c) $$ \operatorname{Tag}\left(-330^{\circ}\right) $$

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UpStudy AI · Accepted Answer

1. Primeiro, encontramos um ângulo coterminal a $$-330^\circ$$. Somando $$360^\circ$$ a $$-330^\circ$$, obtemos:  
   $$
   -330^\circ + 360^\circ = 30^\circ
   $$
   Assim, $$\operatorname{Tag}\left(-330^\circ\right)$$ equivale a $$\operatorname{Tag}\left(30^\circ\right)$$.

2. Sabe-se que a função tangente é dada por:  
   $$
   \operatorname{Tag}(\theta) = \frac{\sin\theta}{\cos\theta}
   $$
   Para $$\theta = 30^\circ$$, temos:  
   $$
   \sin(30^\circ) = \frac{1}{2} \quad \text{e} \quad \cos(30^\circ) = \frac{\sqrt{3}}{2}
   $$

3. Portanto, calculamos:  
   $$
   \operatorname{Tag}(30^\circ) = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}}
   $$

4. Geralmente, racionaliza-se a resposta:  
   $$
   \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}
   $$

Logo,  
$$
\operatorname{Tag}\left(-330^\circ\right)=\frac{\sqrt{3}}{3}
$$
$$ \operatorname{Tag}\left(-330^\circ\right) = \frac{\sqrt{3}}{3} $$

c)

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