English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometria >

cos(2x-180)-sin(x-90)=0

Solução

cos (2 x - 18 0^{\circ}) - sin (x - 9 0^{\circ}) = 0

Solução

x = \frac{72 0 ^{\circ} n}{3}, x = 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

Radianos

x = 0 + \frac{4 π}{3} n, x = \frac{2 π}{3} + \frac{4 π}{3} n

Passos da solução

cos (2 x - 18 0^{\circ}) - sin (x - 9 0^{\circ}) = 0

Reeecreva usando identidades trigonométricas

cos (2 x - 18 0^{\circ}) - sin (x - 9 0^{\circ}) = 0

Reeecreva usando identidades trigonométricas

sin (x - 9 0^{\circ})

Use a identidade de diferença de ângulos:

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

= sin (x) cos (9 0^{\circ}) - cos (x) sin (9 0^{\circ})

Simplificar

sin (x) cos (9 0^{\circ}) - cos (x) sin (9 0^{\circ}) : - cos (x)

sin (x) cos (9 0^{\circ}) - cos (x) sin (9 0^{\circ})

sin (x) cos (9 0^{\circ}) = 0

sin (x) cos (9 0^{\circ})

Simplificar

cos (9 0^{\circ}) : 0

cos (9 0^{\circ})

Utilizar a seguinte identidade trivial:

cos (9 0^{\circ}) = 0

cos (x)

tabela de periodicidade com ciclo de

36 0^{\circ} n

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

= 0 \cdot sin (x)

Aplicar a regra

0 \cdot a = 0

= 0

cos (x) sin (9 0^{\circ}) = cos (x)

cos (x) sin (9 0^{\circ})

Simplificar

sin (9 0^{\circ}) : 1

sin (9 0^{\circ})

Utilizar a seguinte identidade trivial:

sin (9 0^{\circ}) = 1

sin (x)

tabela de periodicidade com ciclo de

36 0^{\circ} n

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= 1 \cdot cos (x)

Multiplicar:

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

= cos (x)

= 0 - cos (x)

0 - cos (x) = - cos (x)

= - cos (x)

= - cos (x)

Use a identidade de diferença de ângulos:

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

= cos (2 x) cos (18 0^{\circ}) + sin (2 x) sin (18 0^{\circ})

Simplificar

cos (2 x) cos (18 0^{\circ}) + sin (2 x) sin (18 0^{\circ}) : - cos (2 x)

cos (2 x) cos (18 0^{\circ}) + sin (2 x) sin (18 0^{\circ})

cos (2 x) cos (18 0^{\circ}) = - cos (2 x)

cos (2 x) cos (18 0^{\circ})

Simplificar

cos (18 0^{\circ}) : - 1

cos (18 0^{\circ})

Utilizar a seguinte identidade trivial:

cos (18 0^{\circ}) = (- 1)

cos (x)

tabela de periodicidade com ciclo de

36 0^{\circ} n

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - 1

= (- 1) cos (2 x)

Simplificar

= - cos (2 x)

= - cos (2 x) + sin (18 0^{\circ}) sin (2 x)

sin (2 x) sin (18 0^{\circ}) = 0

sin (2 x) sin (18 0^{\circ})

Simplificar

sin (18 0^{\circ}) : 0

sin (18 0^{\circ})

Utilizar a seguinte identidade trivial:

sin (18 0^{\circ}) = 0

sin (x)

tabela de periodicidade com ciclo de

36 0^{\circ} n

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= 0 \cdot sin (2 x)

Aplicar a regra

0 \cdot a = 0

= 0

= - cos (2 x) + 0

- cos (2 x) + 0 = - cos (2 x)

= - cos (2 x)

= - cos (2 x)

- cos (2 x) - (- cos (x)) = 0

Simplificar

- cos (2 x) - (- cos (x)) : - cos (2 x) + cos (x)

- cos (2 x) - (- cos (x))

Aplicar a regra

- (- a) = a

= - cos (2 x) + cos (x)

- cos (2 x) + cos (x) = 0

Use a identidade da transformação de soma em produto:

cos (s) - cos (t) = - 2 sin (\frac{s + t}{2}) sin (\frac{s - t}{2})

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

Simplificar

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

- 2 sin (\frac{x + 2 x}{2}) sin (\frac{x - 2 x}{2})

Somar elementos similares:

x + 2 x = 3 x

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

\frac{x - 2 x}{2} = - \frac{x}{2}

\frac{x - 2 x}{2}

Somar elementos similares:

x - 2 x = - x

= \frac{- x}{2}

Aplicar as propriedades das frações:

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

= - \frac{x}{2}

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

Use a identidade de ângulo negativo:

sin (- x) = - sin (x)

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

Aplicar a regra

- (- a) = a

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

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

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

Resolver cada parte separadamente

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

sin (\frac{3 x}{2}) = 0 : x = \frac{72 0 ^{\circ} n}{3}, x = 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

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

Soluções gerais para

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

sin (x)

tabela de periodicidade com ciclo de

36 0^{\circ} n

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{3 x}{2} = 0 + 36 0^{\circ} n, \frac{3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n

\frac{3 x}{2} = 0 + 36 0^{\circ} n, \frac{3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n

Resolver

\frac{3 x}{2} = 0 + 36 0^{\circ} n : x = \frac{72 0 ^{\circ} n}{3}

\frac{3 x}{2} = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

\frac{3 x}{2} = 36 0^{\circ} n

Multiplicar ambos os lados por

2

\frac{3 x}{2} = 36 0^{\circ} n

Multiplicar ambos os lados por

2

\frac{2 \cdot 3 x}{2} = 2 \cdot 36 0^{\circ} n

Simplificar

3 x = 72 0^{\circ} n

3 x = 72 0^{\circ} n

Dividir ambos os lados por

3

3 x = 72 0^{\circ} n

Dividir ambos os lados por

3

\frac{3 x}{3} = \frac{72 0 ^{\circ} n}{3}

Simplificar

x = \frac{72 0 ^{\circ} n}{3}

x = \frac{72 0 ^{\circ} n}{3}

Resolver

\frac{3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n : x = 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

\frac{3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n

Multiplicar ambos os lados por

2

\frac{3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n

Multiplicar ambos os lados por

2

\frac{2 \cdot 3 x}{2} = 36 0^{\circ} + 2 \cdot 36 0^{\circ} n

Simplificar

3 x = 36 0^{\circ} + 72 0^{\circ} n

3 x = 36 0^{\circ} + 72 0^{\circ} n

Dividir ambos os lados por

3

3 x = 36 0^{\circ} + 72 0^{\circ} n

Dividir ambos os lados por

3

\frac{3 x}{3} = 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

Simplificar

x = 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

x = 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

x = \frac{72 0 ^{\circ} n}{3}, x = 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

sin (\frac{x}{2}) = 0 : x = 72 0^{\circ} n, x = 36 0^{\circ} + 72 0^{\circ} n

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

Soluções gerais para

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

sin (x)

tabela de periodicidade com ciclo de

36 0^{\circ} n

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{x}{2} = 0 + 36 0^{\circ} n, \frac{x}{2} = 18 0^{\circ} + 36 0^{\circ} n

\frac{x}{2} = 0 + 36 0^{\circ} n, \frac{x}{2} = 18 0^{\circ} + 36 0^{\circ} n

Resolver

\frac{x}{2} = 0 + 36 0^{\circ} n : x = 72 0^{\circ} n

\frac{x}{2} = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

\frac{x}{2} = 36 0^{\circ} n

Multiplicar ambos os lados por

2

\frac{x}{2} = 36 0^{\circ} n

Multiplicar ambos os lados por

2

\frac{2 x}{2} = 2 \cdot 36 0^{\circ} n

Simplificar

x = 72 0^{\circ} n

x = 72 0^{\circ} n

Resolver

\frac{x}{2} = 18 0^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} + 72 0^{\circ} n

\frac{x}{2} = 18 0^{\circ} + 36 0^{\circ} n

Multiplicar ambos os lados por

2

\frac{x}{2} = 18 0^{\circ} + 36 0^{\circ} n

Multiplicar ambos os lados por

2

\frac{2 x}{2} = 36 0^{\circ} + 2 \cdot 36 0^{\circ} n

Simplificar

x = 36 0^{\circ} + 72 0^{\circ} n

x = 36 0^{\circ} + 72 0^{\circ} n

x = 72 0^{\circ} n, x = 36 0^{\circ} + 72 0^{\circ} n

Combinar toda as soluções

x = \frac{72 0 ^{\circ} n}{3}, x = 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}, x = 72 0^{\circ} n, x = 36 0^{\circ} + 72 0^{\circ} n

Junte intervalos que se sobrepoem

x = \frac{72 0 ^{\circ} n}{3}, x = 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

Gráfico

Exemplos populares

sin(x)tan(x)=0

sin (x) tan (x) = 0

sin(2x)-sin(4x)=0

sin (2 x) - sin (4 x) = 0

cos^2(θ)-cos(θ)-30=0

cos^{2} (θ) - cos (θ) - 30 = 0

2csc(2x)+1=0

2 csc (2 x) + 1 = 0

4sin^2(x)+4sin(x)+1=0

4 sin^{2} (x) + 4 sin (x) + 1 = 0