Respostas

  • Usuário do Brainly
2014-08-18T15:59:51-03:00
Temos que,

A=\dfrac{\text{sen}~120^{\circ}\cdot\text{cos}~180^{\circ}}{\text{tg}~30^{\circ}\cdot\text{cotg}~60^{\circ}}

\text{sen}~60^{\circ}=\dfrac{\sqrt{3}}{2},\text{cos}~60^{\circ}=\dfrac{1}{2} e \text{tg}~60^{\circ}=\sqrt{3}.

Deste modo, \text{cotg}~60^{\circ}=\dfrac{1}{\text{tg}~60^{\circ}}=\dfrac{1}{\sqrt{3}}=\dfrac{\sqrt{3}}{3}.

Além disso, \text{tg}~\dfrac{60}{2}=\text{tg}~30^{\circ}=\dfrac{\sqrt{3}}{3}.

Temos que, \text{sen}~(2x)=2\cdot\text{sen}~x\cdot\text{cos}~x.

Assim, \text{sen}~120^{\circ}=2\cdot\text{sen}~60^{\circ}\cdot\text{cos}~60^{\circ}

\text{sen}~120^{\circ}=2\cdot\dfrac{\sqrt{3}}{2}\cdot\dfrac{1}{2}

\text{sen}~120^{\circ}=\dfrac{2\sqrt{3}}{4}

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

Lembrando que, \text{cos}~180^{\circ}=-1, temos:

A=\dfrac{\frac{\sqrt{3}}{2}\cdot(-1)}{\frac{\sqrt{3}}{3}\cdot\frac{\sqrt{3}}{3}}

A=\dfrac{-\frac{\sqrt{3}}{2}}{\frac{1}{3}}

A=\dfrac{-\sqrt{3}}{2}\cdot\dfrac{3}{1}=\dfrac{-3\sqrt{3}}{2}
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