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Popular Trigonometria >

4=sqrt(2)csc(3x)

Solução

4 = 2 csc (3 x)

Solução

x = \frac{0.36136 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.36136 \dots}{3} + \frac{2 πn}{3}

+1

Graus

x = 6.90160 \dots^{\circ} + 12 0^{\circ} n, x = 53.09839 \dots^{\circ} + 12 0^{\circ} n

Passos da solução

4 = 2 csc (3 x)

Trocar lados

2 csc (3 x) = 4

Dividir ambos os lados por

2

2 csc (3 x) = 4

Dividir ambos os lados por

2

\frac{2 csc ( 3 x )}{2} = \frac{4}{2}

Simplificar

\frac{2 csc ( 3 x )}{2} = \frac{4}{2}

Simplificar

\frac{2 csc ( 3 x )}{2} : csc (3 x)

\frac{2 csc ( 3 x )}{2}

Eliminar o fator comum:

2

= csc (3 x)

Simplificar

\frac{4}{2} : 22

\frac{4}{2}

Fatorar

4 : 2^{2}

Fatorar

4 = 2^{2}

= \frac{2 ^{2}}{2}

Cancelar

\frac{2 ^{2}}{2} : 2^{\frac{3}{2}}

\frac{2 ^{2}}{2}

Aplicar as propriedades dos radicais:

n a = a^{\frac{1}{n}}

2 = 2^{\frac{1}{2}}

= \frac{2 ^{2}}{2 ^{\frac{1}{2}}}

Aplicar as propriedades dos expoentes:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{2 ^{2}}{2 ^{\frac{1}{2}}} = 2^{2 - \frac{1}{2}}

= 2^{2 - \frac{1}{2}}

Subtrair:

2 - \frac{1}{2} = \frac{3}{2}

= 2^{\frac{3}{2}}

= 2^{\frac{3}{2}}

2^{\frac{3}{2}} = 22

2^{\frac{3}{2}}

2^{\frac{3}{2}} = 2^{1 + \frac{1}{2}}

= 2^{1 + \frac{1}{2}}

Aplicar as propriedades dos expoentes:

x^{a + b} = x^{a} x^{b}

= 2^{1} \cdot 2^{\frac{1}{2}}

Simplificar

= 22

= 22

csc (3 x) = 22

csc (3 x) = 22

csc (3 x) = 22

Aplique as propriedades trigonométricas inversas

csc (3 x) = 22

Soluções gerais para

csc (3 x) = 22

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π - arccsc (a) + 2 πn

3 x = arccsc (22) + 2 πn, 3 x = π - arccsc (22) + 2 πn

3 x = arccsc (22) + 2 πn, 3 x = π - arccsc (22) + 2 πn

Resolver

3 x = arccsc (22) + 2 πn : x = \frac{arccsc ( 2 2 )}{3} + \frac{2 πn}{3}

3 x = arccsc (22) + 2 πn

Dividir ambos os lados por

3

3 x = arccsc (22) + 2 πn

Dividir ambos os lados por

3

\frac{3 x}{3} = \frac{arccsc ( 2 2 )}{3} + \frac{2 πn}{3}

Simplificar

x = \frac{arccsc ( 2 2 )}{3} + \frac{2 πn}{3}

x = \frac{arccsc ( 2 2 )}{3} + \frac{2 πn}{3}

Resolver

3 x = π - arccsc (22) + 2 πn : x = \frac{π}{3} - \frac{arccsc ( 2 2 )}{3} + \frac{2 πn}{3}

3 x = π - arccsc (22) + 2 πn

Dividir ambos os lados por

3

3 x = π - arccsc (22) + 2 πn

Dividir ambos os lados por

3

\frac{3 x}{3} = \frac{π}{3} - \frac{arccsc ( 2 2 )}{3} + \frac{2 πn}{3}

Simplificar

x = \frac{π}{3} - \frac{arccsc ( 2 2 )}{3} + \frac{2 πn}{3}

x = \frac{π}{3} - \frac{arccsc ( 2 2 )}{3} + \frac{2 πn}{3}

x = \frac{arccsc ( 2 2 )}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{arccsc ( 2 2 )}{3} + \frac{2 πn}{3}

Mostrar soluções na forma decimal

x = \frac{0.36136 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.36136 \dots}{3} + \frac{2 πn}{3}

Gráfico

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sinh(z)-cosh(z)=0

sinh (z) - cosh (z) = 0

cos(x)=-1.588908648

cos (x) = - 1.588908648

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