Question

determine o coeficiente angular da reta que tem inclinação de 45º

Answer 1

Basta calcular a tangente de 45°

tangente 45° = 1 = coeficiente angular.

Answer 2

✅ Após resolver os cálculos, concluímos que o coeficiente angular da reta cuja inclinação é 45° é:

             $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf m_{r} = 1\:\:\:}}\end{gathered} }$

Seja o ângulo de inclinação:

                   $\Large\displaystyle\begin{gathered} \theta = 45^{\circ}\end{gathered}$

Sabemos que o coeficiente angular da uma reta no plano cartesiano é numericamente igual à tangente do referido ângulo, isto é:

$\Large\displaystyle\begin{gathered} \bf I\end{gathered}$               $\Large\displaystyle\begin{gathered} m_{r} = \tan\theta\end{gathered}$

Substituindo o valor do ângulo na equação "I", temos:

                $\Large\displaystyle\begin{gathered} m_{r} = \tan 45^{\circ}\end{gathered}$

                        $\Large\displaystyle\text{ \begin{gathered} = \frac{\sin 45^{\circ}}{\cos 45^{\circ}}\end{gathered} }$

                        $\Large\displaystyle\text{ \begin{gathered} = \frac{\dfrac{\sqrt{2}}{2}}{\dfrac{\sqrt{2}}{2}}\end{gathered} }$

                         $\Large\displaystyle\text{ \begin{gathered} = \frac{\sqrt{2}}{\!\diagup\!\!\!\!2}\cdot\frac{\!\diagup\!\!\!\!2}{\sqrt{2}}\end{gathered} }$

                         $\Large\displaystyle\text{ \begin{gathered} = \frac{\sqrt{2}}{\sqrt{2}}\end{gathered} }$

                         $\Large\displaystyle\text{ \begin{gathered} = \frac{\sqrt{2}}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}\end{gathered} }$

                         $\Large\displaystyle\text{ \begin{gathered} = \frac{(\sqrt[\diagup\!\!]{2})^{\!\diagup\!\!\!\!2}}{(\sqrt[\!\diagup\!\!]{2})^{\!\diagup\!\!\!\!2}}\end{gathered} }$

                         $\Large\displaystyle\begin{gathered} = \frac{2}{2}\end{gathered}$

                         $\Large\displaystyle\begin{gathered} = 1\end{gathered}$

✅ Portanto, o coeficiente angular é:

                  $\Large\displaystyle\begin{gathered} m_{r} = 1\end{gathered}$

                         

$\LARGE\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered} }$

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