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Popular Trigonometria >

cos(3x)=(sqrt(3))/3

Solução

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

Solução

x = \frac{0.95531 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{0.95531 \dots}{3} + \frac{2 πn}{3}

Graus

x = 18.24520 \dots^{\circ} + 12 0^{\circ} n, x = 101.75479 \dots^{\circ} + 12 0^{\circ} n

Passos da solução

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

Aplique as propriedades trigonométricas inversas

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

Soluções gerais para

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

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

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

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

Resolver

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

3 x = arccos (\frac{3}{3}) + 2 πn

Simplificar

arccos (\frac{3}{3}) + 2 πn : arccos (\frac{1}{3}) + 2 πn

arccos (\frac{3}{3}) + 2 πn

\frac{3}{3} = \frac{1}{3}

\frac{3}{3}

Aplicar as propriedades dos radicais:

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

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

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

Subtrair:

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

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

Aplicar as propriedades dos radicais:

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

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

= \frac{1}{3}

= arccos (\frac{1}{3}) + 2 πn

3 x = arccos (\frac{1}{3}) + 2 πn

Dividir ambos os lados por

3

3 x = arccos (\frac{1}{3}) + 2 πn

Dividir ambos os lados por

3

\frac{3 x}{3} = \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 x}{3} = \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

\frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3} : \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

\frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

arccos (\frac{1}{3}) = arccos (\frac{3}{3})

arccos (\frac{1}{3})

= arccos (\frac{3}{3})

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

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

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

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

Resolver

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

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

Simplificar

2 π - arccos (\frac{3}{3}) + 2 πn : 2 π - arccos (\frac{1}{3}) + 2 πn

2 π - arccos (\frac{3}{3}) + 2 πn

\frac{3}{3} = \frac{1}{3}

\frac{3}{3}

Aplicar as propriedades dos radicais:

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

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

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

Subtrair:

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

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

Aplicar as propriedades dos radicais:

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

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

= \frac{1}{3}

= 2 π - arccos (\frac{1}{3}) + 2 πn

3 x = 2 π - arccos (\frac{1}{3}) + 2 πn

Dividir ambos os lados por

3

3 x = 2 π - arccos (\frac{1}{3}) + 2 πn

Dividir ambos os lados por

3

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

\frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3} : \frac{2 π}{3} - \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

\frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

arccos (\frac{1}{3}) = arccos (\frac{3}{3})

arccos (\frac{1}{3})

= arccos (\frac{3}{3})

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

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

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

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

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

Mostrar soluções na forma decimal

x = \frac{0.95531 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{0.95531 \dots}{3} + \frac{2 πn}{3}

Gráfico

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