Question

complete a tabela
por favor me ajude ​

Answer 1

Resposta correta:

$~~{\because~~\boxed{\begin{gathered}\boxed{\begin{array}{c|c|c|c}{{\sf{Graus}} }\ &{{\sf{Radianos}}}\ &{{\sf{Graus}}}\ &{{\sf{Radianos}}}\\\!\!\!\!\!^{\underline{\qquad\qquad\qquad\quad\qquad\quad\qquad\quad\qquad\quad\qquad\quad\qquad\qquad}}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\ \\\red{{0}^{ \: \tiny{{\text{o}}}}} & \red{{\displaystyle{\frac{0\pi}{180}\approx \: 0}}} &\red{180^{ \: \tiny{{\text{o} }}}} &\red{{ \displaystyle {\pi }\approx \: 3,14 }}\\\!\!\!\!\!^{\underline{\qquad\qquad\qquad\quad \: \: \: }}\!\!\!\!\!\ \\\red{30^{ \: \tiny{{\text{o}}}}} &\red{{ \displaystyle {\frac{\pi}{6}\approx \: 0{,}52}}} &\red{210^{ \: \tiny{{\text{o}}}}} &\red{{ \displaystyle {\frac{7\pi }{6} \approx \: 3{,}66}}}\\\!\!\!\!\!^{\underline{\qquad\qquad\qquad\quad \: \: \: }}\!\!\!\!\\\red{45^{ \: \tiny{{\text{o}}}}} &\red{{ \displaystyle {\frac{\pi}{4}\approx \: 0{,}78}}}&\red{225^{ \: \tiny{{\text{o}}}}} &\red{{ \displaystyle {\frac{5\pi }{4}\approx \: 3{,}92 }}}\\\!\!\!\!\!^{\underline{\qquad\qquad\qquad\quad \: \: \: }}\!\!\!\!\\\red{60^{ \: \tiny{{\text{o}}}}} &\red{{ \displaystyle {\frac{\pi}{3}\approx \: 1{,}04}}}&\red{240^{ \: \tiny{{\text{o}}}}} &\red{{ \displaystyle {\frac{4\pi }{3}\approx \: 4{,}18 }}}\end{array}~~}\end{gathered}} }$

$~~{\therefore~~\boxed{\begin{gathered}\boxed{\begin{array}{c|c|c|c}\red{90^{ \: \tiny{{\text{o}}}}} &\red{{ \displaystyle {\frac{\pi}{2}\approx \: 1{,}57}}}&\red{270^{ \: \tiny{{\text{o}}}}}~~~ &\red{{ \displaystyle {\frac{3\pi }{2}\approx \: 4{,}71 }}}\\\!\!\!\!\!^{\underline{\qquad\qquad\qquad\quad}}\!\!\!\!\\\red{120^{ \: \tiny{{\text{o}}}}} &\red{{ \displaystyle {\frac{2\pi}{3}\approx \: 2{,}09}}}&\red{300^{ \: \tiny{{\text{o}}}}} &\red{{ \displaystyle {\frac{5\pi }{3}\approx \: 5{,}23 }}} \\\!\!\!\!\!^{\underline{\qquad\qquad\qquad\quad}}\!\!\!\!\\ \red{135^{ \: \tiny{{\text{o}}}}} &\red{{ \displaystyle {\frac{3\pi}{4}\approx \: 2{,}35}}}&\red{315^{ \: \tiny{{\text{o}}}}} &\red{{ \displaystyle {\frac{7\pi }{4}\approx \: 5{,}49 }}}\\\!\!\!\!\!^{\underline{\qquad\qquad\qquad\quad}}\!\!\!\!\\\red{150^{ \: \tiny{{\text{o}}}}} &\red{{ \displaystyle {\frac{5\pi}{6}\approx \: 2{,}61}}}&\red{360^{ \: \tiny{{\text{o}}}}} &\red{{ \displaystyle {2\pi}\approx 6,28}}\end{array}~~}\end{gathered}}}$

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$\space\space\space\space\space\huge\mid{\boxed{\bf{\blue{Matem\acute{a}tica}}}\mid}$

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Explicação passo a passo

Para converter graus em radianos, temos que multiplicar o ângulo dado (em graus) por$~\gray{\frac{\pi}{180^{ \: \tiny{{\text{o}}}}}} .~$Para isso, usamos a fórmula geral para converter de graus em radianos. Ou seja:

$\large\underline{ \overline{\boxed{\begin{array}{clr}\\~~~~~~~~ \displaystyle{ \text{Radianos = Graus} \times \frac{\pi}{\text{180}^{ \: \tiny{{\text{o}}}}} }\\~~~~~~~~~~~ \\ \end{array}}}}$

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Vamos resolver um exemplo abaixo:

• $\Large{ \bf{30^{ \: \tiny{{\text{o}}}}~em~radianos}}$

$\large\gray{\space\space\space\space\downarrow}\space\space\space\space\displaystyle\begin{aligned} \frac{\pi}{6} \times \frac{\pi}{\pi} \end{aligned}\left\{\begin{array}{ll}\displaystyle{\text{rad} = {30}^{ \: \tiny{{\text{o}}}} \times \frac{\pi}{\text{180}^{ \: \tiny{{\text{o}}}}} } \\ \\ \displaystyle{30 ^{ \: \tiny{{\text{o}}}}= \frac{\pi}{6} }\\ \\\displaystyle{ \frac{\pi}{6} \times \frac{\pi}{\text{180}^{ \: \tiny{{\text{o}}}}} } \\ \\ \displaystyle{180 ^{ \: \tiny{{\text{o}}}}= \pi }\\ \\~~\displaystyle{= \frac{\pi}{6} \times \frac{\pi}{\pi} ~~} \\ \end{array}\right.$

$\large\gray{\space\space\space\space\downarrow}\space\space\space\space\displaystyle\begin{aligned} \frac{\pi}{6} \: \text{rad}\approx \: 0,52 \: \text{rad} \end{aligned}\left\{\begin{array}{ll}\displaystyle{ \frac{\pi}{6} \times \frac{\pi}{\pi} } \\ \\ \displaystyle{\frac{\pi}{\pi}= 1 }\\ \\\displaystyle{ \frac{\pi}{ 6} \times \not 1 } \\ \\ \displaystyle{\frac{\pi}{6} \approx \: 0,52 }\\ \\~~\displaystyle{= \frac{\pi}{6} \: \text{rad}\approx \: 0,52 \: \text{rad} } \\ \end{array}\right.$

Solução do exemplo:

$~~{\therefore~~\boxed{\boxed{\begin{array}{lr}\red{~30^{ \: \tiny{{\text{o}}}}=\frac{\pi}{6} \: \text{rad}\approx \: 0,52 \: \text{rad}~}\end{array}}}}$

 

$\: \: \: \text{\underline{Att.}}$

${\huge\boxed { {\bf{M}}}\boxed { \red {\bf{y}}} \boxed { \blue {\bf{t}}} \boxed { \gray{\bf{h}}} \boxed { \red {\bf{}}} \boxed { \orange {\bf{P}}} \boxed {\bf{i}}}$

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${~~\vdots~~~\large\boxed {\boxed{03:54h}~10.10.21}}$

$\bf\large\gray{\underline{\qquad \qquad\qquad \qquad \qquad \qquad \qquad \quad }}$

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