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cos(x)=(-4)/(8/3 sqrt(3))

Solução

cos (x) = \frac{- 4}{\frac{8}{3} 3}

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Passos da solução

cos (x) = \frac{- 4}{\frac{8}{3} 3}

Simplificar

\frac{- 4}{\frac{8}{3} 3} : - \frac{3}{2}

\frac{- 4}{\frac{8}{3} 3}

Aplicar as propriedades das frações:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{4}{\frac{8}{3} 3}

Multiplicar

\frac{8}{3} 3 : \frac{8}{3}

\frac{8}{3} 3

Multiplicar frações:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{8 3}{3}

Aplicar as propriedades dos radicais:

n a = a^{\frac{1}{n}}

3 = 3^{\frac{1}{2}}

= \frac{8 \cdot 3 ^{\frac{1}{2}}}{3}

Aplicar as propriedades dos expoentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{3 ^{\frac{1}{2}}}{3 ^{1}} = \frac{1}{3 ^{1 - \frac{1}{2}}}

= \frac{8}{3 ^{1 - \frac{1}{2}}}

Subtrair:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{8}{3 ^{\frac{1}{2}}}

Aplicar as propriedades dos radicais:

a^{\frac{1}{n}} = n a

3^{\frac{1}{2}} = 3

= \frac{8}{3}

= - \frac{4}{\frac{8}{3}}

Aplicar as propriedades das frações:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= - \frac{4 3}{8}

Eliminar o fator comum:

4

= - \frac{3}{2}

Soluções gerais para

cos (x) = - \frac{3}{2}

cos (x)

tabela de periodicidade com ciclo de

2 πn

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

- 2 tan (x) + 6 = 8

2 sin (x) = 1.564

sin (x) = 0.08

sin (x) = 0.05

sin (x) = 0.21