reader-text\">Fun\u00e7\u00e3o tangente<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[22],"tags":[],"class_list":["post-360","post","type-post","status-publish","format-standard","hentry","category-representacao-de-funcao"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Fun\u00e7\u00e3o tangente - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/pt\/funcao-tangente\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Fun\u00e7\u00e3o tangente - Mathority\" \/>\n<meta property=\"og:description\" content=\"Nesta p\u00e1gina voc\u00ea encontrar\u00e1 tudo sobre a fun\u00e7\u00e3o tangente: o que \u00e9, qual a sua f\u00f3rmula, como represent\u00e1-la em um gr\u00e1fico, as caracter\u00edsticas da fun\u00e7\u00e3o, seu per\u00edodo, etc. Al\u00e9m disso, voc\u00ea poder\u00e1 ver exemplos de fun\u00e7\u00f5es tangentes para compreender totalmente o conceito. 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