Question

(VALENDO 100 PONTOS) Simplifique a expressão (Trigonométrica)

Answer 1

Resposta:

Explicação passo a passo:

Vamos lá!

Primeiramente, recorde que:

$-\cos(2\pi/3) = \cos(\pi/3) = 1/2 \\-\sin(4\pi/3) = \sin(\pi/6) = 1/2\\\sin(2\pi/3) = \sin(\pi/3) = \sqrt{3}/2\\-\cos(4\pi) = \cos(\pi/6) = \sqrt{3}/2.$

Dessa forma, segue

$A = \frac{-\cos(2\pi/3) - \sin(4\pi/3)}{\sin(2\pi/3) - \cos(4\pi/3)}\\A = \frac{\cos(\pi/3) + \sin(\pi/6)}{\sin(\pi/3) + \cos(\pi/6)}\\A = \frac{1/2 + 1/2}{\sqrt{3}/2 + \sqrt{3}/2}\\A = \frac{1}{\sqrt{3}}\\A = \frac{\sqrt{3}}{3}.$

Bons estudos!