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Popular Trigonometria >

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

Solução

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

Solução

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

+1

Graus

x = 3 0^{\circ} + 12 0^{\circ} n, x = 9 0^{\circ} + 12 0^{\circ} n

Passos da solução

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

Reeecreva usando identidades trigonométricas

- sin (2 x) sin (x) + cos (2 x) cos (x)

Use a identidade de soma de ângulos:

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

= cos (2 x + x)

cos (2 x + x) = 0

Soluções gerais para

cos (2 x + x) = 0

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}

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

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

Resolver

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

2 x + x = \frac{π}{2} + 2 πn

Somar elementos similares:

2 x + x = 3 x

3 x = \frac{π}{2} + 2 πn

Dividir ambos os lados por

3

3 x = \frac{π}{2} + 2 πn

Dividir ambos os lados por

3

\frac{3 x}{3} = \frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 x}{3} = \frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

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

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

\frac{\frac{π}{2}}{3} = \frac{π}{6}

\frac{\frac{π}{2}}{3}

Aplicar as propriedades das frações:

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

= \frac{π}{2 \cdot 3}

Multiplicar os números:

2 \cdot 3 = 6

= \frac{π}{6}

= \frac{π}{6} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}

Resolver

2 x + x = \frac{3 π}{2} + 2 πn : x = \frac{π}{2} + \frac{2 πn}{3}

2 x + x = \frac{3 π}{2} + 2 πn

Somar elementos similares:

2 x + x = 3 x

3 x = \frac{3 π}{2} + 2 πn

Dividir ambos os lados por

3

3 x = \frac{3 π}{2} + 2 πn

Dividir ambos os lados por

3

\frac{3 x}{3} = \frac{\frac{3 π}{2}}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 x}{3} = \frac{\frac{3 π}{2}}{3} + \frac{2 πn}{3}

Simplificar

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

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

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

\frac{\frac{3 π}{2}}{3} = \frac{π}{2}

\frac{\frac{3 π}{2}}{3}

Aplicar as propriedades das frações:

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

= \frac{3 π}{2 \cdot 3}

Multiplicar os números:

2 \cdot 3 = 6

= \frac{3 π}{6}

Eliminar o fator comum:

3

= \frac{π}{2}

= \frac{π}{2} + \frac{2 πn}{3}

x = \frac{π}{2} + \frac{2 πn}{3}

x = \frac{π}{2} + \frac{2 πn}{3}

x = \frac{π}{2} + \frac{2 πn}{3}

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

Gráfico

Exemplos populares

sin(2x)+cos(2x)-1=0

4tan(x)sin^2(x)+3=4sin^2(x)+3tan(x)

cos(x)=1-sin^2(x/2)