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tan(2θ)=-sqrt(3),0<= θ<= 360

Solução

tan (2 θ) = - 3, 0^{\circ} \leq θ \leq 36 0^{\circ}

θ = 6 0^{\circ}, θ = 15 0^{\circ}, θ = 24 0^{\circ}, θ = 33 0^{\circ}

Radianos

θ = \frac{π}{3}, θ = \frac{5 π}{6}, θ = \frac{4 π}{3}, θ = \frac{11 π}{6}

Passos da solução

tan (2 θ) = - 3, 0^{\circ} \leq θ \leq 36 0^{\circ}

Soluções gerais para

tan (2 θ) = - 3

tan (x)

tabela de periodicidade com ciclo de

18 0^{\circ} n

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

2 θ = 12 0^{\circ} + 18 0^{\circ} n

2 θ = 12 0^{\circ} + 18 0^{\circ} n

Resolver

2 θ = 12 0^{\circ} + 18 0^{\circ} n : θ = 6 0^{\circ} + \frac{18 0 ^{\circ} n}{2}

2 θ = 12 0^{\circ} + 18 0^{\circ} n

Dividir ambos os lados por

2

2 θ = 12 0^{\circ} + 18 0^{\circ} n

Dividir ambos os lados por

2

\frac{2 θ}{2} = \frac{12 0 ^{\circ}}{2} + \frac{18 0 ^{\circ} n}{2}

Simplificar

\frac{2 θ}{2} = \frac{12 0 ^{\circ}}{2} + \frac{18 0 ^{\circ} n}{2}

Simplificar

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

Dividir:

\frac{2}{2} = 1

= θ

Simplificar

\frac{12 0 ^{\circ}}{2} + \frac{18 0 ^{\circ} n}{2} : 6 0^{\circ} + \frac{18 0 ^{\circ} n}{2}

\frac{12 0 ^{\circ}}{2} + \frac{18 0 ^{\circ} n}{2}

\frac{12 0 ^{\circ}}{2} = 6 0^{\circ}

\frac{12 0 ^{\circ}}{2}

Aplicar as propriedades das frações:

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

= \frac{36 0 ^{\circ}}{3 \cdot 2}

Multiplicar os números:

3 \cdot 2 = 6

= 6 0^{\circ}

Eliminar o fator comum:

2

= 6 0^{\circ}

= 6 0^{\circ} + \frac{18 0 ^{\circ} n}{2}

θ = 6 0^{\circ} + \frac{18 0 ^{\circ} n}{2}

θ = 6 0^{\circ} + \frac{18 0 ^{\circ} n}{2}

θ = 6 0^{\circ} + \frac{18 0 ^{\circ} n}{2}

θ = 6 0^{\circ} + \frac{18 0 ^{\circ} n}{2}

Soluções para o intervalo

0 \leq θ \leq 36 0^{\circ}

θ = 6 0^{\circ}, θ = 15 0^{\circ}, θ = 24 0^{\circ}, θ = 33 0^{\circ}