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cos(x/2)=(sqrt(2))/2

Solução

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

Solução

x = \frac{π}{2} + 4 πn, x = \frac{7 π}{2} + 4 πn

+1

Graus

x = 9 0^{\circ} + 72 0^{\circ} n, x = 63 0^{\circ} + 72 0^{\circ} n

Passos da solução

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

Soluções gerais para

cos (\frac{x}{2}) = \frac{2}{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{x}{2} = \frac{π}{4} + 2 πn, \frac{x}{2} = \frac{7 π}{4} + 2 πn

\frac{x}{2} = \frac{π}{4} + 2 πn, \frac{x}{2} = \frac{7 π}{4} + 2 πn

Resolver

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

\frac{x}{2} = \frac{π}{4} + 2 πn

Multiplicar ambos os lados por

2

\frac{x}{2} = \frac{π}{4} + 2 πn

Multiplicar ambos os lados por

2

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

Simplificar

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

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

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

2 \cdot \frac{π}{4} + 2 \cdot 2 πn

2 \cdot \frac{π}{4} = \frac{π}{2}

2 \cdot \frac{π}{4}

Multiplicar frações:

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

= \frac{π 2}{4}

Eliminar o fator comum:

2

= \frac{π}{2}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiplicar os números:

2 \cdot 2 = 4

= 4 πn

= \frac{π}{2} + 4 πn

x = \frac{π}{2} + 4 πn

x = \frac{π}{2} + 4 πn

x = \frac{π}{2} + 4 πn

Resolver

\frac{x}{2} = \frac{7 π}{4} + 2 πn : x = \frac{7 π}{2} + 4 πn

\frac{x}{2} = \frac{7 π}{4} + 2 πn

Multiplicar ambos os lados por

2

\frac{x}{2} = \frac{7 π}{4} + 2 πn

Multiplicar ambos os lados por

2

\frac{2 x}{2} = 2 \cdot \frac{7 π}{4} + 2 \cdot 2 πn

Simplificar

\frac{2 x}{2} = 2 \cdot \frac{7 π}{4} + 2 \cdot 2 πn

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

2 \cdot \frac{7 π}{4} + 2 \cdot 2 πn : \frac{7 π}{2} + 4 πn

2 \cdot \frac{7 π}{4} + 2 \cdot 2 πn

2 \cdot \frac{7 π}{4} = \frac{7 π}{2}

2 \cdot \frac{7 π}{4}

Multiplicar frações:

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

= \frac{7 π 2}{4}

Multiplicar os números:

7 \cdot 2 = 14

= \frac{14 π}{4}

Eliminar o fator comum:

2

= \frac{7 π}{2}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiplicar os números:

2 \cdot 2 = 4

= 4 πn

= \frac{7 π}{2} + 4 πn

x = \frac{7 π}{2} + 4 πn

x = \frac{7 π}{2} + 4 πn

x = \frac{7 π}{2} + 4 πn

x = \frac{π}{2} + 4 πn, x = \frac{7 π}{2} + 4 πn

Exemplos populares

sin (10 5^{\circ})

3tan^3(θ)=tan(θ)

3 tan^{3} (θ) = tan (θ)

csc^{2} (x) - 4 = 0

cos (\frac{π}{12})

sin^{2} (x) - 1 = 0