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Popular Trigonometria >

5cos(6x)+6=9

Solução

5 cos (6 x) + 6 = 9

Solução

x = \frac{0.92729 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{0.92729 \dots}{6} + \frac{πn}{3}

+1

Graus

x = 8.85501 \dots^{\circ} + 6 0^{\circ} n, x = 51.14498 \dots^{\circ} + 6 0^{\circ} n

Passos da solução

5 cos (6 x) + 6 = 9

Mova

6

para o lado direito

5 cos (6 x) + 6 = 9

Subtrair

6

de ambos os lados

5 cos (6 x) + 6 - 6 = 9 - 6

Simplificar

5 cos (6 x) = 3

5 cos (6 x) = 3

Dividir ambos os lados por

5

5 cos (6 x) = 3

Dividir ambos os lados por

5

\frac{5 cos ( 6 x )}{5} = \frac{3}{5}

Simplificar

cos (6 x) = \frac{3}{5}

cos (6 x) = \frac{3}{5}

Aplique as propriedades trigonométricas inversas

cos (6 x) = \frac{3}{5}

Soluções gerais para

cos (6 x) = \frac{3}{5}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

6 x = arccos (\frac{3}{5}) + 2 πn, 6 x = 2 π - arccos (\frac{3}{5}) + 2 πn

6 x = arccos (\frac{3}{5}) + 2 πn, 6 x = 2 π - arccos (\frac{3}{5}) + 2 πn

Resolver

6 x = arccos (\frac{3}{5}) + 2 πn : x = \frac{arccos ( \frac{3}{5} )}{6} + \frac{πn}{3}

6 x = arccos (\frac{3}{5}) + 2 πn

Dividir ambos os lados por

6

6 x = arccos (\frac{3}{5}) + 2 πn

Dividir ambos os lados por

6

\frac{6 x}{6} = \frac{arccos ( \frac{3}{5} )}{6} + \frac{2 πn}{6}

Simplificar

x = \frac{arccos ( \frac{3}{5} )}{6} + \frac{πn}{3}

x = \frac{arccos ( \frac{3}{5} )}{6} + \frac{πn}{3}

Resolver

6 x = 2 π - arccos (\frac{3}{5}) + 2 πn : x = \frac{π}{3} - \frac{arccos ( \frac{3}{5} )}{6} + \frac{πn}{3}

6 x = 2 π - arccos (\frac{3}{5}) + 2 πn

Dividir ambos os lados por

6

6 x = 2 π - arccos (\frac{3}{5}) + 2 πn

Dividir ambos os lados por

6

\frac{6 x}{6} = \frac{2 π}{6} - \frac{arccos ( \frac{3}{5} )}{6} + \frac{2 πn}{6}

Simplificar

\frac{6 x}{6} = \frac{2 π}{6} - \frac{arccos ( \frac{3}{5} )}{6} + \frac{2 πn}{6}

Simplificar

\frac{6 x}{6} : x

\frac{6 x}{6}

Dividir:

\frac{6}{6} = 1

= x

Simplificar

\frac{2 π}{6} - \frac{arccos ( \frac{3}{5} )}{6} + \frac{2 πn}{6} : \frac{π}{3} - \frac{arccos ( \frac{3}{5} )}{6} + \frac{πn}{3}

\frac{2 π}{6} - \frac{arccos ( \frac{3}{5} )}{6} + \frac{2 πn}{6}

Cancelar

\frac{2 π}{6} : \frac{π}{3}

\frac{2 π}{6}

Eliminar o fator comum:

2

= \frac{π}{3}

= \frac{π}{3} - \frac{arccos ( \frac{3}{5} )}{6} + \frac{2 πn}{6}

Cancelar

\frac{2 πn}{6} : \frac{πn}{3}

\frac{2 πn}{6}

Eliminar o fator comum:

2

= \frac{πn}{3}

= \frac{π}{3} - \frac{arccos ( \frac{3}{5} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{3}{5} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{3}{5} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{3}{5} )}{6} + \frac{πn}{3}

x = \frac{arccos ( \frac{3}{5} )}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{arccos ( \frac{3}{5} )}{6} + \frac{πn}{3}

Mostrar soluções na forma decimal

x = \frac{0.92729 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{0.92729 \dots}{6} + \frac{πn}{3}

Gráfico

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