{"id":94800,"date":"2017-01-13T09:28:24","date_gmt":"2017-01-13T11:28:24","guid":{"rendered":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/?p=94800"},"modified":"2026-05-28T18:42:41","modified_gmt":"2026-05-28T20:42:41","slug":"razoes-trigonometricas","status":"publish","type":"post","link":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/razoes-trigonometricas","title":{"rendered":"Raz\u00f5es Trigonom\u00e9tricas"},"content":{"rendered":"<p>A\u00a0<b>trigonometria<\/b>\u00a0\u00e9 um ramo da matem\u00e1tica, cujo significado etimol\u00f3gico \u00e9 \u201ca medi\u00e7\u00e3o de tri\u00e2ngulos \u201c.<\/p>\n<p><b>Em geral, a trigonometria \u00e9 o estudo das rela\u00e7\u00f5es trigonom\u00e9tricas:<\/b>\u00a0seno, cosseno; tangente, co-tangente; secante e co-secante.<\/p>\n<p>Envolvidos direta ou indiretamente em outros ramos da matem\u00e1tica e aplicados em todos os dom\u00ednios em que s\u00e3o necess\u00e1rias medi\u00e7\u00f5es de precis\u00e3o.<\/p>\n<p><b>Trigonometria<\/b>\u00a0se aplica a outros ramos da geometria, como \u00e9 as \u00e1reas de estudo de caso na geometria do espa\u00e7o .<\/p>\n<p><b>Possui in\u00fameras aplica\u00e7\u00f5es, entre as quais:<\/b>\u00a0t\u00e9cnicas de triangula\u00e7\u00e3o, por exemplo, s\u00e3o usados em astronomia para medir dist\u00e2ncias para estrelas pr\u00f3ximas, ao medir dist\u00e2ncias entre pontos geogr\u00e1fica e sistemas de navega\u00e7\u00e3o global por sat\u00e9lite.<\/p>\n<p>As\u00a0<b>raz\u00f5es trigonom\u00e9tricas<\/b>\u00a0s\u00e3o as raz\u00f5es entre os comprimentos dos lados de um tri\u00e2ngulo. Essas raz\u00f5es, em trigonometria, relacionam a propor\u00e7\u00e3o entre os lados de um tri\u00e2ngulo ret\u00e2ngulo e o respectivo \u00e2ngulo. As raz\u00f5es trigonom\u00e9tricas b\u00e1sicas s\u00e3o seno, cosseno e tangente. Outras raz\u00f5es trigonom\u00e9tricas importantes, como cossecante, secante e cotangente, podem ser derivadas usando seno, cosseno e tangente, respectivamente.<\/p>\n<p>A palavra &#8220;trigonometria&#8221; tem origem nas palavras &#8220;trigonon&#8221;, que significa &#8220;tri\u00e2ngulo&#8221;, e &#8220;metron&#8221;, que significa &#8220;medir&#8221;. \u00c9 um ramo da matem\u00e1tica que lida com a rela\u00e7\u00e3o entre os \u00e2ngulos e os lados de um tri\u00e2ngulo ret\u00e2ngulo. De fato, a trigonometria \u00e9 uma das disciplinas mais antigas estudadas por estudiosos em todo o mundo. Vamos entender as raz\u00f5es trigonom\u00e9tricas em detalhes nas se\u00e7\u00f5es a seguir.<\/p>\n<p>As<b>\u00a0raz\u00f5es trigonom\u00e9tricas<\/b>\u00a0s\u00e3o compara\u00e7\u00f5es matem\u00e1ticas (raz\u00f5es) entre os comprimentos dos lados de um tri\u00e2ngulo ret\u00e2ngulo. Elas s\u00e3o usadas para encontrar comprimentos de lados ou \u00e2ngulos desconhecidos dentro de um tri\u00e2ngulo e s\u00e3o fundamentais em \u00e1reas como f\u00edsica, engenharia e arquitetura.<\/p>\n<p>Consideremos um \u00e2ngulo agudo qualquer de medida \u03b1, levando-se em conta os infinitos tri\u00e2ngulos ret\u00e2ngulos que possuem o \u00e2ngulo de medida \u03b1.<\/p>\n<p>Os tri\u00e2ngulos OAB, OCD, OEF e OGH s\u00e3o todos semelhantes.<\/p>\n<p><b>Logo: Respectivamente, as raz\u00f5es (trigonom\u00e9tricas) r<sub>1<\/sub>, r<sub>2<\/sub>, r<sub>3<\/sub> s\u00e3o denominadas de<\/b>:<\/p>\n<p><strong>seno do \u00e2ngulo \u03b1 (sen \u03b1),<\/strong><\/p>\n<p><strong>cosseno do \u00e2ngulo \u03b1 (cos \u03b1) e tangente do \u00e2ngulo (tg \u03b1)<\/strong><\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-94802 alignnone\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_763-Jan.-13-08.20.jpg\" alt=\"Raz\u00f5es Trigonom\u00e9tricas\" width=\"245\" height=\"164\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_763-Jan.-13-08.20.jpg 245w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_763-Jan.-13-08.20-110x75.jpg 110w\" sizes=\"(max-width: 245px) 100vw, 245px\" \/><\/p>\n<p>Co-seno do \u00e2ngulo agudo \u03b1 (cos \u03b1) \u00e9 a raz\u00e3o entre a medida do cateto adjacente a \u03b1 e a medida da hipotenusa.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-94804 size-full\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_765-Jan.-13-08.20.jpg\" alt=\"Raz\u00f5es Trigonom\u00e9tricas\" width=\"265\" height=\"116\" \/><\/p>\n<p>Seno do \u00e2ngulo \u03b1 (sen \u03b1). A raz\u00e3o k \u00e9 uma caracter\u00edstica de cada \u00e2ngulo \u03b1 e seu valor \u00e9 chamado de seno do \u00e2ngulo \u03b1 (sen \u03b1).<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-94808\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_766-Jan.-13-08.23.jpg\" alt=\"Raz\u00f5es Trigonom\u00e9tricas\" width=\"268\" height=\"106\" \/><\/p>\n<p>Tangente do \u00e2ngulo \u03b1 (tg \u03b1) \u00e9 raz\u00e3o entre a medida do cateto oposto a \u03b1 e a medida do cateto adjacente a \u03b1.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-94809\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_767-Jan.-13-08.23.jpg\" alt=\"Raz\u00f5es Trigonom\u00e9tricas\" width=\"276\" height=\"98\" \/><\/p>\n<p><b>F\u00f3rmulas das Raz\u00f5es Trigonom\u00e9tricas<\/b><\/p>\n<p>As\u00a0<b>raz\u00f5es trigonom\u00e9tricas<\/b>\u00a0podem ser calculadas pela raz\u00e3o entre quaisquer dois lados de um tri\u00e2ngulo ret\u00e2ngulo. Podemos calcular o terceiro lado usando o teorema de Pit\u00e1goras, a partir da medida dos outros dois lados.<\/p>\n<p>Podemos usar a forma abreviada das raz\u00f5es trigonom\u00e9tricas para comparar o comprimento de quaisquer dois lados com o \u00e2ngulo da base. O \u00e2ngulo \u03b8 \u00e9 um \u00e2ngulo agudo (\u03b8 &lt; 90\u00ba) e, em geral, \u00e9 medido em rela\u00e7\u00e3o ao eixo x positivo, no sentido anti-hor\u00e1rio.<\/p>\n<p><b>As f\u00f3rmulas b\u00e1sicas das raz\u00f5es trigonom\u00e9tricas s\u00e3o apresentadas abaixo:<\/b><\/p>\n<p><b>sen \u03b8 =<\/b>\u00a0Cateto\/Hipotenusa<br \/>\n<b>cos \u03b8 =<\/b>\u00a0Cateto\/Hipotenusa<br \/>\n<b>tan \u03b8 =<\/b>\u00a0Cateto\/Cabo<br \/>\n<b>sec \u03b8 =<\/b>\u00a0Hipotenusa\/Cabo<br \/>\n<b>cosec \u03b8 =<\/b>\u00a0Hipotenusa\/Caeto<br \/>\n<b>cot \u03b8 =<\/b>\u00a0Cateto\/Cabo<\/p>\n<p>Agora, observemos as f\u00f3rmulas das raz\u00f5es trigonom\u00e9tricas rec\u00edprocas das raz\u00f5es trigonom\u00e9tricas mencionadas acima. Como podemos observar, sen \u03b8 \u00e9 o inverso de cosec \u03b8, cos \u03b8 \u00e9 o inverso de sec \u03b8, tan \u03b8 \u00e9 o inverso de cot \u03b8 e vice-versa.<\/p>\n<p><b>Portanto, o novo conjunto de f\u00f3rmulas para raz\u00f5es trigonom\u00e9tricas \u00e9:<\/b><\/p>\n<p><b>sen \u03b8 =<\/b>\u00a01\/cosec \u03b8<br \/>\n<b>cos \u03b8 =<\/b>\u00a01\/seg \u03b8<br \/>\n<b>bronzeado \u03b8 =<\/b>\u00a01\/ber\u00e7o \u03b8<br \/>\n<b>cosec \u03b8 =<\/b>\u00a01\/sen \u03b8<br \/>\n<b>seg \u03b8 =<\/b>\u00a01\/cos \u03b8<br \/>\n<b>ber\u00e7o \u03b8 =<\/b>\u00a01\/tan \u03b8<\/p>\n<p><strong>Fonte:<\/strong>\u00a0Col\u00e9gio S\u00e3o Francisco\/www.cuemath.com<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A\u00a0trigonometria\u00a0\u00e9 um ramo da matem\u00e1tica, cujo significado etimol\u00f3gico \u00e9 \u201ca medi\u00e7\u00e3o de tri\u00e2ngulos \u201c. Em geral, a trigonometria \u00e9 o estudo das rela\u00e7\u00f5es trigonom\u00e9tricas:\u00a0seno, cosseno; tangente, co-tangente; secante e co-secante. Envolvidos direta ou indiretamente em outros ramos da matem\u00e1tica e aplicados em todos os dom\u00ednios em que s\u00e3o necess\u00e1rias medi\u00e7\u00f5es de precis\u00e3o. Trigonometria\u00a0se aplica a [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[414],"tags":[],"class_list":["post-94800","post","type-post","status-publish","format-standard","hentry","category-matematica"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Raz\u00f5es Trigonom\u00e9tricas, Matem\u00e1tica, Tri\u00e2ngulo Raz\u00f5es Trigonom\u00e9tricas<\/title>\n<meta name=\"description\" content=\"Raz\u00f5es Trigonom\u00e9tricas, Matem\u00e1tica, Tri\u00e2ngulo, Ret\u00e2ngulo, Tangente, Trigonometria, Comprimentos, Medida, Lados, Raz\u00f5es Trigonom\u00e9tricas\" \/>\n<meta name=\"robots\" content=\"noindex, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<meta property=\"og:locale\" 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