Question

X = (sin⁡〖2π/3 -〗 cos⁡π)/tan⁡〖π/6〗

Answer 1

Resposta:

Olá bom dia!

Convertendo 2π/3 para graus:

π = 180

2π/3 = x

πx = 180(2π/3)

πx = 360π/3

x = 360/3

x = 120°

120° é um arco côngruo a 60°. Portanto:

sen 2π/3 = sen 120° = sen 60° = √3/2

cos π = 1

tg (π/6) = tg 30° = √3 / 2

Logo:

X = (sin⁡〖2π/3 - cos⁡π)] / tan⁡〖π/6〗

X = [(√3 / 2) - 1] / √3 / 2

X = (√3 - 2) / 2 * 2√3

X = (√3 - 2) * √3

X = √3 * √3 * 2√3

X = 3*2√3

X = 6√3