Question

O valor da expressão abaixo é :
2 sen 90° - cos 330° / -6 cos 180° + 3 sen 240°

Pfv me ajudem

Answer 1

Explicação passo-a-passo:

$\sf E=\dfrac{2\cdot sen~90^{\circ}-cos~330^{\circ}}{-6\cdot cos~180^{\circ}+3\cdot sen~240^{\circ}}$

=> $\sf sen~90^{\circ}=1$

=> $\sf cos~330^{\circ}=cos~(360^{\circ}-330^{\circ})$

$\sf cos~330^{\circ}=cos~30^{\circ}$

$\sf cos~330^{\circ}=\dfrac{\sqrt{3}}{2}$

=> $\sf cos~180^{\circ}=-1$

=> $\sf sen~240^{\circ}=-sen~(240^{\circ}-180^{\circ})$

$\sf sen~240^{\circ}=-sen~60^{\circ}$

$\sf sen~240^{\circ}=-\dfrac{\sqrt{3}}{2}$

Logo:

$\sf E=\dfrac{2\cdot1-\frac{\sqrt{3}}{2}}{-6\cdot(-1)+3\cdot\Big(-\frac{\sqrt{3}}{2}\Big)}$

$\sf E=\dfrac{2-\frac{\sqrt{3}}{2}}{6-\frac{3\sqrt{3}}{2}}$

$\sf E=\dfrac{\frac{4-\sqrt{3}}{2}}{\frac{12-3\sqrt{3}}{2}}$

$\sf E=\dfrac{4-\sqrt{3}}{2}\cdot\dfrac{2}{12-3\sqrt{3}}$

$\sf E=\dfrac{4-\sqrt{3}}{12-3\sqrt{3}}$

Racionalizando:

$\sf E=\dfrac{4-\sqrt{3}}{12-3\sqrt{3}}\cdot\dfrac{12+3\sqrt{3}}{12+3\sqrt{3}}$

$\sf E=\dfrac{48-12\sqrt{3}+12\sqrt{3}-3\cdot3}{12^2-(3\sqrt{3})^2}$

$\sf E=\dfrac{48-12\sqrt{3}+12\sqrt{3}-9}{144-27}$

$\sf E=\dfrac{39}{117}$

$\sf \red{E=\dfrac{1}{3}}$