Question

me ajude com essas conta de matematica , todas com a conta completa por favor

Answer 1

Explicação passo-a-passo:

a) Temos que:

$\text{cos}~\dfrac{2\pi}{3}=\text{cos}~120^{\circ}=-\dfrac{1}{2}$

$\text{sen}~\dfrac{4\pi}{3}=\text{sen}~240^{\circ}=-\dfrac{\sqrt{3}}{2}$

$\text{sen}~\dfrac{2\pi}{3}=\text{sen}~120^{\circ}=\dfrac{\sqrt{3}}{2}$

$\text{cos}~\dfrac{4\pi}{3}=\text{cos}~240^{\circ}=-\dfrac{1}{2}$

Assim:

$A=\dfrac{-\left(-\frac{1}{2}\right)-\left(-\frac{\sqrt{3}}{2}\right)}{\frac{\sqrt{3}}{2}-\left(-\frac{1}{2}\right)}$

$A=\dfrac{\frac{1}{2}+\frac{\sqrt{3}}{2}}{\frac{\sqrt{3}}{2}+\frac{1}{2}}$

$\boxed{A=1}$

b) Veja que:

$\text{sen}~\dfrac{7\pi}{4}=\text{sen}~315^{\circ}=-\dfrac{\sqrt{2}}{2}$

$\text{cos}~\dfrac{5\pi}{4}=\text{cos}~225^{\circ}=-\dfrac{\sqrt{2}}{2}$

$\text{cos}~\dfrac{3\pi}{4}=\text{cos}~135^{\circ}=-\dfrac{\sqrt{2}}{2}$

$\text{sen}~\dfrac{3\pi}{4}=\text{sen}~135^{\circ}=\dfrac{\sqrt{2}}{2}$

Desse modo:

$B=\dfrac{-\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}}$

$\boxed{B=1}$

c) Temos que:

$\text{cos}~1080^{\circ}=\text{cos}~0^{\circ}=1$

$\text{sen}~(-315^{\circ})=-\text{sen}~315^{\circ}=\dfrac{\sqrt{2}}{2}$

$\text{sen}~405^{\circ}=\text{sen}~45^{\circ}=\dfrac{\sqrt{2}}{2}$

$\text{cos}~11\pi=\text{cos}~\pi=\text{cos}~180^{\circ}=-1$

Então:

$C=\dfrac{1+\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}-(-1)}$

$C=\dfrac{1+\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}+1}$

$\boxed{C=1}$

d) Note que:

$\text{tg}~45^{\circ}=1$

$\text{sen}~180^{\circ}=0$

$\text{cos}~90^{\circ}=0$

$\text{cos}~30^{\circ}=\dfrac{\sqrt{3}}{2}$

$\text{tg}~180^{\circ}=0$

Assim:

$D=\dfrac{1+0+3\cdot0}{8\cdot\frac{\sqrt{3}}{2}-0}$

$D=\dfrac{1}{4\sqrt{3}}$

$D=\dfrac{1}{4\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}$

$D=\dfrac{\sqrt{3}}{4\cdot3}$

$\boxed{D=\dfrac{\sqrt{3}}{12}}$

e) Lembre-se que:

$\text{cos}~\dfrac{\pi}{6}=\text{cos}~30^{\circ}=\dfrac{\sqrt{3}}{2}$

$\text{sen}~\dfrac{\pi}{3}=\text{sen}~60^{\circ}=\dfrac{\sqrt{3}}{2}$

Logo:

$E=\dfrac{2\cdot\frac{\sqrt{3}}{2}-4\cdot\frac{\sqrt{3}}{2}}{4\cdot\frac{\sqrt{3}}{2}+8\cdot\frac{\sqrt{3}}{2}}$

$E=\dfrac{\sqrt{3}-2\sqrt{3}}{2\sqrt{3}+4\sqrt{3}}$

$E=\dfrac{-\sqrt{3}}{6\sqrt{3}}$

$\boxed{E=-\dfrac{1}{6}}$