2) Considere f(x)=operatorname(sen)(x) e G(x)=cos (x) . Calcule f((pi)/(3))-g((pi)/(3)) ; (f(pi / 6))/(g(pi / 6))

Para calcular \( f\left(\frac{\pi}{3}\right)-g\left(\frac{\pi}{3}\right) \), substituímos \( x \) por \( \frac{\pi}{3} \) nas funções \( f(x) \) e \( G(x) \):<br /><br />\( f\left(\frac{\pi}{3}\right) = \operatorname{sen}\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2} \)<br /><br />\( G\left(\frac{\pi}{3}\right) = \cos\left(\frac{\pi}{3}\right) = \frac{1}{2} \)<br /><br />Portanto, \( f\left(\frac{\pi}{3}\right)-g\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2} - \frac{1}{2} = \frac{\sqrt{3} - 1}{2} \).<br /><br />Para calcular \( \frac{f(\pi / 6)}{g(\pi / 6)} \), substituímos \( x \) por \( \frac{\pi}{6} \) nas funções \( f(x) \) e \( G(x) \):<br /><br />\( f\left(\frac{\pi}{6}\right) = \operatorname{sen}\left(\frac{\pi}{6}\right) = \frac{1}{2} \)<br /><br />\( G\left(\frac{\pi}{6}\right) = \cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2} \)<br /><br />Portanto, \( \frac{f(\pi / 6)}{g(\pi / 6)} = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3} \).