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Popular Trigonometria >

tan(x/2-pi/2)=sqrt(2)

Solução

tan (\frac{x}{2} - \frac{π}{2}) = 2

Solução

x = 2 \cdot 0.95531 \dots + 2 πn + π

+1

Graus

x = 289.47122 \dots^{\circ} + 36 0^{\circ} n

Passos da solução

tan (\frac{x}{2} - \frac{π}{2}) = 2

Aplique as propriedades trigonométricas inversas

tan (\frac{x}{2} - \frac{π}{2}) = 2

Soluções gerais para

tan (\frac{x}{2} - \frac{π}{2}) = 2

tan (x) = a \Rightarrow x = arctan (a) + πn

\frac{x}{2} - \frac{π}{2} = arctan (2) + πn

\frac{x}{2} - \frac{π}{2} = arctan (2) + πn

Resolver

\frac{x}{2} - \frac{π}{2} = arctan (2) + πn : x = 2 arctan (2) + 2 πn + π

\frac{x}{2} - \frac{π}{2} = arctan (2) + πn

Mova

\frac{π}{2}

para o lado direito

\frac{x}{2} - \frac{π}{2} = arctan (2) + πn

Adicionar

\frac{π}{2}

a ambos os lados

\frac{x}{2} - \frac{π}{2} + \frac{π}{2} = arctan (2) + πn + \frac{π}{2}

Simplificar

\frac{x}{2} = arctan (2) + πn + \frac{π}{2}

\frac{x}{2} = arctan (2) + πn + \frac{π}{2}

Multiplicar ambos os lados por

2

\frac{x}{2} = arctan (2) + πn + \frac{π}{2}

Multiplicar ambos os lados por

2

\frac{2 x}{2} = 2 arctan (2) + 2 πn + 2 \cdot \frac{π}{2}

Simplificar

\frac{2 x}{2} = 2 arctan (2) + 2 πn + 2 \cdot \frac{π}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

2 arctan (2) + 2 πn + 2 \cdot \frac{π}{2} : 2 arctan (2) + 2 πn + π

2 arctan (2) + 2 πn + 2 \cdot \frac{π}{2}

2 \cdot \frac{π}{2} = π

2 \cdot \frac{π}{2}

Multiplicar frações:

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

= \frac{π 2}{2}

Eliminar o fator comum:

2

= π

= 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

Mostrar soluções na forma decimal

x = 2 \cdot 0.95531 \dots + 2 πn + π

Gráfico

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