Question

aplicando as formulas da adicao calcule sem 75

Answer 1

Sen 75=(30+45) Sen (a+b)= Sen a . Cos b + Sen b. Cos a Sen (30+45)= Sen 30 . Cos 45 + Sen 45 . Cos 30 Sen (30+45) = 1/2 × raiz de 2/2 + raiz de 2/2 × raiz de 3/2 Sen (30+45)= Raiz de 2/4 +raiz de 6/4 Como não podemos juntar as raízes fica Sen 75= Raiz de 2/4 +raiz de 6/4

Answer 2

✅ Após resolver os cálculos, concluímos que o seno de 75° é:

        $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf \sin75^{\circ} = \frac{\sqrt{6} + \sqrt{2}}{4}\:\:\:}}\end{gathered} }$

Se temos, o seguinte dado:

                              $\Large\displaystyle\begin{gathered} \sin75^{\circ}\end{gathered}$

Para calcular o seno de 75° devemos utilizar a fórmula do seno da soma de dois arcos, que é:

   $\Large\displaystyle\begin{gathered} \sin(a + b) = \sin a\cdot \cos b + \sin b \cdot \cos a\end{gathered}$

Então, temos:

     $\Large\displaystyle\begin{gathered} \sin 75^{\circ} = \sin(45^{\circ} + 30^{\circ})\end{gathered}$

                     $\Large\displaystyle\begin{gathered} = \sin45^{\circ}\cdot\cos30^{\circ} + \sin30^{\circ}\cdot\cos45^{\circ}\end{gathered}$

                     $\Large\displaystyle\text{ \begin{gathered} = \frac{\sqrt{2}}{2}\cdot\frac{\sqrt{3}}{2} + \frac{1}{2}\cdot\frac{\sqrt{2}}{2} \end{gathered} }$

                     $\Large\displaystyle\text{ \begin{gathered} = \frac{\sqrt{2\cdot3}}{4} + \frac{1\cdot\sqrt{2}}{4}\end{gathered} }$

                      $\Large\displaystyle\text{ \begin{gathered} = \frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4}\end{gathered} }$

                      $\Large\displaystyle\text{ \begin{gathered} = \frac{\sqrt{6} + \sqrt{2}}{4}\end{gathered} }$

✅ Portanto, o valor do seno 75° é:

        $\Large\displaystyle\text{ \begin{gathered} \sin75^{\circ} = \frac{\sqrt{6} + \sqrt{2}}{4}\end{gathered} }$

Saiba mais:

1. https://brainly.com.br/tarefa/2178501
2. https://brainly.com.br/tarefa/6461790