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Popular Trigonometria >

1715/70 =tan(45+θ/2)

Solução

\frac{1715}{70} = tan (4 5^{\circ} + \frac{θ}{2})

Solução

θ = 2 \cdot 1.53000 \dots + 36 0^{\circ} n - 9 0^{\circ}

+1

Radianos

θ = 2 \cdot 1.53000 \dots - \frac{π}{2} + 2 πn

Passos da solução

\frac{1715}{70} = tan (4 5^{\circ} + \frac{θ}{2})

Trocar lados

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{1715}{70}

Eliminar o fator comum:

35

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{49}{2}

Aplique as propriedades trigonométricas inversas

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{49}{2}

Soluções gerais para

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{49}{2}

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

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

Resolver

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n : θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

Mova

4 5^{\circ}

para o lado direito

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

Subtrair

4 5^{\circ}

de ambos os lados

4 5^{\circ} + \frac{θ}{2} - 4 5^{\circ} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

Simplificar

\frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

\frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

Multiplicar ambos os lados por

2

\frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

Multiplicar ambos os lados por

2

\frac{2 θ}{2} = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplificar

\frac{2 θ}{2} = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplificar

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

Dividir:

\frac{2}{2} = 1

= θ

Simplificar

2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ} : 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

2 arctan (\frac{49}{2}) + 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{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

Mostrar soluções na forma decimal

θ = 2 \cdot 1.53000 \dots + 36 0^{\circ} n - 9 0^{\circ}

Gráfico

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