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Popular Trigonometria >

7cos(4x)=6

Solução

7 cos (4 x) = 6

Solução

x = \frac{0.54109 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{0.54109 \dots}{4} + \frac{πn}{2}

+1

Graus

x = 7.75067 \dots^{\circ} + 9 0^{\circ} n, x = 82.24932 \dots^{\circ} + 9 0^{\circ} n

Passos da solução

7 cos (4 x) = 6

Dividir ambos os lados por

7

7 cos (4 x) = 6

Dividir ambos os lados por

7

\frac{7 cos ( 4 x )}{7} = \frac{6}{7}

Simplificar

cos (4 x) = \frac{6}{7}

cos (4 x) = \frac{6}{7}

Aplique as propriedades trigonométricas inversas

cos (4 x) = \frac{6}{7}

Soluções gerais para

cos (4 x) = \frac{6}{7}

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

4 x = arccos (\frac{6}{7}) + 2 πn, 4 x = 2 π - arccos (\frac{6}{7}) + 2 πn

4 x = arccos (\frac{6}{7}) + 2 πn, 4 x = 2 π - arccos (\frac{6}{7}) + 2 πn

Resolver

4 x = arccos (\frac{6}{7}) + 2 πn : x = \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

4 x = arccos (\frac{6}{7}) + 2 πn

Dividir ambos os lados por

4

4 x = arccos (\frac{6}{7}) + 2 πn

Dividir ambos os lados por

4

\frac{4 x}{4} = \frac{arccos ( \frac{6}{7} )}{4} + \frac{2 πn}{4}

Simplificar

x = \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

x = \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

Resolver

4 x = 2 π - arccos (\frac{6}{7}) + 2 πn : x = \frac{π}{2} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

4 x = 2 π - arccos (\frac{6}{7}) + 2 πn

Dividir ambos os lados por

4

4 x = 2 π - arccos (\frac{6}{7}) + 2 πn

Dividir ambos os lados por

4

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{2 πn}{4}

Simplificar

\frac{4 x}{4} : x

\frac{4 x}{4}

Dividir:

\frac{4}{4} = 1

= x

Simplificar

\frac{2 π}{4} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{2 πn}{4} : \frac{π}{2} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

\frac{2 π}{4} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{2 πn}{4}

Cancelar

\frac{2 π}{4} : \frac{π}{2}

\frac{2 π}{4}

Eliminar o fator comum:

2

= \frac{π}{2}

= \frac{π}{2} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{2 πn}{4}

Cancelar

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Eliminar o fator comum:

2

= \frac{πn}{2}

= \frac{π}{2} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

x = \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

Mostrar soluções na forma decimal

x = \frac{0.54109 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{0.54109 \dots}{4} + \frac{πn}{2}

Gráfico

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