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tan(2x-n/4)=-1,0<x<= 360

Solução

tan (2 x - \frac{n}{4}) = - 1, 0^{\circ} < x \leq 36 0^{\circ}

Sem solu \overset{c}{\c} \tilde{a} o para x \in R

Passos da solução

tan (2 x - \frac{n}{4}) = - 1, 0^{\circ} < x \leq 36 0^{\circ}

Soluções gerais para

tan (2 x - \frac{n}{4}) = - 1

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 x - \frac{n}{4} = 13 5^{\circ} + 18 0^{\circ} n

2 x - \frac{n}{4} = 13 5^{\circ} + 18 0^{\circ} n

Resolver

2 x - \frac{n}{4} = 13 5^{\circ} + 18 0^{\circ} k : x = \frac{54 0 ^{\circ} + n}{8} + \frac{18 0 ^{\circ} k}{2}

2 x - \frac{n}{4} = 13 5^{\circ} + 18 0^{\circ} k

Mova

\frac{n}{4}

para o lado direito

2 x - \frac{n}{4} = 13 5^{\circ} + 18 0^{\circ} k

Adicionar

\frac{n}{4}

a ambos os lados

2 x - \frac{n}{4} + \frac{n}{4} = 13 5^{\circ} + 18 0^{\circ} k + \frac{n}{4}

Simplificar

2 x - \frac{n}{4} + \frac{n}{4} = 13 5^{\circ} + 18 0^{\circ} k + \frac{n}{4}

Simplificar

2 x - \frac{n}{4} + \frac{n}{4} : 2 x

2 x - \frac{n}{4} + \frac{n}{4}

Somar elementos similares:

- \frac{n}{4} + \frac{n}{4} = 0

= 2 x

Simplificar

13 5^{\circ} + 18 0^{\circ} k + \frac{n}{4} : \frac{54 0 ^{\circ} + n}{4} + 18 0^{\circ} k

13 5^{\circ} + 18 0^{\circ} k + \frac{n}{4}

Combinar as frações usando o mínimo múltiplo comum:

\frac{54 0 ^{\circ} + n}{4}

Aplicar a regra

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

= \frac{54 0 ^{\circ} + n}{4}

= \frac{n + 54 0 ^{\circ}}{4} + 18 0^{\circ} k

= \frac{54 0 ^{\circ} + n}{4} + 18 0^{\circ} k

2 x = \frac{54 0 ^{\circ} + n}{4} + 18 0^{\circ} k

2 x = \frac{54 0 ^{\circ} + n}{4} + 18 0^{\circ} k

2 x = \frac{54 0 ^{\circ} + n}{4} + 18 0^{\circ} k

Dividir ambos os lados por

2

2 x = \frac{54 0 ^{\circ} + n}{4} + 18 0^{\circ} k

Dividir ambos os lados por

2

\frac{2 x}{2} = \frac{\frac{54 0 ^{\circ} + n}{4}}{2} + \frac{18 0 ^{\circ} k}{2}

Simplificar

\frac{2 x}{2} = \frac{\frac{54 0 ^{\circ} + n}{4}}{2} + \frac{18 0 ^{\circ} k}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{\frac{54 0 ^{\circ} + n}{4}}{2} + \frac{18 0 ^{\circ} k}{2} : \frac{54 0 ^{\circ} + n}{8} + \frac{18 0 ^{\circ} k}{2}

\frac{\frac{54 0 ^{\circ} + n}{4}}{2} + \frac{18 0 ^{\circ} k}{2}

\frac{\frac{54 0 ^{\circ} + n}{4}}{2} = \frac{54 0 ^{\circ} + n}{8}

\frac{\frac{54 0 ^{\circ} + n}{4}}{2}

Aplicar as propriedades das frações:

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

= \frac{54 0 ^{\circ} + n}{4 \cdot 2}

Multiplicar os números:

4 \cdot 2 = 8

= \frac{54 0 ^{\circ} + n}{8}

= \frac{n + 54 0 ^{\circ}}{8} + \frac{18 0 ^{\circ} k}{2}

x = \frac{54 0 ^{\circ} + n}{8} + \frac{18 0 ^{\circ} k}{2}

x = \frac{54 0 ^{\circ} + n}{8} + \frac{18 0 ^{\circ} k}{2}

x = \frac{54 0 ^{\circ} + n}{8} + \frac{18 0 ^{\circ} k}{2}

x = \frac{54 0 ^{\circ} + n}{8} + \frac{18 0 ^{\circ} k}{2}

Soluções para o intervalo

0 < x \leq 36 0^{\circ}

Sem solu \overset{c}{\c} \tilde{a} o para x \in R

tan (θ) = - 1, 0 \leq θ \leq 2 π

0.85 = \frac{1 - sin ( x )}{1 + sin ( x )}

sin (θ) = 0.12

2 sec (x) - 2 = 0

(tan (x)) (sin^{2} (x) - a) (sec (x) - a) = 0