{"id":21284,"date":"2021-05-12T12:29:45","date_gmt":"2021-05-12T15:29:45","guid":{"rendered":"https:\/\/beduka.com\/blog\/?p=21284"},"modified":"2021-05-12T12:29:48","modified_gmt":"2021-05-12T15:29:48","slug":"exercicios-de-funcoes-trigonometricas","status":"publish","type":"post","link":"https:\/\/beduka.com\/blog\/exercicios\/exercicios-de-funcoes-trigonometricas\/","title":{"rendered":"Os 10 melhores exerc\u00edcios de fun\u00e7\u00f5es trigonom\u00e9tricas"},"content":{"rendered":"\n<blockquote class=\"wp-block-quote\"><p><strong>As fun\u00e7\u00f5es trigonom\u00e9tricas s\u00e3o fun\u00e7\u00f5es peri\u00f3dicas que relacionam, por meio do ciclo trigonom\u00e9trico, o valor do \u00e2ngulo, em graus ou radianos, com o valor da raz\u00e3o trigonom\u00e9trica. Leia o resumo e em seguida resolva as exerc\u00edcios sobre fun\u00e7\u00f5es trigonom\u00e9tricas com gabarito para entender como funciona.<\/strong><\/p><\/blockquote>\n\n\n\n<p><strong>Quer seguir diretamente para alguma parte espec\u00edfica?<\/strong> Clique em algum dos t\u00f3picos abaixo<\/p>\n\n\n\n<ul><li><a href=\"#fun\u00e7\u00f5es-peri\u00f3dicas\">O que s\u00e3o fun\u00e7\u00f5es peri\u00f3dicas?<\/a><\/li><li><a href=\"#fun\u00e7\u00f5es-trigonom\u00e9tricas\">O que s\u00e3o fun\u00e7\u00f5es trigonom\u00e9tricas?<\/a><\/li><li><a href=\"#exerc\u00edcios-sobre-fun\u00e7\u00f5es-trigonom\u00e9tricas\">Exerc\u00edcios sobre fun\u00e7\u00f5es trigonom\u00e9tricas.<\/a><\/li><li><a href=\"#gabarito-dos-exerc\u00edcios-sobre-as-fun\u00e7\u00f5es-trigonom\u00e9tricas\">Gabarito dos exerc\u00edcios sobre as fun\u00e7\u00f5es trigonom\u00e9tricas.<\/a><\/li><\/ul>\n\n\n\n<p>Quando voc\u00ea terminar os exerc\u00edcios de fun\u00e7\u00f5es trigonom\u00e9tricas, que tal testar seus conhecimentos no <a href=\"https:\/\/beduka.com\/simulado-enem\/#\/\" target=\"_blank\" rel=\"noreferrer noopener\">Melhor Simulado Enem do Brasil<\/a>?<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"fun\u00e7\u00f5es-peri\u00f3dicas\">O que s\u00e3o fun\u00e7\u00f5es peri\u00f3dicas?<\/h2>\n\n\n\n<p><strong>Fun\u00e7\u00f5es peri\u00f3dicas s\u00e3o aquelas que descrevem um fen\u00f4meno que se repete num determinado intervalo de tempo<\/strong>, sendo o per\u00edodo o menor intervalo de tempo em que acontece a repeti\u00e7\u00e3o.&nbsp;<\/p>\n\n\n\n<ul><li><strong>S\u00e3o mais de 200 resumos gratuitos para o ENEM<\/strong> no <a href=\"https:\/\/www.instagram.com\/beduka_oficial\/\" target=\"_blank\" rel=\"noreferrer noopener\">Instagram do Beduka<\/a>, aproveite!<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"fun\u00e7\u00f5es-trigonom\u00e9tricas\">O que s\u00e3o fun\u00e7\u00f5es trigonom\u00e9tricas?<\/h2>\n\n\n\n<p>Fun\u00e7\u00f5es trigonom\u00e9tricas s\u00e3o aquelas que relacionam, atrav\u00e9s do ciclo trigonom\u00e9trico, o valor do \u00e2ngulo, em graus ou radianos, com o valor da raz\u00e3o trigonom\u00e9trica. Existem 3 tipos de fun\u00e7\u00f5es trigonom\u00e9tricas: <strong>fun\u00e7\u00e3o seno, fun\u00e7\u00e3o cosseno e fun\u00e7\u00e3o tangente<\/strong>.<\/p>\n\n\n\n<p><strong>Falaremos mais detalhadamente sobre cada uma abaixo:<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Fun\u00e7\u00e3o seno<\/h3>\n\n\n\n<p><strong>A fun\u00e7\u00e3o seno \u00e9 uma fun\u00e7\u00e3o peri\u00f3dica cujo per\u00edodo \u00e9 2\u03c0 e possui imagem entre -1 e 1 (-1 \u2264 senx \u22641) sendo expressa por: f(x)= sen x<\/strong>. O dom\u00ednio da fun\u00e7\u00e3o seno, que s\u00e3o os poss\u00edveis valores de x, s\u00e3o infinitos, posto que h\u00e1 infinitas possibilidades de valores de \u00e2ngulo.<\/p>\n\n\n\n<p>Seu sinal muda a depender do quadrante em que se encontra: positivo quando x estiver nos 1\u00ba e 2\u00ba quadrantes e negativo quando estiver nos 3\u00ba e 4\u00ba quadrantes. A fun\u00e7\u00e3o seno ser\u00e1 crescente nos 1\u00ba e 4\u00ba quadrantes, bem como decrescente nos 2\u00ba e 3\u00ba quadrantes.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Fun\u00e7\u00e3o Cosseno<\/h3>\n\n\n\n<p><strong>A fun\u00e7\u00e3o cosseno tem defini\u00e7\u00e3o igual \u00e0 fun\u00e7\u00e3o seno<\/strong>, mas suas representa\u00e7\u00f5es gr\u00e1ficas diferem uma da outra. Assim, o per\u00edodo da fun\u00e7\u00e3o cosseno ser\u00e1 tamb\u00e9m de 2\u03c0, bem como sua imagem estar\u00e1 entre -1 e 1(-1 \u2264 cosx \u22641). A fun\u00e7\u00e3o cosseno \u00e9 expressa por: <strong>f(x) = cos x<\/strong>.&nbsp;<\/p>\n\n\n\n<p>Assim como na fun\u00e7\u00e3o seno, o dom\u00ednio \u00e9 representado pelos infinitos valores de x, posto que h\u00e1 infinitas possibilidades.<\/p>\n\n\n\n<p>O sinal ser\u00e1 positivo quando x estiver nos 1\u00ba e 4\u00ba quadrantes e negativo quando estiver nos 2\u00ba e 3\u00ba quadrantes. A fun\u00e7\u00e3o cosseno ser\u00e1 crescente nos 3\u00ba e 4\u00ba quadrantes, e decrescente nos 1\u00ba e 2\u00ba quadrantes.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Fun\u00e7\u00e3o Tangente<\/h3>\n\n\n\n<p><strong>A fun\u00e7\u00e3o tangente se d\u00e1 pela raz\u00e3o entre seno e cosseno, tendo como condi\u00e7\u00e3o para sua exist\u00eancia que o cosseno difira de 0<\/strong>.&nbsp;<\/p>\n\n\n\n<p>Diferente das fun\u00e7\u00f5es seno e cosseno, a fun\u00e7\u00e3o tangente n\u00e3o tem imagem limitada, podendo assumir qualquer valor. O per\u00edodo da fun\u00e7\u00e3o tangente \u00e9 \u03c0 e ela se expressa por: <strong>f(x) = tan x<\/strong>.&nbsp;<\/p>\n\n\n\n<p>A fun\u00e7\u00e3o tangente ter\u00e1 dom\u00ednio limitado, n\u00e3o havendo valor se a fun\u00e7\u00e3o estiver no eixo dos senos.<\/p>\n\n\n\n<p>Como as demais fun\u00e7\u00f5es trigonom\u00e9tricas, a fun\u00e7\u00e3o tangente varia o sinal a depender do quadrante em que x se encontra. Se x estiver nos 1\u00ba e 3\u00ba quadrantes, a fun\u00e7\u00e3o tangente ter\u00e1 sinal positivo; se pertencer aos 2 e 4\u00ba quadrantes, a fun\u00e7\u00e3o tangente ter\u00e1 sinal negativo. <strong>A fun\u00e7\u00e3o tangente \u00e9 sempre crescente<\/strong>.<\/p>\n\n\n\n<ul><li>Gostou deste resumo? Acesse o <a href=\"https:\/\/beduka.com\/blog\/materias\/matematica\/funcoes-trigonometricas\/\" target=\"_blank\" rel=\"noreferrer noopener\">artigo sobre fun\u00e7\u00f5es trigonom\u00e9tricas<\/a> no nosso blog<strong> <\/strong>e leia um pouco mais sobre fun\u00e7\u00f5es trigonom\u00e9tricas.<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"exerc\u00edcios-sobre-fun\u00e7\u00f5es-trigonom\u00e9tricas\">Exerc\u00edcios sobre fun\u00e7\u00f5es trigonom\u00e9tricas<\/h2>\n\n\n\n<p><strong>Quest\u00e3o 1- (<\/strong><a href=\"http:\/\/www.utfpr.edu.br\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Cefet-PR<\/strong><\/a><strong>)<\/strong> A fun\u00e7\u00e3o real f(x) = a + b. sen cx tem imagem igual a [-7, 9] e seu per\u00edodo \u00e9 \u03c0\/2 rad. Assim, a + b + c vale:<\/p>\n\n\n\n<p><strong>a) <\/strong>13<\/p>\n\n\n\n<p><strong>b) <\/strong>9<\/p>\n\n\n\n<p><strong>c) <\/strong>8<\/p>\n\n\n\n<p><strong>d) <\/strong>\u2013 4<\/p>\n\n\n\n<p><strong>e)<\/strong> 10<\/p>\n\n\n\n<p><strong>Quest\u00e3o 2- (<\/strong><a href=\"http:\/\/www.ufrgs.br\/ufrgs\/inicial\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>UFRGS 2016<\/strong><\/a><strong>)<\/strong> Considere as fun\u00e7\u00f5es f e g definidas por f (x) = sen x e g (x) = cos x. O n\u00famero de ra\u00edzes da equa\u00e7\u00e3o f (x) = g(x) no intervalo [\u20132\u03c0, 2c] \u00e9:<\/p>\n\n\n\n<p><strong>a)<\/strong> 3<\/p>\n\n\n\n<p><strong>b) <\/strong>4<\/p>\n\n\n\n<p><strong>c) <\/strong>5<\/p>\n\n\n\n<p><strong>d) <\/strong>6<\/p>\n\n\n\n<p><strong>e) <\/strong>7<\/p>\n\n\n\n<p><strong>Quest\u00e3o 3-<\/strong> <strong>(<\/strong><a href=\"https:\/\/www.fuvest.br\/\"><strong>Fuvest<\/strong><\/a><strong>)<\/strong> Dentre os n\u00fameros a seguir, o mais pr\u00f3ximo de sen50\u00b0 \u00e9:<\/p>\n\n\n\n<p><strong>a) <\/strong>0,2<\/p>\n\n\n\n<p><strong>b) <\/strong>0,4<\/p>\n\n\n\n<p><strong>c) <\/strong>0,6<\/p>\n\n\n\n<p><strong>d) <\/strong>0,8<\/p>\n\n\n\n<p><strong>e) <\/strong>1,0<\/p>\n\n\n\n<p><strong>Quest\u00e3o 4- (<\/strong><a href=\"https:\/\/www.cesgranrio.org.br\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Cesgranrio<\/strong><\/a><strong>)<\/strong> Se senx &#8211; cosx = 1\/2, o valor de senx.cosx \u00e9 igual a:<\/p>\n\n\n\n<p>a) -3\/16<\/p>\n\n\n\n<p>b) -3\/8<\/p>\n\n\n\n<p>c) 3\/8<\/p>\n\n\n\n<p>d) 3\/4<\/p>\n\n\n\n<p>e) 3\/2<\/p>\n\n\n\n<p><strong>Quest\u00e3o 5- (<\/strong><a href=\"http:\/\/www.ufrgs.br\/ufrgs\/inicial\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>UFRGS 2015<\/strong><\/a><strong>)<\/strong> O gr\u00e1fico da fun\u00e7\u00e3o f, definida por f(x) = cos x , e o gr\u00e1fico da fun\u00e7\u00e3o g, quando representados no mesmo sistema de coordenadas, possuem somente dois pontos em comum.<\/p>\n\n\n\n<p>Assim, das alternativas abaixo, a que pode representar a fun\u00e7\u00e3o g \u00e9:<\/p>\n\n\n\n<p><strong>a)<\/strong> g(x) = (sen x)\u00b2 + (cos x)\u00b2.<\/p>\n\n\n\n<p><strong>b) <\/strong>g(x) = x\u00b2.<\/p>\n\n\n\n<p><strong>c)<\/strong> g(x) = 2x\u00b2.<\/p>\n\n\n\n<p><strong>d)<\/strong> g(x) = logx.<\/p>\n\n\n\n<p><strong>e) <\/strong>g(x) = sen x.<\/p>\n\n\n\n<ul><li><strong>Muito bem! <\/strong>Voc\u00ea chegou \u00e0 metade dos Exerc\u00edcios sobre fun\u00e7\u00f5es trigonom\u00e9tricas. Continue fazendo o restante.<\/li><\/ul>\n\n\n\n<p><strong>Quest\u00e3o 6- (<\/strong><a href=\"https:\/\/www.cefetmg.br\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Cefet\/MG &#8211; 2017<\/strong><\/a><strong>)<\/strong> Em um tri\u00e2ngulo ret\u00e2ngulo, a tangente de um de seus \u00e2ngulos agudos \u00e9 2. Sabendo-se que a hipotenusa desse tri\u00e2ngulo \u00e9 5, o valor do seno desse mesmo \u00e2ngulo \u00e9<\/p>\n\n\n\n<p><strong>a) <\/strong>4\/5<\/p>\n\n\n\n<p><strong>b) <\/strong>\u221a5\/4<\/p>\n\n\n\n<p><strong>c) <\/strong>\u221a5\/5<\/p>\n\n\n\n<p><strong>d) <\/strong>2\u221a5\/5<\/p>\n\n\n\n<p><strong>e) <\/strong>5\/2<\/p>\n\n\n\n<p><strong>Quest\u00e3o 7- (<\/strong><a href=\"http:\/\/www.urca.br\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>URCA 2016\/1<\/strong><\/a><strong>)<\/strong> Se tg(x)=2 ent\u00e3o \u00e9 CORRETO afirmar que:<\/p>\n\n\n\n<p><strong>a) <\/strong>cos(x) = 1\/2 e sen(x) = 1.<\/p>\n\n\n\n<p><strong>b) <\/strong>cos(x)=\u221a2\/2 e sen(x)=\u221a2<\/p>\n\n\n\n<p><strong>c) <\/strong>sen(x)=1\/\u221a5 ou sen(x)=\u22121\/\u221a5.<\/p>\n\n\n\n<p><strong>d) <\/strong>cos(x)=1\/\u221a5 ou cos(x)=\u22121\/\u221a5.<\/p>\n\n\n\n<p><strong>e) <\/strong>cos(x)=\u221a3\/2 e sen(x)=\u221a3.<\/p>\n\n\n\n<p><strong>Quest\u00e3o 8- (<\/strong><a href=\"https:\/\/www.unitau.br\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Unitau<\/strong><\/a><strong>)<\/strong> O per\u00edodo da fun\u00e7\u00e3o y=sen(\u03c0\/\u221a2.x) \u00e9:<\/p>\n\n\n\n<p><strong>a) <\/strong>\u221a2\/2.<\/p>\n\n\n\n<p><strong>b) <\/strong>\u221a\u03c0\/2.<\/p>\n\n\n\n<p><strong>c) <\/strong>\u03c0\/2<\/p>\n\n\n\n<p><strong>d) <\/strong>\u221a2<\/p>\n\n\n\n<p><strong>e) <\/strong>\u221a2\/2<\/p>\n\n\n\n<p><strong>Quest\u00e3o 9- (<\/strong><a href=\"https:\/\/portal.uel.br\/home\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Uel<\/strong><\/a><strong>)<\/strong> O valor express\u00e3o cos (2\u03c0\/3) + sen (3\u03c0\/2) + tg (5\u03c0\/4) \u00e9:<\/p>\n\n\n\n<p><strong>a)<\/strong> (\u221a2-3)\/2<\/p>\n\n\n\n<p><strong>b)<\/strong> -1\/2<\/p>\n\n\n\n<p><strong>c)<\/strong> 0<\/p>\n\n\n\n<p><strong>d)<\/strong> 1\/2<\/p>\n\n\n\n<p><strong>e)<\/strong> \u221a3\/2<\/p>\n\n\n\n<p><strong>Quest\u00e3o 10. (<\/strong><a href=\"https:\/\/portal.uel.br\/home\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Uel<\/strong><\/a><strong>)<\/strong> O valor da express\u00e3o [sen(8\u03c0\/3) &#8211; cos(5\u03c0)] \/ tg(13\u03c0\/6) \u00e9:<\/p>\n\n\n\n<p><strong>a)<\/strong> (3+2\u221a3)\/2<\/p>\n\n\n\n<p><strong>b) <\/strong>(3\u221a2 + 2\u221a3)\/2<\/p>\n\n\n\n<p><strong>c)<\/strong> 3+2\u221a3<\/p>\n\n\n\n<p><strong>d) <\/strong>3\u221a2 + 2\u221a3<\/p>\n\n\n\n<p><strong>e) <\/strong>3( \u221a2 + \u221a3)<\/p>\n\n\n\n<ul><li><strong>Parab\u00e9ns,<\/strong> voc\u00ea fez todos os exerc\u00edcios sobre fun\u00e7\u00f5es trigonom\u00e9tricas. Confira agora o Gabarito:<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"gabarito-dos-exerc\u00edcios-sobre-as-fun\u00e7\u00f5es-trigonom\u00e9tricas\">Gabarito dos exerc\u00edcios sobre as fun\u00e7\u00f5es trigonom\u00e9tricas.<\/h2>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 1 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: letra <strong>a) <\/strong>13<\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 2 &#8211;<\/strong><\/p>\n\n\n\n<p>alternativa correta: letra <strong>b) <\/strong>4<\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 3 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: letra <strong>d) <\/strong>0,8<\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 4 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: letra <strong>c) <\/strong>3\/8<\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 5 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: letra <strong>b) <\/strong>g(x) = x\u00b2.<\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 6 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: letra <strong>d) <\/strong>2\u221a5\/5<\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 7 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: letra <strong>d) <\/strong>cos(x)=1\/\u221a5 ou cos(x)=\u22121\/\u221a5<\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 8 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: letra <strong>d) <\/strong>\u221a2<\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 9 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: letra <strong>b) <\/strong>-1\/2<\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 10 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: letra <strong>a) <\/strong>(3+2\u221a3)\/2<\/p>\n\n\n\n<p>Estude para o Enem com o <a href=\"https:\/\/beduka.com\/simulado\" target=\"_blank\" rel=\"noreferrer noopener\">Simulado Beduka.<\/a> <strong>\u00c9 gratuito!<\/strong><\/p>\n\n\n\n<p><strong>Gostou das nossas quest\u00f5es sobre as fun\u00e7\u00f5es trigonom\u00e9tricas? <\/strong>Compartilhe com os seus amigos e comente abaixo sobre as \u00e1reas que voc\u00ea deseja mais explica\u00e7\u00f5es.<\/p>\n\n\n\n<p><strong>Queremos te ajudar a encontrar a FACULDADE IDEAL! <\/strong>Logo abaixo, fa\u00e7a uma pesquisa por curso e cidade que te mostraremos todas as faculdades que podem te atender.<strong> <\/strong>Informamos a nota de corte, valor de mensalidade, nota do MEC, avalia\u00e7\u00e3o dos alunos, modalidades de ensino e muito mais.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Neste resumo, falamos o que s\u00e3o as fun\u00e7\u00f5es trigonom\u00e9tricas e todas as suas nuances. Tamb\u00e9m fornecemos exerc\u00edcios sobre fun\u00e7\u00f5es trigonom\u00e9tricas com gabarito.<\/p>\n","protected":false},"author":1,"featured_media":21308,"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":[568,610],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.10 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Os 10 melhores exerc\u00edcios de fun\u00e7\u00f5es trigonom\u00e9tricas<\/title>\n<meta name=\"description\" content=\"Neste resumo, falamos o que s\u00e3o as fun\u00e7\u00f5es trigonom\u00e9tricas e todas as suas nuances. 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