{"id":160244,"date":"2026-09-29T13:39:48","date_gmt":"2026-09-29T16:39:48","guid":{"rendered":"https:\/\/vestibulares.estrategia.com\/portal\/?p=160244"},"modified":"2026-09-29T13:39:52","modified_gmt":"2026-09-29T16:39:52","slug":"radianos-conceito-conversao-e-aplicacoes","status":"publish","type":"post","link":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/radianos-conceito-conversao-e-aplicacoes\/","title":{"rendered":"Radianos: conceito, convers\u00e3o e aplica\u00e7\u00f5es"},"content":{"rendered":"<p class=\"wp-block-paragraph\">Os radianos s&atilde;o uma unidade de medida de &acirc;ngulos muito utilizada na Matem&aacute;tica, especialmente em trigonometria, geometria e fun&ccedil;&otilde;es circulares. Sua defini&ccedil;&atilde;o est&aacute; diretamente relacionada ao comprimento do arco e ao raio da circunfer&ecirc;ncia.<p class=\"wp-block-paragraph\">Compreender a rela&ccedil;&atilde;o entre graus e radianos &eacute; essencial para resolver diversos problemas. Al&eacute;m das convers&otilde;es, o radiano aparece no c&aacute;lculo de comprimentos de arcos, &aacute;reas de setores e em aplica&ccedil;&otilde;es envolvendo movimentos circulares.<\/p><p class=\"wp-block-paragraph\">Nesse texto, voc&ecirc; vai entender o conceito de radiano, a convers&atilde;o para graus, os principais valores do ciclo trigonom&eacute;trico e suas aplica&ccedil;&otilde;es. Acompanhe abaixo.<\/p><p class=\"wp-block-paragraph\"><div class=\"cta-medio\" style=\"background-image: url(https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2024\/08\/curso-enem-e-vestibulares-2-estrategia-vestibulares-ctamedio.png.jpg);\"><h3>Pacote Vestibulares Platinum<\/h3><p>Conhe\u00e7a nosso curso<\/p><div class=\"cta-botao\"><a id=\"cta-medio\" href=\"https:\/\/vestibulares.estrategia.com\/curso\/vestibulares-platinum\/\" target=\"_blank\" style=\"background:rgb(255,150,0)\">Compre agora<\/a><\/div><\/div>\n\n\n\n<\/p><div id=\"ez-toc-container\" class=\"ez-toc-v2_0_86 counter-hierarchy ez-toc-counter ez-toc-transparent ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\"><p class=\"ez-toc-title\" style=\"cursor:inherit\">Navegue pelo conte\u00fado<\/p>\n<\/div><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/radianos-conceito-conversao-e-aplicacoes\/#Conceito-de-radiano-e-medida-de-arcos\" >Conceito de radiano e medida de arcos<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/radianos-conceito-conversao-e-aplicacoes\/#Relacao-matematica-entre-graus-e-radianos\" >Rela&ccedil;&atilde;o matem&aacute;tica entre graus e radianos<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/radianos-conceito-conversao-e-aplicacoes\/#Calculo-do-comprimento-de-arco-de-circunferencia\" >C&aacute;lculo do comprimento de arco de circunfer&ecirc;ncia<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/radianos-conceito-conversao-e-aplicacoes\/#Como-os-radianos-aparecem-no-vestibular\" >Como os radianos aparecem no vestibular<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/radianos-conceito-conversao-e-aplicacoes\/#Questao-do-vestibular-sobre-radianos\" >Quest&atilde;o do vestibular sobre radianos<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/radianos-conceito-conversao-e-aplicacoes\/#Prepare-se-para-o-vestibular-com-o-Estrategia\" >Prepare-se para o vestibular com o Estrat&eacute;gia!<\/a><\/li><\/ul><\/nav><\/div>\n<h2 id=\"h-conceito-de-radiano-e-medida-de-arcos\" class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Conceito-de-radiano-e-medida-de-arcos\"><\/span>Conceito de radiano e medida de arcos<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">Imagine uma circunfer&ecirc;ncia de raio <em>r<\/em>. Considere um arco dessa circunfer&ecirc;ncia cujo comprimento seja exatamente igual ao raio:<\/p><p class=\"has-text-align-center wp-block-paragraph\">s = r<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"766\" height=\"418\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-1.jpeg\" alt=\"\" class=\"wp-image-160245\" style=\"aspect-ratio:1.832610435002316;width:446px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">O &acirc;ngulo central que determina esse arco mede 1 radiano. Portanto, geometricamente o radiano &eacute; o &acirc;ngulo central que subtende um arco cujo comprimento &eacute; igual ao raio da circunfer&ecirc;ncia.<\/p><p class=\"wp-block-paragraph\">Essa defini&ccedil;&atilde;o pode ser escrita matematicamente como:<\/p><p class=\"has-text-align-center wp-block-paragraph\"><em>&theta;<\/em> = s\/r<\/p><p class=\"wp-block-paragraph\">em que:<\/p><ul class=\"wp-block-list\">\n<li><em>&theta;<\/em> &eacute; a medida do &acirc;ngulo em radianos;<\/li>\n\n\n\n<li><em>s<\/em> &eacute; o comprimento do arco;<\/li>\n\n\n\n<li><em>r<\/em> &eacute; o raio da circunfer&ecirc;ncia.<\/li>\n<\/ul><p class=\"wp-block-paragraph\">Observe que tanto <em>s<\/em> quanto <em>r <\/em>s&atilde;o comprimentos. Assim, suas unidades se cancelam:<\/p><p class=\"has-text-align-center wp-block-paragraph\">&theta;=m\/m<\/p><p class=\"wp-block-paragraph\">Por isso, o radiano &eacute; considerado uma grandeza adimensional. Embora escrevemos &ldquo;rad&rdquo; para indicar que estamos trabalhando com &acirc;ngulos, matematicamente o radiano resulta da raz&atilde;o entre dois comprimentos.<\/p><p class=\"wp-block-paragraph\"><strong>Quantos radianos existem em uma volta?<\/strong><\/p><p class=\"wp-block-paragraph\">O comprimento total de uma <a href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/elementos-da-circunferencia-definicoes-propriedades-e-aplicacoes\/\" target=\"_blank\">circunfer&ecirc;ncia<\/a> &eacute;:<\/p><p class=\"has-text-align-center wp-block-paragraph\">C=2&pi;r<\/p><p class=\"wp-block-paragraph\">Como cada radiano corresponde a um arco de comprimento r, basta perguntar quantos segmentos de comprimento r cabem na circunfer&ecirc;ncia:<\/p><p class=\"has-text-align-center wp-block-paragraph\">&theta; = 2&pi;r \/ r = 2&pi;<\/p><p class=\"wp-block-paragraph\">Logo:<\/p><p class=\"has-text-align-center wp-block-paragraph\">1 volta = 2&pi; rad<\/p><p class=\"wp-block-paragraph\">Como &pi;&asymp;3,14:<\/p><p class=\"has-text-align-center wp-block-paragraph\">2&pi; &asymp; 6,28<\/p><p class=\"wp-block-paragraph\">Assim, uma volta completa corresponde aproximadamente a 6,28 radianos.<\/p><h2 id=\"h-relacao-matematica-entre-graus-e-radianos\" class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Relacao-matematica-entre-graus-e-radianos\"><\/span>Rela&ccedil;&atilde;o matem&aacute;tica entre graus e radianos<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">Uma volta completa tamb&eacute;m pode ser expressa em graus:<\/p><p class=\"has-text-align-center wp-block-paragraph\">360<sup>&deg;<\/sup><\/p><p class=\"wp-block-paragraph\">J&aacute; em radianos, ela corresponde a:<\/p><p class=\"has-text-align-center wp-block-paragraph\">2&pi; rad<\/p><p class=\"wp-block-paragraph\">Portanto:<\/p><p class=\"has-text-align-center wp-block-paragraph\">360&deg; = 2&pi; rad<\/p><p class=\"wp-block-paragraph\">Dividindo ambos os lados por 2:<\/p><p class=\"has-text-align-center wp-block-paragraph\">180&deg; = &pi; rad<\/p><p class=\"wp-block-paragraph\">Essa &eacute; a equival&ecirc;ncia fundamental. A partir dela, qualquer &acirc;ngulo pode ser convertido de graus para radianos ou de radianos para graus.<\/p><h3 class=\"wp-block-heading\">Convers&atilde;o de Graus para radianos<\/h3><p class=\"wp-block-paragraph\">Uma maneira segura de fazer a convers&atilde;o &eacute; utilizar a <a href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/razao-e-proporcao\/\" target=\"_blank\">propor&ccedil;&atilde;o<\/a>:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"183\" height=\"69\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-29.png\" alt=\"\" class=\"wp-image-160275\" style=\"aspect-ratio:2.6525481313703283;width:145px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">Por exemplo: Converta 60&deg; em radianos<\/p><p class=\"wp-block-paragraph\">Montamos:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"94\" height=\"68\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-30.png\" alt=\"\" class=\"wp-image-160276\" style=\"aspect-ratio:1.382440818202712;width:72px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">Multiplicando em cruz:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"126\" height=\"42\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-31.png\" alt=\"\" class=\"wp-image-160277\" style=\"aspect-ratio:3.0007443245254932;width:100px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">Logo:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"86\" height=\"68\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-32.png\" alt=\"\" class=\"wp-image-160278\" style=\"aspect-ratio:1.2647667202941852;width:66px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">Simplificando:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"60\" height=\"63\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-35.png\" alt=\"\" class=\"wp-image-160281\" style=\"aspect-ratio:0.9523691391714215;width:48px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">Portanto:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"126\" height=\"63\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-36.png\" alt=\"\" class=\"wp-image-160282\" style=\"aspect-ratio:2.000248077400149;width:88px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">Uma forma ainda mais r&aacute;pida, bastante &uacute;til em provas, &eacute; multiplicar diretamente o &acirc;ngulo em graus por:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"40\" height=\"63\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-23.png\" alt=\"\" class=\"wp-image-160251\" style=\"aspect-ratio:0.6349875930521092;width:36px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">Por exemplo:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"138\" height=\"63\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-37.png\" alt=\"\" class=\"wp-image-160283\" style=\"aspect-ratio:2.190771520714463;width:106px;height:auto\"><\/figure>\n<\/div><h3 class=\"wp-block-heading\">Convertendo radianos para graus<\/h3><p class=\"wp-block-paragraph\">O racioc&iacute;nio &eacute; o inverso. Como: &pi; rad=180&deg; podemos substituir &pi; por 180&deg;. Por exemplo:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"73\" height=\"69\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-25.png\" alt=\"\" class=\"wp-image-160261\" style=\"aspect-ratio:1.0579841449603624;width:61px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">Substituindo:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"256\" height=\"69\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-38.png\" alt=\"\" class=\"wp-image-160284\" style=\"aspect-ratio:3.710758776896942;width:196px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">Portanto:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"153\" height=\"69\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-24.png\" alt=\"\" class=\"wp-image-160259\" style=\"aspect-ratio:2.2176670441676105;width:125px;height:auto\" srcset=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-24.png 153w, https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-24-150x69.png 150w\" sizes=\"(max-width: 153px) 100vw, 153px\" \/><\/figure>\n<\/div><h3 class=\"wp-block-heading\">Valores not&aacute;veis no ciclo trigonom&eacute;trico<\/h3><p class=\"wp-block-paragraph\">Os principais &acirc;ngulos do primeiro quadrante s&atilde;o:<\/p><figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Graus<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Radianos<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">0&deg;<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">30&deg;<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img decoding=\"async\" src=\"blob:https:\/\/vestibulares.estrategia.com\/62f2eb44-663b-435c-90d1-2849939fc091\" width=\"11\" height=\"43\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">45&deg;<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img decoding=\"async\" src=\"blob:https:\/\/vestibulares.estrategia.com\/701980cf-7593-4b7b-a6bb-b0da901d2828\" width=\"11\" height=\"43\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">60&deg;<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img decoding=\"async\" src=\"blob:https:\/\/vestibulares.estrategia.com\/3dde60c9-cbb6-48d3-90fc-f378e8e30b89\" width=\"11\" height=\"43\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">90&deg;<\/td><td class=\"has-text-align-center\" data-align=\"center\"><img decoding=\"async\" src=\"blob:https:\/\/vestibulares.estrategia.com\/be2a2c0b-e5d9-4290-9e88-26eb23a45a7f\" width=\"11\" height=\"43\"><\/td><\/tr><\/tbody><\/table><\/figure><p class=\"wp-block-paragraph\">Esses valores aparecem constantemente em quest&otilde;es de trigonometria. A partir deles, podemos localizar os principais pontos do ciclo:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"94\" height=\"42\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-39.png\" alt=\"\" class=\"wp-image-160285\" style=\"aspect-ratio:2.2385560104205435;width:80px;height:auto\"><\/figure>\n<\/div><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"108\" height=\"68\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-40.png\" alt=\"\" class=\"wp-image-160286\" style=\"aspect-ratio:1.5883704895426338;width:88px;height:auto\"><\/figure>\n<\/div><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"108\" height=\"42\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-41.png\" alt=\"\" class=\"wp-image-160287\" style=\"aspect-ratio:2.572013397841459;width:80px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">Uma maneira eficiente de memorizar &eacute; pensar na sequ&ecirc;ncia:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"157\" height=\"63\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-42.png\" alt=\"\" class=\"wp-image-160288\" style=\"aspect-ratio:2.4924336392954602;width:113px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">e lembrar que:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"94\" height=\"42\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-43.png\" alt=\"\" class=\"wp-image-160289\" style=\"aspect-ratio:2.2385560104205435;width:74px;height:auto\"><\/figure>\n<\/div><h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Calculo-do-comprimento-de-arco-de-circunferencia\"><\/span>C&aacute;lculo do comprimento de arco de circunfer&ecirc;ncia<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">Imagine duas circunfer&ecirc;ncias diferentes. Em ambas, podemos considerar um &acirc;ngulo de:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"60\" height=\"63\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-44.png\" alt=\"\" class=\"wp-image-160290\" style=\"aspect-ratio:0.9523691391714215;width:50px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">A abertura angular &eacute; exatamente a mesma: trata-se de um quarto de volta. Entretanto, os comprimentos dos arcos ser&atilde;o diferentes se os raios forem diferentes. Isso acontece porque:<\/p><p class=\"has-text-align-center wp-block-paragraph\">s = &theta;.r<\/p><p class=\"wp-block-paragraph\">Ou seja, o comprimento do arco depende de duas informa&ccedil;&otilde;es:<\/p><ul class=\"wp-block-list\">\n<li>do &acirc;ngulo &theta;;<\/li>\n\n\n\n<li>do raio r.<\/li>\n<\/ul><p class=\"wp-block-paragraph\">Por exemplo, para &theta; = &pi;\/2:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"74\" height=\"63\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-45.png\" alt=\"\" class=\"wp-image-160291\" style=\"aspect-ratio:1.174646489704788;width:62px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">Se r = 2m:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"160\" height=\"63\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-46.png\" alt=\"\" class=\"wp-image-160292\" style=\"aspect-ratio:2.5400645001240387;width:120px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">Se r = 10m:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"187\" height=\"63\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-47.png\" alt=\"\" class=\"wp-image-160293\" style=\"aspect-ratio:2.9687422475812455;width:151px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">O &acirc;ngulo &eacute; o mesmo, mas o arco &eacute; cinco vezes maior na segunda circunfer&ecirc;ncia.<\/p><h3 class=\"wp-block-heading\">Comprimento de arco pelo &acirc;ngulo central<\/h3><p class=\"wp-block-paragraph\">A f&oacute;rmula fundamental &eacute;:<\/p><p class=\"has-text-align-center wp-block-paragraph\">s = &theta;.r<\/p><p class=\"wp-block-paragraph\">em que:<\/p><ul class=\"wp-block-list\">\n<li>s= comprimento do arco;<\/li>\n\n\n\n<li>r= raio;<\/li>\n\n\n\n<li>&theta;= &acirc;ngulo central em radianos.<\/li>\n<\/ul><p class=\"wp-block-paragraph\">Essa &uacute;ltima condi&ccedil;&atilde;o &eacute; indispens&aacute;vel.<\/p><p class=\"wp-block-paragraph\"><strong>Aten&ccedil;&atilde;o &agrave; pegadinha!<\/strong><\/p><p class=\"wp-block-paragraph\">Suponha que uma roda tenha raio de 20cm e um ponto da sua borda percorre um arco correspondente a 60&deg;. N&atilde;o podemos simplesmente fazer:<\/p><p class=\"has-text-align-center wp-block-paragraph\">s = 60&sdot;20<\/p><p class=\"wp-block-paragraph\">Isso est&aacute; errado porque 60 est&aacute; em graus.<\/p><p class=\"wp-block-paragraph\">Primeiro devemos converter:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"126\" height=\"63\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-26.png\" alt=\"\" class=\"wp-image-160266\" style=\"aspect-ratio:2.000248077400149;width:96px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">Agora aplicamos:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"68\" height=\"42\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-49.png\" alt=\"\" class=\"wp-image-160297\" style=\"aspect-ratio:1.6192780052102718;width:52px;height:auto\"><\/figure>\n<\/div><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"102\" height=\"63\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-50.png\" alt=\"\" class=\"wp-image-160298\" style=\"aspect-ratio:1.6192011907715207;width:78px;height:auto\"><\/figure>\n<\/div><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"127\" height=\"68\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-48.png\" alt=\"\" class=\"wp-image-160296\" style=\"aspect-ratio:1.867846472075385;width:97px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">Se a quest&atilde;o pedir uma aproxima&ccedil;&atilde;o e considerar &pi;&asymp;3,14:<\/p><p class=\"has-text-align-center wp-block-paragraph\">s &asymp; 20,93 cm<\/p><p class=\"wp-block-paragraph\"><strong>Estrat&eacute;gia de prova:<\/strong> sempre que enxergar s = &theta;.r, confira imediatamente se o &acirc;ngulo est&aacute; em radianos.<\/p><h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Como-os-radianos-aparecem-no-vestibular\"><\/span>Como os radianos aparecem no vestibular<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">O radiano n&atilde;o aparece apenas em exerc&iacute;cios de convers&atilde;o. Ele &eacute; fundamental para diversos conte&uacute;dos.<\/p><h3 class=\"wp-block-heading\">Fun&ccedil;&otilde;es trigonom&eacute;tricas<\/h3><p class=\"wp-block-paragraph\">Nos gr&aacute;ficos de:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"126\" height=\"42\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-51.png\" alt=\"\" class=\"wp-image-160299\" style=\"aspect-ratio:3.0007443245254932;width:108px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">e<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"130\" height=\"42\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-27.png\" alt=\"\" class=\"wp-image-160272\" style=\"aspect-ratio:3.096017863788612;width:108px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">o eixo x normalmente utiliza radianos.<\/p><p class=\"wp-block-paragraph\">Por exemplo, um per&iacute;odo completo de seno ou cosseno corresponde a:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"84\" height=\"71\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-28.png\" alt=\"\" class=\"wp-image-160273\" style=\"aspect-ratio:1.183399383531484;width:62px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">e n&atilde;o a 360&deg; quando estamos trabalhando na representa&ccedil;&atilde;o em radianos.<\/p><h3 class=\"wp-block-heading\">Geometria<\/h3><p class=\"wp-block-paragraph\">O radiano tamb&eacute;m aparece no c&aacute;lculo de <a href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/area-do-setor-circular-como-calcular-formulas-e-questoes\/\" target=\"_blank\">setores circulares<\/a>. Quando &theta; est&aacute; em radianos:<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"84\" height=\"71\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-28.png\" alt=\"\" class=\"wp-image-160271\" style=\"aspect-ratio:1.183399383531484;width:68px;height:auto\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">Essa f&oacute;rmula permite calcular diretamente a &aacute;rea de um setor circular.<\/p><h3 class=\"wp-block-heading\">F&iacute;sica: movimento circular<\/h3><p class=\"wp-block-paragraph\">Na F&iacute;sica, a velocidade angular &eacute; normalmente expressa em:<\/p><p class=\"has-text-align-center wp-block-paragraph\">rad\/s<\/p><p class=\"wp-block-paragraph\">A rela&ccedil;&atilde;o entre velocidade angular e velocidade linear &eacute;:<\/p><p class=\"has-text-align-center wp-block-paragraph\">v=&omega;r<\/p><p class=\"wp-block-paragraph\">Observe como ela possui estrutura semelhante &agrave; f&oacute;rmula do comprimento de arco:<\/p><p class=\"has-text-align-center wp-block-paragraph\">s = &theta;r<\/p><p class=\"wp-block-paragraph\">Isso n&atilde;o &eacute; coincid&ecirc;ncia: ambas relacionam uma grandeza angular a uma grandeza linear por meio do raio.<\/p><h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Questao-do-vestibular-sobre-radianos\"><\/span>Quest&atilde;o do vestibular sobre radianos<span class=\"ez-toc-section-end\"><\/span><\/h2><h3 class=\"wp-block-heading\">Uerj (2026)<\/h3><p class=\"wp-block-paragraph\">Sabe-se que 1 radiano &eacute; a medida do &acirc;ngulo central &theta; = A&Ocirc;B de uma circunfer&ecirc;ncia cujo arco AB tem o mesmo comprimento do raio OA.<\/p><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"179\" height=\"168\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2026\/09\/image-52.png\" alt=\"\" class=\"wp-image-160300\"><\/figure>\n<\/div><p class=\"wp-block-paragraph\">Admita que uma part&iacute;cula percorra, em uma trajet&oacute;ria circular de raio OA igual a 300 cm, um arco de circunfer&ecirc;ncia AB que mede 600 cm.&nbsp;<\/p><p class=\"wp-block-paragraph\">Nesse caso, a medida do &acirc;ngulo central A&Ocirc;B, em radianos, &eacute; igual a:&nbsp;<\/p><p class=\"wp-block-paragraph\"><strong>A)<\/strong> 2<br><strong>B)<\/strong> 1,5<br><strong>C)<\/strong> 1<br><strong>D)<\/strong> 0,5<\/p><details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary><strong>Resposta:<\/strong><\/summary>\n<p class=\"wp-block-paragraph\">Utilizando a f&oacute;rmula que relaciona o &acirc;ngulo central &theta;, em radianos, com o comprimento do arco S e o raio da circunfer&ecirc;ncia R:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">&theta; = S\/R<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aplicando os valores S = 600 cm e R = 300 cm, vamos encontrar o &acirc;ngulo &theta;, em radianos.<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">&theta;&nbsp; = 600\/300<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">&theta;&nbsp; = 2 rad<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Alternativa correta:<strong> A<\/strong><\/p>\n<\/details><h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Prepare-se-para-o-vestibular-com-o-Estrategia\"><\/span>Prepare-se para o vestibular com o Estrat&eacute;gia!<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">Nos cursos preparat&oacute;rios da Coruja, os alunos s&atilde;o treinados para conectar diferentes &aacute;reas do conhecimento e aplicar essas informa&ccedil;&otilde;es em simulados e provas.<\/p><p class=\"wp-block-paragraph\">As aulas s&atilde;o ministradas por professores especialistas, com nossos Livros Digitais Interativos (LDI), al&eacute;m de contar com simulados exclusivos. Clique no banner e comece seus estudos com o Estrat&eacute;gia Vestibulares!<\/p><p class=\"wp-block-paragraph\"><div class=\"cta-medio\" style=\"background-image: url(https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2024\/08\/curso-enem-1-estrategia-vestibulares-ctamedio.jpg);\"><h3>Pacote Enem TOP <\/h3> <p>Estude com o Estrat\u00e9gia Vestibulares<\/p><div class=\"cta-botao\"><a id=\"cta-medio\" href=\"https:\/\/vestibulares.estrategia.com\/curso\/enem-top\/\" target=\"_blank\" style=\"background:rgb(255,150,0)\">Saiba mais<\/a><\/div><\/div>\n\n\n\n<\/p><p class=\"wp-block-paragraph\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"Entenda o conceito de radiano, a convers\u00e3o para graus, os principais valores do ciclo trigonom\u00e9trico e aplica\u00e7\u00f5es\n","protected":false},"author":59,"featured_media":160302,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[29],"tags":[],"class_list":["post-160244","post","type-post","status-publish","format-standard","has-post-thumbnail","category-matematica"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v25.9 (Yoast SEO v28.2) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Radianos: conceito, convers\u00e3o e aplica\u00e7\u00f5es<\/title>\n<meta name=\"description\" content=\"Saiba mais sobre o conceito de radiano, a convers\u00e3o para graus, os principais valores do ciclo trigonom\u00e9trico e suas aplica\u00e7\u00f5es.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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