{"id":15558,"date":"2020-04-15T14:49:32","date_gmt":"2020-04-15T17:49:32","guid":{"rendered":"https:\/\/beduka.com\/blog\/?p=15558"},"modified":"2020-08-20T10:20:00","modified_gmt":"2020-08-20T13:20:00","slug":"o-que-e-seno-cosseno-e-tangente","status":"publish","type":"post","link":"https:\/\/beduka.com\/blog\/materias\/matematica\/o-que-e-seno-cosseno-e-tangente\/","title":{"rendered":"O que \u00e9 Seno, Cosseno e Tangente? Descubra o que \u00e9, como calcular e as suas propriedades!"},"content":{"rendered":"\n<p>O que \u00e9 Seno, Cosseno e Tangente? S\u00e3o rela\u00e7\u00f5es matem\u00e1ticas que encontramos dividindo lados por \u00e2ngulos. Pode parecer meio vago e sem sentido mas, neste artigo, vamos te mostrar com imagens e exemplos todos os detalhes: como fazer o c\u00e1lculo, para que ele serve e o que significam.<\/p>\n\n\n\n<p>Neste artigo sobre o que \u00e9 Seno, Cosseno e Tangente voc\u00ea encontrar\u00e1:<\/p>\n\n\n\n<ol><li>Tri\u00e2ngulo ret\u00e2ngulo (introdu\u00e7\u00e3o)<\/li><li>O que \u00e9 Seno, Cosseno e Tangente<\/li><li>Propriedades e observa\u00e7\u00f5es importantes<\/li><li>Exemplos num\u00e9ricos e aplica\u00e7\u00e3o (para qu\u00ea serve)<\/li><\/ol>\n\n\n\n<ul><li>Treine para as provas com nosso <a href=\"https:\/\/beduka.com\/blog\/dicas\/enem-dicas\/simulados-para-enem-online-e-gratuito\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">Simulado online e gratuito!<\/a> Voc\u00ea pode at\u00e9 personaliz\u00e1-lo com as mat\u00e9rias que mais precisa!<\/li><\/ul>\n\n\n\n<ul><li>Entenda como funciona o <a rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\" href=\"https:\/\/beduka.com\/blog\/sisu\/como-funciona-o-sisu\/\" target=\"_blank\">Sisu,<\/a> o <a href=\"https:\/\/beduka.com\/blog\/enem\/como-se-preparar-para-o-enem\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">Enem,<\/a> o <a rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\" href=\"https:\/\/beduka.com\/blog\/prouni\/como-funciona-o-prouni\/\" target=\"_blank\">ProUni<\/a> e o <a rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\" href=\"https:\/\/beduka.com\/blog\/fies\/como-funciona-o-fies\/\" target=\"_blank\">Fies<\/a>!<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Tri\u00e2ngulo ret\u00e2ngulo e trigonometria<\/h2>\n\n\n\n<p>Antes de falar propriamente sobre o que \u00e9 Seno, Cosseno e Tangente, precisamos <strong>relembrar algumas caracter\u00edsticas <\/strong>do tri\u00e2ngulo Ret\u00e2ngulo, pois vamos <strong>precisar delas l\u00e1 na frente:<\/strong><\/p>\n\n\n\n<ul><li>O tri\u00e2ngulo ret\u00e2ngulo apresenta um \u00e2ngulo interno reto (90\u00ba).&nbsp;<\/li><li>O lado oposto ao \u00e2ngulo de 90\u00ba \u00e9 chamado de hipotenusa e os outros de catetos.<\/li><li>Dependendo da posi\u00e7\u00e3o dos catetos <strong>em rela\u00e7\u00e3o ao \u00e2ngulo,<\/strong> chamamos de oposto ou adjacente.<\/li><\/ul>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-1 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/tri\u00e2ngulos-ret\u00e2ngulos.jpg\" alt=\"tri\u00e2ngulos-ret\u00e2ngulos\" data-id=\"15559\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15559\" class=\"wp-image-15559\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/tri\u00e2ngulos-ret\u00e2ngulos.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/tri\u00e2ngulos-ret\u00e2ngulos-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/tri\u00e2ngulos-ret\u00e2ngulos-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<p>Por ora, estes detalhes bastam para continuarmos. Mas aqui vai um artigo para <strong>saber mais sobre <\/strong><a href=\"https:\/\/beduka.com\/blog\/materias\/matematica\/trigonometria-no-triangulo-retangulo\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">trigonometria no tri\u00e2ngulo ret\u00e2ngulo<\/a>!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">O que \u00e9 Seno, Cosseno e Tangente<\/h2>\n\n\n\n<p>Visto que j\u00e1 sabemos das caracter\u00edsticas dos tri\u00e2ngulos ret\u00e2ngulos e que as rela\u00e7\u00f5es trigonom\u00e9tricas se baseiam na rela\u00e7\u00e3o entre divis\u00e3o de \u00e2ngulos e lados, vamos \u00e0s defini\u00e7\u00f5es!<\/p>\n\n\n\n<ul><li>Falando em trigonometria, saiba <a href=\"https:\/\/beduka.com\/blog\/materias\/matematica\/como-transformar-graus-em-radianos\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">como transformar graus em radianos<\/a>.<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">O que \u00e9 Seno<\/h3>\n\n\n\n<p>O Seno <strong>de qualquer \u00e2ngulo<\/strong> \u00e9 o valor que encontramos ao dividir o seu cateto oposto pela hipotenusa. Veja a f\u00f3rmula do Seno:<\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-3 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/f\u00f3rmula-de-seno.jpg\" alt=\"f\u00f3rmula-de-seno\" data-id=\"15560\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15560\" class=\"wp-image-15560\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/f\u00f3rmula-de-seno.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/f\u00f3rmula-de-seno-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/f\u00f3rmula-de-seno-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<ul><li>De onde veio essa f\u00f3rmula? O que isso significa no ciclo trigonom\u00e9trico?<\/li><\/ul>\n\n\n\n<p>Uma<strong> outra defini\u00e7\u00e3o para Seno<\/strong> \u00e9:<\/p>\n\n\n\n<p><strong>\u201cProje\u00e7\u00e3o da medida do \u00e2ngulo no eixo das coordenadas <\/strong>(eixo y).\u201d<\/p>\n\n\n\n<p>Vamos relembrar que no Ciclo trigonom\u00e9trico <strong>o raio \u00e9 sempre unit\u00e1rio<\/strong>, ou seja, vale 1. Por isso, o <strong>seno sempre ser\u00e1 um n\u00famero entre 0 e 1.<\/strong><\/p>\n\n\n\n<p><strong>No ciclo trigonom\u00e9trico, <\/strong>a proje\u00e7\u00e3o do valor do seno no eixo y <strong>\u00e9 igual ao tamanho do cateto oposto<\/strong> (observe a imagem).&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-5 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-no-ciclo-trigonom\u00e9trico.jpg\" alt=\"\" data-id=\"15561\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15561\" class=\"wp-image-15561\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-no-ciclo-trigonom\u00e9trico.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-no-ciclo-trigonom\u00e9trico-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-no-ciclo-trigonom\u00e9trico-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<p>Com base nisso, os matem\u00e1ticos perceberam que estas medidas <strong>s\u00f3 eram iguais porque a hipotenusa vale 1<\/strong> (lembre-se que o raio \u00e9 unit\u00e1rio no ciclo).<\/p>\n\n\n\n<p>Portanto, <strong>se tiv\u00e9ssemos um tri\u00e2ngulo<\/strong> <strong>fora do ciclo <\/strong>trigonom\u00e9trico,<strong> n\u00e3o poder\u00edamos dizer que o valor do seno \u00e9 igual ao do cateto oposto.<\/strong>&nbsp;<\/p>\n\n\n\n<p>Diante disso, foi preciso estabelecer uma <strong>f\u00f3rmula gen\u00e9rica<\/strong> que se aplique <strong>tanto aos tri\u00e2ngulos do ciclo quanto aos de fora.<\/strong><\/p>\n\n\n\n<p>Da\u00ed surgiu a f\u00f3rmula. Ao estabelecer que o valor do seno \u00e9 o cateto oposto dividido pela hipotenusa, o resultado <strong>se adequa a qualquer medida que um tri\u00e2ngulo ret\u00e2ngulo possuir.<\/strong> Afinal, a<strong> <\/strong>raz\u00e3o<strong> <\/strong>entre 8 e 4 <strong>\u00e9 a mesma <\/strong>que a<strong> raz\u00e3o <\/strong>entre 64 e 32.<\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-7 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-em-tri\u00e2ngulos-semelhantes.jpg\" alt=\"seno-em-tri\u00e2ngulos-semelhantes\" data-id=\"15562\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15562\" class=\"wp-image-15562\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-em-tri\u00e2ngulos-semelhantes.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-em-tri\u00e2ngulos-semelhantes-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-em-tri\u00e2ngulos-semelhantes-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<p><strong>IMPORTANTE<\/strong><\/p>\n\n\n\n<p>Observe que <strong>o resultado de ambos os senos s\u00e3o iguais<\/strong>.&nbsp;<\/p>\n\n\n\n<p>Isso ocorreu pois os<strong> tri\u00e2ngulos s\u00e3o semelhantes: apesar de terem lados diferentes, como essa diferen\u00e7a \u00e9 a mesma (constante), seus \u00e2ngulos s\u00e3o iguais.<\/strong><\/p>\n\n\n\n<p>Da\u00ed, tiramos mais uma conclus\u00e3o: <strong>o valor do seno \u00e9 essencialmente determinado pelo valor do \u00e2ngulo<\/strong>, e <strong>n\u00e3o do lado.<\/strong>&nbsp;<\/p>\n\n\n\n<p>Portanto, os lados podem ter qualquer medida mas <strong>um mesmo \u00e2ngulo sempre ter\u00e1 um mesmo seno.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">O que \u00e9 Cosseno<\/h3>\n\n\n\n<p>O Cosseno <strong>de qualquer \u00e2ngulo <\/strong>\u00e9 o valor que encontramos ao dividir o seu cateto adjacente pela hipotenusa. Veja a f\u00f3rmula do Cosseno:<\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-9 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/f\u00f3rmula-do-cosseno.jpg\" alt=\"f\u00f3rmula-do-cosseno\" data-id=\"15563\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15563\" class=\"wp-image-15563\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/f\u00f3rmula-do-cosseno.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/f\u00f3rmula-do-cosseno-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/f\u00f3rmula-do-cosseno-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<ul><li>De onde veio essa f\u00f3rmula? O que isso significa no ciclo trigonom\u00e9trico?<\/li><\/ul>\n\n\n\n<p>Uma<strong> outra defini\u00e7\u00e3o para Cosseno<\/strong> \u00e9:<\/p>\n\n\n\n<p><strong>\u201cProje\u00e7\u00e3o da medida do \u00e2ngulo no eixo das abscissas <\/strong>(eixo x).\u201d<\/p>\n\n\n\n<p>Vamos relembrar que no Ciclo trigonom\u00e9trico <strong>o raio \u00e9 sempre unit\u00e1rio<\/strong>, ou seja, vale 1. Por isso, o <strong>cosseno sempre ser\u00e1 um n\u00famero entre 0 e 1.<\/strong><\/p>\n\n\n\n<p><strong>No ciclo trigonom\u00e9trico, <\/strong>a proje\u00e7\u00e3o do valor do cosseno no eixo x <strong>\u00e9 igual ao tamanho do cateto adjacente<\/strong> (observe a imagem).&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-11 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/cosseno-no-ciclo-trigonom\u00e9trico.jpg\" alt=\"cosseno-no-ciclo-trigonom\u00e9trico\" data-id=\"15564\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15564\" class=\"wp-image-15564\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/cosseno-no-ciclo-trigonom\u00e9trico.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/cosseno-no-ciclo-trigonom\u00e9trico-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/cosseno-no-ciclo-trigonom\u00e9trico-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<p>Com base nisso, os matem\u00e1ticos perceberam que estas medidas <strong>s\u00f3 eram iguais porque a hipotenusa vale 1<\/strong> (lembre-se que o raio \u00e9 unit\u00e1rio no ciclo).<\/p>\n\n\n\n<p>Portanto, <strong>se tiv\u00e9ssemos um tri\u00e2ngulo<\/strong> <strong>fora do ciclo <\/strong>trigonom\u00e9trico,<strong> n\u00e3o poder\u00edamos dizer que o valor do cosseno \u00e9 igual ao do cateto adjacente.<\/strong>&nbsp;<\/p>\n\n\n\n<p style=\"text-align:left\">Diante disso, foi preciso estabelecer uma <strong>f\u00f3rmula gen\u00e9rica<\/strong> que se aplique <strong>tanto aos tri\u00e2ngulos do ciclo quanto aos de fora.<\/strong><\/p>\n\n\n\n<p>Da\u00ed surgiu a f\u00f3rmula. Ao estabelecer que o valor do cosseno \u00e9 o cateto adjacente dividido pela hipotenusa, o resultado <strong>se adequa a qualquer medida que um tri\u00e2ngulo ret\u00e2ngulo possuir.<\/strong> Afinal, a<strong> <\/strong>raz\u00e3o<strong> <\/strong>entre 4 e 2 <strong>\u00e9 a mesma <\/strong>que a<strong> raz\u00e3o <\/strong>entre 16 e 8.<\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-13 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/cosseno-em-tri\u00e2ngulos-semelhantes.jpg\" alt=\"cosseno-em-tri\u00e2ngulos-semelhantes\" data-id=\"15565\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15565\" class=\"wp-image-15565\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/cosseno-em-tri\u00e2ngulos-semelhantes.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/cosseno-em-tri\u00e2ngulos-semelhantes-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/cosseno-em-tri\u00e2ngulos-semelhantes-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<p><strong>IMPORTANTE<\/strong><\/p>\n\n\n\n<p>Observe que <strong>o resultado de ambos os cossenos s\u00e3o iguais<\/strong>.&nbsp;<\/p>\n\n\n\n<p>Isso ocorreu pois os<strong> tri\u00e2ngulos s\u00e3o semelhantes: apesar de terem lados diferentes, como essa diferen\u00e7a \u00e9 a mesma( constante), seus \u00e2ngulos s\u00e3o iguais.<\/strong><\/p>\n\n\n\n<p style=\"text-align:left\">Da\u00ed, tiramos mais uma conclus\u00e3o: <strong>o valor do cosseno \u00e9 essencialmente determinado pelo valor do \u00e2ngulo<\/strong>, e <strong>n\u00e3o do lado.<\/strong>&nbsp;<\/p>\n\n\n\n<p>Portanto, os lados podem ter qualquer medida mas <strong>um mesmo \u00e2ngulo sempre ter\u00e1 um mesmo cosseno.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">O que \u00e9 Tangente<\/h3>\n\n\n\n<p>A Tangente <strong>de qualquer \u00e2ngulo <\/strong>\u00e9 o valor que encontramos ao dividir o seu cateto oposto pelo cateto adjacente. Veja a f\u00f3rmula da Tangente:<\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-15 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/f\u00f3rmula-da-tangente.jpg\" alt=\"f\u00f3rmula-da-tangente\" data-id=\"15566\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15566\" class=\"wp-image-15566\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/f\u00f3rmula-da-tangente.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/f\u00f3rmula-da-tangente-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/f\u00f3rmula-da-tangente-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<ul><li>De onde veio essa f\u00f3rmula? O que isso significa no ciclo trigonom\u00e9trico?<\/li><\/ul>\n\n\n\n<p>Uma<strong> outra defini\u00e7\u00e3o para Tangente<\/strong> \u00e9:<\/p>\n\n\n\n<p><strong>\u201cProje\u00e7\u00e3o da medida do \u00e2ngulo no eixo tangente ao ciclo trigonom\u00e9trico<\/strong>\u201d<\/p>\n\n\n\n<p>A<strong> tangente n\u00e3o tem um limite m\u00ednimo ou m\u00e1ximo de valor, <\/strong>veja no desenho para entender melhor:<\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-17 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/tangente-no-ciclo-trigonom\u00e9trico.jpg\" alt=\"\" data-id=\"15567\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15567\" class=\"wp-image-15567\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/tangente-no-ciclo-trigonom\u00e9trico.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/tangente-no-ciclo-trigonom\u00e9trico-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/tangente-no-ciclo-trigonom\u00e9trico-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<p>Com isso, os matem\u00e1ticos observaram que para encontrar esse valor que est\u00e1 al\u00e9m do ciclo, era preciso <strong>dividir o valor do seno pelo cosseno<\/strong>, pois <strong>somente eles possu\u00edam a hipotenusa em comum;<\/strong> e a <strong>tangente se d\u00e1 justamente pelo prolongamento da hipotenusa.&nbsp;<\/strong><\/p>\n\n\n\n<p>Da\u00ed surgiu a f\u00f3rmula: na hora de fazer os c\u00e1lculos, obtemos:<\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-19 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/como-chegar-na-f\u00f3rmula-da-tangente.jpg\" alt=\"como-chegar-na-f\u00f3rmula-da-tangente\" data-id=\"15568\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15568\" class=\"wp-image-15568\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/como-chegar-na-f\u00f3rmula-da-tangente.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/como-chegar-na-f\u00f3rmula-da-tangente-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/como-chegar-na-f\u00f3rmula-da-tangente-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<p><strong>IMPORTANTE<\/strong><\/p>\n\n\n\n<p>Da\u00ed, tiramos mais uma conclus\u00e3o: <strong>o valor da tangente \u00e9 essencialmente determinado pelo valor do \u00e2ngulo<\/strong>, e <strong>n\u00e3o do lado.<\/strong> Pois deriva de seno e cosseno e estes tamb\u00e9m o s\u00e3o.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Macete<\/h2>\n\n\n\n<p><strong>Pra decorar as f\u00f3rmulas com facilidade:<\/strong><\/p>\n\n\n\n<ol><li>Andou de\u00a0<strong>COS<\/strong>tas?\u00a0<strong>CA<\/strong>\u00a0<strong>Hi<\/strong>\u00a0(COSseno = Cateto Adjacente dividido pela Hipotenusa)<\/li><li>Est\u00e1\u00a0<strong>SEN<\/strong>o roubado?\u00a0<strong>CO<\/strong>r<strong>HI\u00a0<\/strong>(SENo = Cateto Oposto dividido pela Hipotenusa)<\/li><li><strong>T<\/strong>\u00e1\u00a0<strong>G<\/strong>ostoso?\u00a0<strong>CO<\/strong>\u00a0<strong>CA<\/strong>\u00a0(Tangente = Cateto Oposto dividido pelo Cateto Adjacente)<\/li><\/ol>\n\n\n\n<p>\u00c9 f\u00e1cil memorizar coisas bestas! rsrs<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Propriedades e observa\u00e7\u00f5es importantes<\/h2>\n\n\n\n<p>Agora que j\u00e1 sabemos o que \u00e9 Seno, Cosseno e Tangente; podemos entender algumas propriedades.<br><\/p>\n\n\n\n<ul><li>Saiba <a href=\"https:\/\/beduka.com\/blog\/materias\/matematica\/como-aprender-matematica-sozinho\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">como aprender matem\u00e1tica sozinho!<\/a><\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Tri\u00e2ngulos semelhantes<\/h3>\n\n\n\n<p>O valor do Seno, Cosseno e Tangente s\u00e3o determinados pelos \u00e2ngulos. Logo, em tri\u00e2ngulos semelhantes, os valores dessas raz\u00f5es trigonom\u00e9tricas ser\u00e3o iguais porque os \u00e2ngulos s\u00e3o iguais.&nbsp;<\/p>\n\n\n\n<p>J\u00e1 explicamos o porqu\u00ea disso anteriormente.<\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-21 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/trigonometria-em-tri\u00e2ngulos-semelhantes.jpg\" alt=\"trigonometria-em-tri\u00e2ngulos-semelhantes\" data-id=\"15569\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15569\" class=\"wp-image-15569\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/trigonometria-em-tri\u00e2ngulos-semelhantes.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/trigonometria-em-tri\u00e2ngulos-semelhantes-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/trigonometria-em-tri\u00e2ngulos-semelhantes-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u00c2ngulos Not\u00e1veis<\/h3>\n\n\n\n<p>Na matem\u00e1tica,<strong> definiu-se que existem 3 \u00e2ngulos not\u00e1veis (30\u00b0,45\u00b0 e 60\u00b0)<\/strong>, ou seja, \u00e2ngulos <strong>recorrentes e f\u00e1ceis de se identificar.&nbsp;<\/strong><\/p>\n\n\n\n<p>Eles s\u00e3o <strong>os mais cobrados <\/strong>nas provas e <strong>devemos saber <\/strong>os valores de seus Senos,Cossenos e Tangentes <strong>de c\u00f3r.<\/strong><\/p>\n\n\n\n<p>\n\nPara isso, h\u00e1 uma tabelinha muito famosa que<strong> todo estudante deve saber:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-23 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/tabela-\u00e2ngulos-not\u00e1veis.jpg\" alt=\"tabela-\u00e2ngulos-not\u00e1veis\" data-id=\"15570\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15570\" class=\"wp-image-15570\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/tabela-\u00e2ngulos-not\u00e1veis.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/tabela-\u00e2ngulos-not\u00e1veis-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/tabela-\u00e2ngulos-not\u00e1veis-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<ul><li><strong>Voc\u00ea pode encontrar <a href=\"https:\/\/www.youtube.com\/results?search_query=angulos+notaveis+m%C3%BAsica\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">diversas m\u00fasicas<\/a> para te ajudar a decorar !<\/strong><\/li><\/ul>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-25 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/\u00e3ngulos-not\u00e1veis-no-ciclo-trigonom\u00e9trico.jpg\" alt=\"\u00e3ngulos-not\u00e1veis-no-ciclo-trigonom\u00e9trico\" data-id=\"15598\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15598\" class=\"wp-image-15598\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/\u00e3ngulos-not\u00e1veis-no-ciclo-trigonom\u00e9trico.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/\u00e3ngulos-not\u00e1veis-no-ciclo-trigonom\u00e9trico-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/\u00e3ngulos-not\u00e1veis-no-ciclo-trigonom\u00e9trico-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-27 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-cosseno-e-tangente-30-\u00b0-1.jpg\" alt=\"seno-cosseno-e-tangente-30-\u00b0-1\" data-id=\"15600\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15600\" class=\"wp-image-15600\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-cosseno-e-tangente-30-\u00b0-1.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-cosseno-e-tangente-30-\u00b0-1-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-cosseno-e-tangente-30-\u00b0-1-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-29 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-cosseno-e-tangente-de-45\u00b0-1.jpg\" alt=\"seno-cosseno-e-tangente-de-45\u00b0-1\" data-id=\"15599\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15599\" class=\"wp-image-15599\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-cosseno-e-tangente-de-45\u00b0-1.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-cosseno-e-tangente-de-45\u00b0-1-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-cosseno-e-tangente-de-45\u00b0-1-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-31 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-cosseno-e-tangente-de-60\u00b0-1.jpg\" alt=\"seno-cosseno-e-tangente-de-60\u00b0-1\" data-id=\"15601\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15601\" class=\"wp-image-15601\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-cosseno-e-tangente-de-60\u00b0-1.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-cosseno-e-tangente-de-60\u00b0-1-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-cosseno-e-tangente-de-60\u00b0-1-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<p><strong>Os demais \u00e2ngulos n\u00e3o s\u00e3o obrigat\u00f3rios sabermos.<\/strong> Se o professor cobrar, dever\u00e1 dar o valor ou a tabela. Se ele der a t<strong>abela que cont\u00e9m os valores decimais <\/strong>dos \u00e2ngulos not\u00e1veis, use os valores da tabela. Veja:<\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-33 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/tabela-seno-cosseno-e-tangente-1.jpg\" alt=\"tabela-seno-cosseno-e-tangente-1\" data-id=\"15605\" data-link=\"https:\/\/beduka.com\/blog\/materias\/matematica\/o-que-e-seno-cosseno-e-tangente\/attachment\/tabela-seno-cosseno-e-tangente-1\/\" class=\"wp-image-15605\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/tabela-seno-cosseno-e-tangente-1.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/tabela-seno-cosseno-e-tangente-1-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/tabela-seno-cosseno-e-tangente-1-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<p>Ou ainda, ele pode dar o seno e o cosseno de um \u00e2ngulo n\u00e3o-not\u00e1vel e pedir os valores do seno e cosseno de seu \u00e2ngulo complementar. <strong>Neste caso, voc\u00ea ter\u00e1 de lembrar da propriedade que veremos a seguir:<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u00c2ngulos Complementares<\/h3>\n\n\n\n<p><strong>Se voc\u00ea \u00e9 um aluno atento<\/strong>, deve ter notado que o seno do 30\u00b0 \u00e9 igual ao cosseno do 60\u00b0 e que o cosseno de 30\u00b0 \u00e9 igual ao seno do 60\u00b0<\/p>\n\n\n\n<p>Aqui temos mais uma propriedade: <strong>quando se trata de \u00e2ngulos complementares<\/strong> ( que somados formam 90\u00b0), <strong>o seno de um \u00e9 igual ao cosseno de outro e vice versa.&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Quanto \u00e0 tangente, a rela\u00e7\u00e3o \u00e9 o inverso. <\/strong>Veja:<\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-35 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-cosseno-e-tangente-em-\u00e2ngulos-complementares.jpg\" alt=\"seno-cosseno-e-tangente-em-\u00e2ngulos-complementares\" data-id=\"15573\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15573\" class=\"wp-image-15573\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-cosseno-e-tangente-em-\u00e2ngulos-complementares.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-cosseno-e-tangente-em-\u00e2ngulos-complementares-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/seno-cosseno-e-tangente-em-\u00e2ngulos-complementares-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<ul><li>O mesmo serve para quaisquer \u00e2ngulos complementares (50\u00b0 e 40\u00b0, 45\u00b0 e 45\u00b0, etc)<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Rela\u00e7\u00e3o trigonom\u00e9trica fundamental<\/h3>\n\n\n\n<p>Esta rela\u00e7\u00e3o <strong>\u00e9 quase um macete,<\/strong> pois serve quando conhecemos o valor do seno de um \u00e2ngulo e queremos saber qual \u00e9 o cosseno deste \u00e2ngulo, <strong>mas nenhuma outra informa\u00e7\u00e3o foi dada.&nbsp;<\/strong><\/p>\n\n\n\n<p>Neste caso, <strong>n\u00e3o seria poss\u00edvel aplicar as f\u00f3rmulas cl\u00e1ssicas,<\/strong> s\u00f3 poder\u00edamos usar essa rela\u00e7\u00e3o:<\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-37 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/rela\u00e7\u00e3o-fundamental-trigonometria.jpg\" alt=\"rela\u00e7\u00e3o-fundamental-trigonometria\" data-id=\"15574\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15574\" class=\"wp-image-15574\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/rela\u00e7\u00e3o-fundamental-trigonometria.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/rela\u00e7\u00e3o-fundamental-trigonometria-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/rela\u00e7\u00e3o-fundamental-trigonometria-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<p>Essa f\u00f3rmula se originou por meio do uso de <a href=\"https:\/\/beduka.com\/blog\/exercicios\/matematica-exercicios\/exercicios-sobre-o-teorema-de-pitagoras\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">teorema de pit\u00e1goras<\/a>. Mas sua demonstra\u00e7\u00e3o n\u00e3o \u00e9 essencial para compreendermos as quest\u00f5es. Vamos aos exerc\u00edcios!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Exemplos num\u00e9ricos e aplica\u00e7\u00e3o<\/h2>\n\n\n\n<p>A trigonometria \u00e9 muito importante n\u00e3o s\u00f3 para resolver as quest\u00f5es das provas mas, principalmente, para o desenvolvimento das ci\u00eancias exatas, como f<strong>\u00edsica e engenharia.<\/strong><\/p>\n\n\n\n<p><strong>Foi por meio desses c\u00e1lculos que grande parte das nossas constru\u00e7\u00f5es est\u00e3o de p\u00e9.<\/strong><\/p>\n\n\n\n<p>Agora que voc\u00ea j\u00e1 sabe da import\u00e2ncia pr\u00e1tica dessa \u00e1rea, vamos <strong>treinar os exerc\u00edcios para acabar com qualquer d\u00favida:<\/strong><\/p>\n\n\n\n<ul><li>Se quiser, pode j\u00e1 ir treinando <strong>sozinho <\/strong>os outros <a href=\"https:\/\/beduka.com\/blog\/exercicios\/matematica-exercicios\/exercicios-de-trigonometria\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">exerc\u00edcios de trigonometria!<\/a><\/li><\/ul>\n\n\n\n<p>1)Encontre os valores do seno, cosseno e tangente do \u00e2ngulo  do tri\u00e2ngulo abaixo.<\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-39 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/exerc\u00edcio-1-de-trigonometria.jpg\" alt=\"exerc\u00edcio-1-de-trigonometria\" data-id=\"15575\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15575\" class=\"wp-image-15575\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/exerc\u00edcio-1-de-trigonometria.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/exerc\u00edcio-1-de-trigonometria-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/exerc\u00edcio-1-de-trigonometria-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<p>Primeiro, devemos <strong>substituir<\/strong> a medida de cada lado do tri\u00e2ngulo <strong>nas f\u00f3rmulas.<\/strong><\/p>\n\n\n\n<p>Observando a imagem, identificamos que o cateto oposto mede 5 cm, o cateto adjacente mede 12 cm e a hipotenusa \u00e9 13 cm.&nbsp;<\/p>\n\n\n\n<p><strong>Logo:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-41 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/resolu\u00e7\u00e3o-exerc\u00edcio-1-de-trigonometria-I.jpg\" alt=\"resolu\u00e7\u00e3o-exerc\u00edcio-1-de-trigonometria-I\" data-id=\"15576\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15576\" class=\"wp-image-15576\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/resolu\u00e7\u00e3o-exerc\u00edcio-1-de-trigonometria-I.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/resolu\u00e7\u00e3o-exerc\u00edcio-1-de-trigonometria-I-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/resolu\u00e7\u00e3o-exerc\u00edcio-1-de-trigonometria-I-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-43 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/resolu\u00e7\u00e3o-cosseno-1.jpg\" alt=\"resolu\u00e7\u00e3o-cosseno-1\" data-id=\"15603\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15603\" class=\"wp-image-15603\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/resolu\u00e7\u00e3o-cosseno-1.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/resolu\u00e7\u00e3o-cosseno-1-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/resolu\u00e7\u00e3o-cosseno-1-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-45 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/resolu\u00e7\u00e3o-exerc\u00edcio-1-de-trigonometria-III.jpg\" alt=\"resolu\u00e7\u00e3o-exerc\u00edcio-1-de-trigonometria-III\" data-id=\"15578\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15578\" class=\"wp-image-15578\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/resolu\u00e7\u00e3o-exerc\u00edcio-1-de-trigonometria-III.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/resolu\u00e7\u00e3o-exerc\u00edcio-1-de-trigonometria-III-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/resolu\u00e7\u00e3o-exerc\u00edcio-1-de-trigonometria-III-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<p>2)Determine o valor de x :<\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-47 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/exerc\u00edcio-2-de-trigonometria-1.jpg\" alt=\"exerc\u00edcio-2-de-trigonometria-1\" data-id=\"15580\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15580\" class=\"wp-image-15580\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/exerc\u00edcio-2-de-trigonometria-1.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/exerc\u00edcio-2-de-trigonometria-1-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/exerc\u00edcio-2-de-trigonometria-1-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<p>Primeiro, <strong>observe quais elementos voc\u00ea j\u00e1 tem <\/strong>e <strong>em qual f\u00f3rmula d\u00e1 para encaixar<\/strong> de modo que s\u00f3 reste uma inc\u00f3gnita. Esta voc\u00ea consegue calcular manipulando a equa\u00e7\u00e3o.<\/p>\n\n\n\n<p>Temos a <strong>hipotenusa <\/strong>(10 cm) e queremos descobrir x &#8211; que \u00e9 o <strong>cateto oposto<\/strong> ao \u00e2ngulo de 45\u00ba. Assim, aplicaremos a f\u00f3rmula do <strong>seno.<\/strong><\/p>\n\n\n\n<p>Na tabela trigonom\u00e9trica, o valor do seno de 45.\u00ba \u00e9 igual a 0,7071. Assim:<\/p>\n\n\n\n<ul class=\"wp-block-gallery aligncenter columns-1 is-cropped wp-block-gallery-49 is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/resolu\u00e7\u00e3o-exerc\u00edcio-2-de-trigonometria.jpg\" alt=\"resolu\u00e7\u00e3o-exerc\u00edcio-2-de-trigonometria\" data-id=\"15581\" data-link=\"https:\/\/beduka.com\/blog\/?attachment_id=15581\" class=\"wp-image-15581\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/resolu\u00e7\u00e3o-exerc\u00edcio-2-de-trigonometria.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/resolu\u00e7\u00e3o-exerc\u00edcio-2-de-trigonometria-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/04\/resolu\u00e7\u00e3o-exerc\u00edcio-2-de-trigonometria-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/li><\/ul>\n\n\n\n<p>Logo, o lado x mede 7,071 cm.<\/p>\n\n\n\n<p>Gostou do nosso artigo sobre o que \u00e9 Seno,Cosseno e Tangente? Confira outros artigos do nosso blog e se prepare para o Enem da melhor maneira! Voc\u00ea tamb\u00e9m pode se organizar com o nosso <a href=\"https:\/\/beduka.com\/blog\/dicas\/enem-dicas\/plano-de-estudos-gratuito\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">plano de estudos<\/a>, o mais completo da internet, e o melhor: totalmente gratuito!<\/p>\n\n\n\n<p>Queremos te ajudar a encontrar a FACULDADE IDEAL! Logo abaixo, fa\u00e7a uma pesquisa por curso e cidade que te mostraremos todas as faculdades que podem te atender. Informamos a nota de corte, valor de mensalidade, nota do MEC, avalia\u00e7\u00e3o dos alunos, modalidades de ensino e muito mais.<\/p>\n\n\n\n<p>Experimente agora!<br><\/p>\n","protected":false},"excerpt":{"rendered":"<p>O que \u00e9 Seno, Cosseno e Tangente? S\u00e3o rela\u00e7\u00f5es matem\u00e1ticas que encontramos dividindo lados por \u00e2ngulos. Pode parecer meio vago e sem sentido mas, neste artigo, vamos te mostrar com imagens e exemplos todos os detalhes: como fazer o c\u00e1lculo, para que ele serve e o que significam. Neste artigo sobre o que \u00e9 Seno, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":15583,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0},"categories":[487],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.10 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>O que \u00e9 Seno, Cosseno e Tangente? 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