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Popular Trigonometria >

csc(2x)=2,x0<x<360

Solução

csc (2 x) = 2, x 0^{\circ} < x < 36 0^{\circ}

Solução

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

Passos da solução

csc (2 x) = 2, x \cdot 0^{\circ} < x < 36 0^{\circ}

Soluções gerais para

csc (2 x) = 2

csc (x)

tabela de periodicidade com ciclo de

36 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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

2 x = 3 0^{\circ} + 36 0^{\circ} n, 2 x = 15 0^{\circ} + 36 0^{\circ} n

2 x = 3 0^{\circ} + 36 0^{\circ} n, 2 x = 15 0^{\circ} + 36 0^{\circ} n

Resolver

2 x = 3 0^{\circ} + 36 0^{\circ} n : x = 1 5^{\circ} + 18 0^{\circ} n

2 x = 3 0^{\circ} + 36 0^{\circ} n

Dividir ambos os lados por

2

2 x = 3 0^{\circ} + 36 0^{\circ} n

Dividir ambos os lados por

2

\frac{2 x}{2} = \frac{3 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

Simplificar

\frac{2 x}{2} = \frac{3 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{3 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} : 1 5^{\circ} + 18 0^{\circ} n

\frac{3 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

\frac{3 0 ^{\circ}}{2} = 1 5^{\circ}

\frac{3 0 ^{\circ}}{2}

Aplicar as propriedades das frações:

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

= \frac{18 0 ^{\circ}}{6 \cdot 2}

Multiplicar os números:

6 \cdot 2 = 12

= 1 5^{\circ}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

Dividir:

\frac{2}{2} = 1

= 18 0^{\circ} n

= 1 5^{\circ} + 18 0^{\circ} n

x = 1 5^{\circ} + 18 0^{\circ} n

x = 1 5^{\circ} + 18 0^{\circ} n

x = 1 5^{\circ} + 18 0^{\circ} n

Resolver

2 x = 15 0^{\circ} + 36 0^{\circ} n : x = 7 5^{\circ} + 18 0^{\circ} n

2 x = 15 0^{\circ} + 36 0^{\circ} n

Dividir ambos os lados por

2

2 x = 15 0^{\circ} + 36 0^{\circ} n

Dividir ambos os lados por

2

\frac{2 x}{2} = \frac{15 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

Simplificar

\frac{2 x}{2} = \frac{15 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

\frac{15 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} : 7 5^{\circ} + 18 0^{\circ} n

\frac{15 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

\frac{15 0 ^{\circ}}{2} = 7 5^{\circ}

\frac{15 0 ^{\circ}}{2}

Aplicar as propriedades das frações:

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

= \frac{90 0 ^{\circ}}{6 \cdot 2}

Multiplicar os números:

6 \cdot 2 = 12

= 7 5^{\circ}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

Dividir:

\frac{2}{2} = 1

= 18 0^{\circ} n

= 7 5^{\circ} + 18 0^{\circ} n

x = 7 5^{\circ} + 18 0^{\circ} n

x = 7 5^{\circ} + 18 0^{\circ} n

x = 7 5^{\circ} + 18 0^{\circ} n

x = 1 5^{\circ} + 18 0^{\circ} n, x = 7 5^{\circ} + 18 0^{\circ} n

Soluções para o intervalo

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

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

Gráfico

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