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Popular Trigonometria >

cos(x+5)= 1/2 sqrt(3),0<= x<= 2pi

Solução

cos (x + 5) = \frac{1}{2} 3, 0 \leq x \leq 2 π

Solução

x = \frac{11 π - 30}{6}, x = \frac{13 π - 30}{6}

Passos da solução

cos (x + 5) = \frac{1}{2} 3, 0 \leq x \leq 2 π

Simplificar

\frac{1}{2} 3 : \frac{3}{2}

\frac{1}{2} 3

Multiplicar frações:

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

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

Multiplicar:

1 \cdot 3 = 3

= \frac{3}{2}

Soluções gerais para

cos (x + 5) = \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 + 5 = \frac{π}{6} + 2 πn, x + 5 = \frac{11 π}{6} + 2 πn

x + 5 = \frac{π}{6} + 2 πn, x + 5 = \frac{11 π}{6} + 2 πn

Resolver

x + 5 = \frac{π}{6} + 2 πn : x = \frac{π}{6} + 2 πn - 5

x + 5 = \frac{π}{6} + 2 πn

Mova

5

para o lado direito

x + 5 = \frac{π}{6} + 2 πn

Subtrair

5

de ambos os lados

x + 5 - 5 = \frac{π}{6} + 2 πn - 5

Simplificar

x = \frac{π}{6} + 2 πn - 5

x = \frac{π}{6} + 2 πn - 5

Resolver

x + 5 = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{6} + 2 πn - 5

x + 5 = \frac{11 π}{6} + 2 πn

Mova

5

para o lado direito

x + 5 = \frac{11 π}{6} + 2 πn

Subtrair

5

de ambos os lados

x + 5 - 5 = \frac{11 π}{6} + 2 πn - 5

Simplificar

x = \frac{11 π}{6} + 2 πn - 5

x = \frac{11 π}{6} + 2 πn - 5

x = \frac{π}{6} + 2 πn - 5, x = \frac{11 π}{6} + 2 πn - 5

Soluções para o intervalo

0 \leq x \leq 2 π

x = \frac{11 π - 30}{6}, x = \frac{13 π - 30}{6}

Gráfico

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