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Popular Trigonometria >

2/(sqrt(3))cos(3θ)=1

Solução

\frac{2}{3} cos (3 θ) = 1

Solução

θ = \frac{π}{18} + \frac{2 πn}{3}, θ = \frac{11 π}{18} + \frac{2 πn}{3}

Radianos

θ = \frac{π}{18} + \frac{2 π}{3} n, θ = \frac{11 π}{18} + \frac{2 π}{3} n

Passos da solução

\frac{2}{3} cos (3 θ) = 1

Simplificar

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

\frac{2}{3}

Multiplicar pelo conjugado

\frac{3}{3}

= \frac{2 3}{3 3}

33 = 3

33

Aplicar as propriedades dos radicais:

a a = a

33 = 3

= 3

= \frac{2 3}{3}

\frac{2 3}{3} cos (3 θ) = 1

Multiplicar ambos os lados por

3

\frac{2 3}{3} cos (3 θ) = 1

Multiplicar ambos os lados por

3

3 \cdot \frac{2 3}{3} cos (3 θ) = 1 \cdot 3

Simplificar

23 cos (3 θ) = 3

23 cos (3 θ) = 3

Dividir ambos os lados por

23

23 cos (3 θ) = 3

Dividir ambos os lados por

23

\frac{2 3 cos ( 3 θ )}{2 3} = \frac{3}{2 3}

Simplificar

\frac{2 3 cos ( 3 θ )}{2 3} = \frac{3}{2 3}

Simplificar

\frac{2 3 cos ( 3 θ )}{2 3} : cos (3 θ)

\frac{2 3 cos ( 3 θ )}{2 3}

Dividir:

\frac{2}{2} = 1

= \frac{3 cos ( 3 θ )}{3}

Eliminar o fator comum:

3

= cos (3 θ)

Simplificar

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

\frac{3}{2 3}

Aplicar as propriedades dos radicais:

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

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

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

Aplicar as propriedades dos expoentes:

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

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

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

Subtrair:

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

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

Aplicar as propriedades dos radicais:

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

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

= \frac{3}{2}

cos (3 θ) = \frac{3}{2}

cos (3 θ) = \frac{3}{2}

cos (3 θ) = \frac{3}{2}

Soluções gerais para

cos (3 θ) = \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}

3 θ = \frac{π}{6} + 2 πn, 3 θ = \frac{11 π}{6} + 2 πn

3 θ = \frac{π}{6} + 2 πn, 3 θ = \frac{11 π}{6} + 2 πn

Resolver

3 θ = \frac{π}{6} + 2 πn : θ = \frac{π}{18} + \frac{2 πn}{3}

3 θ = \frac{π}{6} + 2 πn

Dividir ambos os lados por

3

3 θ = \frac{π}{6} + 2 πn

Dividir ambos os lados por

3

\frac{3 θ}{3} = \frac{\frac{π}{6}}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 θ}{3} = \frac{\frac{π}{6}}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Dividir:

\frac{3}{3} = 1

= θ

Simplificar

\frac{\frac{π}{6}}{3} + \frac{2 πn}{3} : \frac{π}{18} + \frac{2 πn}{3}

\frac{\frac{π}{6}}{3} + \frac{2 πn}{3}

\frac{\frac{π}{6}}{3} = \frac{π}{18}

\frac{\frac{π}{6}}{3}

Aplicar as propriedades das frações:

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

= \frac{π}{6 \cdot 3}

Multiplicar os números:

6 \cdot 3 = 18

= \frac{π}{18}

= \frac{π}{18} + \frac{2 πn}{3}

θ = \frac{π}{18} + \frac{2 πn}{3}

θ = \frac{π}{18} + \frac{2 πn}{3}

θ = \frac{π}{18} + \frac{2 πn}{3}

Resolver

3 θ = \frac{11 π}{6} + 2 πn : θ = \frac{11 π}{18} + \frac{2 πn}{3}

3 θ = \frac{11 π}{6} + 2 πn

Dividir ambos os lados por

3

3 θ = \frac{11 π}{6} + 2 πn

Dividir ambos os lados por

3

\frac{3 θ}{3} = \frac{\frac{11 π}{6}}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 θ}{3} = \frac{\frac{11 π}{6}}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Dividir:

\frac{3}{3} = 1

= θ

Simplificar

\frac{\frac{11 π}{6}}{3} + \frac{2 πn}{3} : \frac{11 π}{18} + \frac{2 πn}{3}

\frac{\frac{11 π}{6}}{3} + \frac{2 πn}{3}

\frac{\frac{11 π}{6}}{3} = \frac{11 π}{18}

\frac{\frac{11 π}{6}}{3}

Aplicar as propriedades das frações:

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

= \frac{11 π}{6 \cdot 3}

Multiplicar os números:

6 \cdot 3 = 18

= \frac{11 π}{18}

= \frac{11 π}{18} + \frac{2 πn}{3}

θ = \frac{11 π}{18} + \frac{2 πn}{3}

θ = \frac{11 π}{18} + \frac{2 πn}{3}

θ = \frac{11 π}{18} + \frac{2 πn}{3}

θ = \frac{π}{18} + \frac{2 πn}{3}, θ = \frac{11 π}{18} + \frac{2 πn}{3}

Gráfico

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tan (x) = - 0.5

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7sec^2(x)-7sec(x)=14

7 sec^{2} (x) - 7 sec (x) = 14

0=1+2sin(2x)

0 = 1 + 2 sin (2 x)

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0 = 1 + 2 cos (3 θ)