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Popular Trigonometria >

sec(2x-10)=csc(32)

Solução

sec (2 x - 1 0^{\circ}) = csc (3 2^{\circ})

Solução

x = 18 0^{\circ} n + 5^{\circ} + \frac{1.01229 \dots}{2}, x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{1.01229 \dots}{2}

Radianos

x = \frac{π}{36} + \frac{1.01229 \dots}{2} + πn, x = π + \frac{π}{36} - \frac{1.01229 \dots}{2} + πn

Passos da solução

sec (2 x - 1 0^{\circ}) = csc (3 2^{\circ})

Aplique as propriedades trigonométricas inversas

sec (2 x - 1 0^{\circ}) = csc (3 2^{\circ})

Soluções gerais para

sec (2 x - 1 0^{\circ}) = csc (3 2^{\circ})

sec (x) = a \Rightarrow x = arcsec (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arcsec (a) + 36 0^{\circ} n

2 x - 1 0^{\circ} = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n, 2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n

2 x - 1 0^{\circ} = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n, 2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n

Resolver

2 x - 1 0^{\circ} = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n : x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

2 x - 1 0^{\circ} = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n

Mova

1 0^{\circ}

para o lado direito

2 x - 1 0^{\circ} = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n

Adicionar

1 0^{\circ}

a ambos os lados

2 x - 1 0^{\circ} + 1 0^{\circ} = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

Simplificar

2 x = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

2 x = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

Dividir ambos os lados por

2

2 x = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

Dividir ambos os lados por

2

\frac{2 x}{2} = \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

Simplificar

\frac{2 x}{2} = \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

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

\frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

Agrupar termos semelhantes

= \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2} + \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

\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

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

\frac{1 0 ^{\circ}}{2}

Aplicar as propriedades das frações:

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

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

Multiplicar os números:

18 \cdot 2 = 36

= 5^{\circ}

= 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

Resolver

2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n : x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n

Mova

1 0^{\circ}

para o lado direito

2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n

Adicionar

1 0^{\circ}

a ambos os lados

2 x - 1 0^{\circ} + 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

Simplificar

2 x = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

2 x = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

Dividir ambos os lados por

2

2 x = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

Dividir ambos os lados por

2

\frac{2 x}{2} = 18 0^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

Simplificar

\frac{2 x}{2} = 18 0^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

18 0^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2} : 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

18 0^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

Agrupar termos semelhantes

= 18 0^{\circ} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

18 0^{\circ} = 18 0^{\circ}

18 0^{\circ}

Dividir:

\frac{2}{2} = 1

= 18 0^{\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

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

\frac{1 0 ^{\circ}}{2}

Aplicar as propriedades das frações:

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

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

Multiplicar os números:

18 \cdot 2 = 36

= 5^{\circ}

= 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}, x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

Mostrar soluções na forma decimal

x = 18 0^{\circ} n + 5^{\circ} + \frac{1.01229 \dots}{2}, x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{1.01229 \dots}{2}

Gráfico

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