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Popular Trigonometria >

-2cos(2x-pi/3)=2sin(2x-pi/6)

Solução

- 2 cos (2 x - \frac{π}{3}) = 2 sin (2 x - \frac{π}{6})

Solução

x = πn, x = \frac{π}{2} + πn

Graus

x = 0^{\circ} + 18 0^{\circ} n, x = 9 0^{\circ} + 18 0^{\circ} n

Passos da solução

- 2 cos (2 x - \frac{π}{3}) = 2 sin (2 x - \frac{π}{6})

Reeecreva usando identidades trigonométricas

- 2 cos (2 x - \frac{π}{3}) = 2 sin (2 x - \frac{π}{6})

Reeecreva usando identidades trigonométricas

cos (2 x - \frac{π}{3})

Use a identidade de diferença de ângulos:

cos (s - t) = cos (s) cos (t) + sin (s) sin (t)

= cos (2 x) cos (\frac{π}{3}) + sin (2 x) sin (\frac{π}{3})

Simplificar

cos (2 x) cos (\frac{π}{3}) + sin (2 x) sin (\frac{π}{3}) : \frac{1}{2} cos (2 x) + \frac{3}{2} sin (2 x)

cos (2 x) cos (\frac{π}{3}) + sin (2 x) sin (\frac{π}{3})

Simplificar

cos (\frac{π}{3}) : \frac{1}{2}

cos (\frac{π}{3})

Utilizar a seguinte identidade trivial:

cos (\frac{π}{3}) = \frac{1}{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}

= \frac{1}{2}

= \frac{1}{2} cos (2 x) + sin (\frac{π}{3}) sin (2 x)

Simplificar

sin (\frac{π}{3}) : \frac{3}{2}

sin (\frac{π}{3})

Utilizar a seguinte identidade trivial:

sin (\frac{π}{3}) = \frac{3}{2}

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{3}{2}

= \frac{1}{2} cos (2 x) + \frac{3}{2} sin (2 x)

= \frac{1}{2} cos (2 x) + \frac{3}{2} sin (2 x)

Use a identidade de diferença de ângulos:

sin (s - t) = sin (s) cos (t) - cos (s) sin (t)

= sin (2 x) cos (\frac{π}{6}) - cos (2 x) sin (\frac{π}{6})

Simplificar

sin (2 x) cos (\frac{π}{6}) - cos (2 x) sin (\frac{π}{6}) : \frac{3}{2} sin (2 x) - \frac{1}{2} cos (2 x)

sin (2 x) cos (\frac{π}{6}) - cos (2 x) sin (\frac{π}{6})

Simplificar

cos (\frac{π}{6}) : \frac{3}{2}

cos (\frac{π}{6})

Utilizar a seguinte identidade trivial:

cos (\frac{π}{6}) = \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}

= \frac{3}{2}

= \frac{3}{2} sin (2 x) - sin (\frac{π}{6}) cos (2 x)

Simplificar

sin (\frac{π}{6}) : \frac{1}{2}

sin (\frac{π}{6})

Utilizar a seguinte identidade trivial:

sin (\frac{π}{6}) = \frac{1}{2}

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{3}{2} sin (2 x) - \frac{1}{2} cos (2 x)

= \frac{3}{2} sin (2 x) - \frac{1}{2} cos (2 x)

- 2 (\frac{1}{2} cos (2 x) + \frac{3}{2} sin (2 x)) = 2 (\frac{3}{2} sin (2 x) - \frac{1}{2} cos (2 x))

Simplificar

- 2 (\frac{1}{2} cos (2 x) + \frac{3}{2} sin (2 x)) : - cos (2 x) - 3 sin (2 x)

- 2 (\frac{1}{2} cos (2 x) + \frac{3}{2} sin (2 x))

Colocar os parênteses utilizando:

a (b + c) = ab + a c

a = - 2, b = \frac{1}{2} cos (2 x), c = \frac{3}{2} sin (2 x)

= - 2 \cdot \frac{1}{2} cos (2 x) + (- 2) \frac{3}{2} sin (2 x)

Aplicar as regras dos sinais

+ (- a) = - a

= - 2 \cdot \frac{1}{2} cos (2 x) - 2 \cdot \frac{3}{2} sin (2 x)

Simplificar

- 2 \cdot \frac{1}{2} cos (2 x) - 2 \cdot \frac{3}{2} sin (2 x) : - cos (2 x) - 3 sin (2 x)

- 2 \cdot \frac{1}{2} cos (2 x) - 2 \cdot \frac{3}{2} sin (2 x)

2 \cdot \frac{1}{2} cos (2 x) = cos (2 x)

2 \cdot \frac{1}{2} cos (2 x)

Multiplicar frações:

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

= \frac{1 \cdot 2}{2} cos (2 x)

Eliminar o fator comum:

2

= cos (2 x) \cdot 1

Multiplicar:

cos (2 x) \cdot 1 = cos (2 x)

= cos (2 x)

2 \cdot \frac{3}{2} sin (2 x) = 3 sin (2 x)

2 \cdot \frac{3}{2} sin (2 x)

Multiplicar frações:

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

= \frac{2 3}{2} sin (2 x)

Eliminar o fator comum:

2

= sin (2 x) 3

= - cos (2 x) - 3 sin (2 x)

= - cos (2 x) - 3 sin (2 x)

Simplificar

2 (\frac{3}{2} sin (2 x) - \frac{1}{2} cos (2 x)) : 3 sin (2 x) - cos (2 x)

2 (\frac{3}{2} sin (2 x) - \frac{1}{2} cos (2 x))

Colocar os parênteses utilizando:

a (b - c) = ab - a c

a = 2, b = \frac{3}{2} sin (2 x), c = \frac{1}{2} cos (2 x)

= 2 \cdot \frac{3}{2} sin (2 x) - 2 \cdot \frac{1}{2} cos (2 x)

Simplificar

2 \cdot \frac{3}{2} sin (2 x) - 2 \cdot \frac{1}{2} cos (2 x) : 3 sin (2 x) - cos (2 x)

2 \cdot \frac{3}{2} sin (2 x) - 2 \cdot \frac{1}{2} cos (2 x)

2 \cdot \frac{3}{2} sin (2 x) = 3 sin (2 x)

2 \cdot \frac{3}{2} sin (2 x)

Multiplicar frações:

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

= \frac{2 3}{2} sin (2 x)

Eliminar o fator comum:

2

= sin (2 x) 3

2 \cdot \frac{1}{2} cos (2 x) = cos (2 x)

2 \cdot \frac{1}{2} cos (2 x)

Multiplicar frações:

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

= \frac{1 \cdot 2}{2} cos (2 x)

Eliminar o fator comum:

2

= cos (2 x) \cdot 1

Multiplicar:

cos (2 x) \cdot 1 = cos (2 x)

= cos (2 x)

= 3 sin (2 x) - cos (2 x)

= 3 sin (2 x) - cos (2 x)

- cos (2 x) - 3 sin (2 x) = 3 sin (2 x) - cos (2 x)

- cos (2 x) - 3 sin (2 x) = 3 sin (2 x) - cos (2 x)

Subtrair

3 sin (2 x) - cos (2 x)

de ambos os lados

- 23 sin (2 x) = 0

Dividir ambos os lados por

- 23

- 23 sin (2 x) = 0

Dividir ambos os lados por

- 23

\frac{- 2 3 sin ( 2 x )}{- 2 3} = \frac{0}{- 2 3}

Simplificar

sin (2 x) = 0

sin (2 x) = 0

Soluções gerais para

sin (2 x) = 0

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

2 x = 0 + 2 πn, 2 x = π + 2 πn

2 x = 0 + 2 πn, 2 x = π + 2 πn

Resolver

2 x = 0 + 2 πn : x = πn

2 x = 0 + 2 πn

0 + 2 πn = 2 πn

2 x = 2 πn

Dividir ambos os lados por

2

2 x = 2 πn

Dividir ambos os lados por

2

\frac{2 x}{2} = \frac{2 πn}{2}

Simplificar

x = πn

x = πn

Resolver

2 x = π + 2 πn : x = \frac{π}{2} + πn

2 x = π + 2 πn

Dividir ambos os lados por

2

2 x = π + 2 πn

Dividir ambos os lados por

2

\frac{2 x}{2} = \frac{π}{2} + \frac{2 πn}{2}

Simplificar

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

x = πn, x = \frac{π}{2} + πn

Gráfico

Exemplos populares

tan(x)=5sin(pi/4)sin((3pi)/4)

tan (x) = 5 sin (\frac{π}{4}) sin (\frac{3 π}{4})

cot(θ)=-12/5

cot (θ) = - \frac{12}{5}

2-2sqrt(3)tan(x+pi/3)=0

2 - 23 tan (x + \frac{π}{3}) = 0

(cos(x))^2=0

(cos (x))^{2} = 0

tan(x)= 2/8

tan (x) = \frac{2}{8}