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Popular Trigonometria >

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

Solução

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

Solução

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Graus

x = 4 5^{\circ} + 18 0^{\circ} n, x = 13 5^{\circ} + 18 0^{\circ} n

Passos da solução

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

Reeecreva usando identidades trigonométricas

- 2 (sin^{2} (x) - cos^{2} (x))

Utilizar a identidade trigonométrica do arco duplo:

cos^{2} (x) - sin^{2} (x) = cos (2 x)

- cos^{2} (x) + sin^{2} (x) = - cos (2 x)

= - 2 (- cos (2 x))

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

Dividir ambos os lados por

- 2

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

Dividir ambos os lados por

- 2

\frac{- 2 ( - cos ( 2 x ) )}{- 2} = \frac{0}{- 2}

Simplificar

- cos (2 x) = 0

- cos (2 x) = 0

Dividir ambos os lados por

- 1

- cos (2 x) = 0

Dividir ambos os lados por

- 1

\frac{- cos ( 2 x )}{- 1} = \frac{0}{- 1}

Simplificar

cos (2 x) = 0

cos (2 x) = 0

Soluções gerais para

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

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

Resolver

2 x = \frac{π}{2} + 2 πn : x = \frac{π}{4} + πn

2 x = \frac{π}{2} + 2 πn

Dividir ambos os lados por

2

2 x = \frac{π}{2} + 2 πn

Dividir ambos os lados por

2

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

Simplificar

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

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{\frac{π}{2}}{2} + \frac{2 πn}{2} : \frac{π}{4} + πn

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

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

Aplicar as propriedades das frações:

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

= \frac{π}{2 \cdot 2}

Multiplicar os números:

2 \cdot 2 = 4

= \frac{π}{4}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividir:

\frac{2}{2} = 1

= πn

= \frac{π}{4} + πn

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

Resolver

2 x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{4} + πn

2 x = \frac{3 π}{2} + 2 πn

Dividir ambos os lados por

2

2 x = \frac{3 π}{2} + 2 πn

Dividir ambos os lados por

2

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

Simplificar

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

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{\frac{3 π}{2}}{2} + \frac{2 πn}{2} : \frac{3 π}{4} + πn

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

\frac{\frac{3 π}{2}}{2} = \frac{3 π}{4}

\frac{\frac{3 π}{2}}{2}

Aplicar as propriedades das frações:

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

= \frac{3 π}{2 \cdot 2}

Multiplicar os números:

2 \cdot 2 = 4

= \frac{3 π}{4}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividir:

\frac{2}{2} = 1

= πn

= \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Gráfico

Exemplos populares

2sin^2(x)-5sin(x)-4=0

2 sin^{2} (x) - 5 sin (x) - 4 = 0

sin(θ)=0.4815

sin (θ) = 0.4815

6cos^2(2x)=sin(2x)+5

6 cos^{2} (2 x) = sin (2 x) + 5

sin(A)= 4/5 ,sin(2A)

sin (A) = \frac{4}{5}, sin (2 A)

1/2 (1+cos(x))=0.6294095226

\frac{1}{2} (1 + cos (x)) = 0.6294095226