Resposta:
Explicação passo a passo:
Vamos lá!
Primeiramente, recorde que:
[tex]-\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.[/tex]
Dessa forma, segue
[tex]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}.[/tex]
Bons estudos!
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Resposta:
Explicação passo a passo:
Vamos lá!
Primeiramente, recorde que:
[tex]-\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.[/tex]
Dessa forma, segue
[tex]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}.[/tex]
Bons estudos!