Question

Calcule o valor das expressões abaixo.

Answer 1

$cos\frac{2 \pi }{3} = -cos( \pi - \frac{2 \pi }{3}) = -cos(3 \pi -2 \pi )/3=-cos \frac{ \pi }{3}=- \frac{1}{2} \\ \\ cos \pi =-1 \\ \\ sen \frac{ \pi }{4}= \frac{ \sqrt{2} }{2} \\ \\ cos \frac{ \pi }{2}=0 \\ \\ cos \frac{4 \pi }{3}=-cos( \frac{4 \pi }{3}- \pi )=-cos(4 \pi - \pi )/3=-cos \frac{ \pi }{3} =- \frac{1}{2} \\ \\ sen \frac{5 \pi }{6}=sen( \pi - \frac{5 \pi }{6})=sen(6 \pi -5 \pi )/6=sen \frac{ \pi }{6}= \frac{1}{2}$

$a) \frac{cos \frac{2 \pi }{3}+cos \pi }{sen \frac{ \pi }{4} } = \frac{- \frac{1}{2}-1}{ \frac{ \sqrt{2} }{2} } = \frac{ \frac{-1-2}{2} }{ \frac{ \sqrt{2} }{2} }= \frac{-3}{2}* \frac{2}{ \sqrt{2} } =- \frac{3}{ \sqrt{2} } =- \frac{3 \sqrt{2} }{2} \\ \\ b) \frac{cos \frac{ \pi }{2}-cos \frac{4 \pi }{3} }{2sen \frac{5 \pi }{6} }= \frac{0-(- \frac{1}{2}) }{2* \frac{1}{2} } = \frac{ \frac{1}{2} }{1}= \frac{1}{2}$