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Popular Trigonometria >

0.56=tan^2(45+x/2)

Solução

0.56 = tan^{2} (4 5^{\circ} + \frac{x}{2})

Solução

x = 2 \cdot 0.64243 \dots + 36 0^{\circ} n - 9 0^{\circ}, x = - 2 \cdot 0.64243 \dots + 36 0^{\circ} n - 9 0^{\circ}

Radianos

x = 2 \cdot 0.64243 \dots - \frac{π}{2} + 2 πn, x = - 2 \cdot 0.64243 \dots - \frac{π}{2} + 2 πn

Passos da solução

0.56 = tan^{2} (4 5^{\circ} + \frac{x}{2})

Trocar lados

tan^{2} (4 5^{\circ} + \frac{x}{2}) = 0.56

Usando o método de substituição

tan^{2} (4 5^{\circ} + \frac{x}{2}) = 0.56

Sea:

tan (4 5^{\circ} + \frac{x}{2}) = u

u^{2} = 0.56

u^{2} = 0.56 : u = 0.56, u = - 0.56

u^{2} = 0.56

Para

x^{2} = f (a)

as soluções são

x = f (a), - f (a)

u = 0.56, u = - 0.56

Substituir na equação

u = tan (4 5^{\circ} + \frac{x}{2})

tan (4 5^{\circ} + \frac{x}{2}) = 0.56, tan (4 5^{\circ} + \frac{x}{2}) = - 0.56

tan (4 5^{\circ} + \frac{x}{2}) = 0.56, tan (4 5^{\circ} + \frac{x}{2}) = - 0.56

tan (4 5^{\circ} + \frac{x}{2}) = 0.56 : x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

tan (4 5^{\circ} + \frac{x}{2}) = 0.56

Aplique as propriedades trigonométricas inversas

tan (4 5^{\circ} + \frac{x}{2}) = 0.56

Soluções gerais para

tan (4 5^{\circ} + \frac{x}{2}) = 0.56

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (0.56) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (0.56) + 18 0^{\circ} n

Resolver

4 5^{\circ} + \frac{x}{2} = arctan (0.56) + 18 0^{\circ} n : x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

4 5^{\circ} + \frac{x}{2} = arctan (0.56) + 18 0^{\circ} n

Mova

4 5^{\circ}

para o lado direito

4 5^{\circ} + \frac{x}{2} = arctan (0.56) + 18 0^{\circ} n

Subtrair

4 5^{\circ}

de ambos os lados

4 5^{\circ} + \frac{x}{2} - 4 5^{\circ} = arctan (0.56) + 18 0^{\circ} n - 4 5^{\circ}

Simplificar

\frac{x}{2} = arctan (0.56) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{2} = arctan (0.56) + 18 0^{\circ} n - 4 5^{\circ}

Multiplicar ambos os lados por

2

\frac{x}{2} = arctan (0.56) + 18 0^{\circ} n - 4 5^{\circ}

Multiplicar ambos os lados por

2

\frac{2 x}{2} = 2 arctan (0.56) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplificar

\frac{2 x}{2} = 2 arctan (0.56) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

2 arctan (0.56) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ} : 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

2 arctan (0.56) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 \cdot 4 5^{\circ} = 9 0^{\circ}

2 \cdot 4 5^{\circ}

Multiplicar frações:

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

= 9 0^{\circ}

Eliminar o fator comum:

2

= 9 0^{\circ}

= 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

tan (4 5^{\circ} + \frac{x}{2}) = - 0.56 : x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

tan (4 5^{\circ} + \frac{x}{2}) = - 0.56

Aplique as propriedades trigonométricas inversas

tan (4 5^{\circ} + \frac{x}{2}) = - 0.56

Soluções gerais para

tan (4 5^{\circ} + \frac{x}{2}) = - 0.56

tan (x) = - a \Rightarrow x = arctan (- a) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (- 0.56) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (- 0.56) + 18 0^{\circ} n

Resolver

4 5^{\circ} + \frac{x}{2} = arctan (- 0.56) + 18 0^{\circ} n : x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

4 5^{\circ} + \frac{x}{2} = arctan (- 0.56) + 18 0^{\circ} n

Simplificar

arctan (- 0.56) + 18 0^{\circ} n : - arctan (\frac{14}{5}) + 18 0^{\circ} n

arctan (- 0.56) + 18 0^{\circ} n

arctan (- 0.56) = - arctan (\frac{14}{5})

arctan (- 0.56)

= arctan (- \frac{14}{25})

Utilizar a seguinte propriedade:

arctan (- x) = - arctan (x)

arctan (- \frac{14}{25}) = - arctan (\frac{14}{25})

= - arctan (\frac{14}{25})

= - arctan (\frac{14}{5})

= - arctan (\frac{14}{5}) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = - arctan (\frac{14}{5}) + 18 0^{\circ} n

Mova

4 5^{\circ}

para o lado direito

4 5^{\circ} + \frac{x}{2} = - arctan (\frac{14}{5}) + 18 0^{\circ} n

Subtrair

4 5^{\circ}

de ambos os lados

4 5^{\circ} + \frac{x}{2} - 4 5^{\circ} = - arctan (\frac{14}{5}) + 18 0^{\circ} n - 4 5^{\circ}

Simplificar

\frac{x}{2} = - arctan (\frac{14}{5}) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{2} = - arctan (\frac{14}{5}) + 18 0^{\circ} n - 4 5^{\circ}

Multiplicar ambos os lados por

2

\frac{x}{2} = - arctan (\frac{14}{5}) + 18 0^{\circ} n - 4 5^{\circ}

Multiplicar ambos os lados por

2

\frac{2 x}{2} = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplificar

\frac{2 x}{2} = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

- 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ} : - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

- 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 \cdot 4 5^{\circ} = 9 0^{\circ}

2 \cdot 4 5^{\circ}

Multiplicar frações:

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

= 9 0^{\circ}

Eliminar o fator comum:

2

= 9 0^{\circ}

= - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

Combinar toda as soluções

x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}, x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

Mostrar soluções na forma decimal

x = 2 \cdot 0.64243 \dots + 36 0^{\circ} n - 9 0^{\circ}, x = - 2 \cdot 0.64243 \dots + 36 0^{\circ} n - 9 0^{\circ}

Gráfico

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