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Popular Trigonometria >

solvefor x,f[g]=cos(1/(x^2))

Solução

resolver para

x, f [g] = cos (\frac{1}{x ^{2}})

Solução

x = \frac{1}{arccos ( f g ) + 2 πn}, x = - \frac{1}{arccos ( f g ) + 2 πn}, x = \frac{1}{- arccos ( f g ) + 2 πn}, x = - \frac{1}{- arccos ( f g ) + 2 πn}

Passos da solução

f [g] = cos (\frac{1}{x ^{2}})

Trocar lados

cos (\frac{1}{x ^{2}}) = f [g]

Remover os parênteses:

(a) = a

cos (\frac{1}{x ^{2}}) = f g

Aplique as propriedades trigonométricas inversas

cos (\frac{1}{x ^{2}}) = f g

Soluções gerais para

cos (\frac{1}{x ^{2}}) = f g

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

\frac{1}{x ^{2}} = arccos (f g) + 2 πn, \frac{1}{x ^{2}} = - arccos (f g) + 2 πn

\frac{1}{x ^{2}} = arccos (f g) + 2 πn, \frac{1}{x ^{2}} = - arccos (f g) + 2 πn

Resolver

\frac{1}{x ^{2}} = arccos (f g) + 2 πn : x = \frac{1}{arccos ( f g ) + 2 πn}, x = - \frac{1}{arccos ( f g ) + 2 πn}; f \neq = \frac{cos ( - 2 πn )}{g}

\frac{1}{x ^{2}} = arccos (f g) + 2 πn

Multiplicar ambos os lados por

x^{2}

\frac{1}{x ^{2}} = arccos (f g) + 2 πn

Multiplicar ambos os lados por

x^{2}

\frac{1}{x ^{2}} x^{2} = arccos (f g) x^{2} + 2 πn x^{2}

Simplificar

1 = arccos (f g) x^{2} + 2 πn x^{2}

1 = arccos (f g) x^{2} + 2 πn x^{2}

Resolver

1 = arccos (f g) x^{2} + 2 πn x^{2} : x = \frac{1}{arccos ( f g ) + 2 πn}, x = - \frac{1}{arccos ( f g ) + 2 πn}; f \neq = \frac{cos ( - 2 πn )}{g}

1 = arccos (f g) x^{2} + 2 πn x^{2}

Trocar lados

arccos (f g) x^{2} + 2 πn x^{2} = 1

Fatorar

arccos (f g) x^{2} + 2 πn x^{2} : x^{2} (arccos (f g) + 2 πn)

arccos (f g) x^{2} + 2 πn x^{2}

Fatorar o termo comum

x^{2}

= x^{2} (arccos (f g) + 2 πn)

x^{2} (arccos (f g) + 2 πn) = 1

Dividir ambos os lados por

arccos (f g) + 2 πn; f \neq = \frac{cos ( - 2 πn )}{g}

x^{2} (arccos (f g) + 2 πn) = 1

Dividir ambos os lados por

arccos (f g) + 2 πn; f \neq = \frac{cos ( - 2 πn )}{g}

\frac{x ^{2} ( arccos ( f g ) + 2 πn )}{arccos ( f g ) + 2 πn} = \frac{1}{arccos ( f g ) + 2 πn}; f \neq = \frac{cos ( - 2 πn )}{g}

Simplificar

x^{2} = \frac{1}{arccos ( f g ) + 2 πn}; f \neq = \frac{cos ( - 2 πn )}{g}

x^{2} = \frac{1}{arccos ( f g ) + 2 πn}; f \neq = \frac{cos ( - 2 πn )}{g}

Para

x^{2} = f (a)

as soluções são

x = f (a), - f (a)

x = \frac{1}{arccos ( f g ) + 2 πn}, x = - \frac{1}{arccos ( f g ) + 2 πn}; f \neq = \frac{cos ( - 2 πn )}{g}

x = \frac{1}{arccos ( f g ) + 2 πn}, x = - \frac{1}{arccos ( f g ) + 2 πn}; f \neq = \frac{cos ( - 2 πn )}{g}

Resolver

\frac{1}{x ^{2}} = - arccos (f g) + 2 πn : x = \frac{1}{- arccos ( f g ) + 2 πn}, x = - \frac{1}{- arccos ( f g ) + 2 πn}; f \neq = \frac{cos ( 2 πn )}{g}

\frac{1}{x ^{2}} = - arccos (f g) + 2 πn

Multiplicar ambos os lados por

x^{2}

\frac{1}{x ^{2}} = - arccos (f g) + 2 πn

Multiplicar ambos os lados por

x^{2}

\frac{1}{x ^{2}} x^{2} = - arccos (f g) x^{2} + 2 πn x^{2}

Simplificar

1 = - arccos (f g) x^{2} + 2 πn x^{2}

1 = - arccos (f g) x^{2} + 2 πn x^{2}

Resolver

1 = - arccos (f g) x^{2} + 2 πn x^{2} : x = \frac{1}{- arccos ( f g ) + 2 πn}, x = - \frac{1}{- arccos ( f g ) + 2 πn}; f \neq = \frac{cos ( 2 πn )}{g}

1 = - arccos (f g) x^{2} + 2 πn x^{2}

Trocar lados

- arccos (f g) x^{2} + 2 πn x^{2} = 1

Fatorar

- arccos (f g) x^{2} + 2 πn x^{2} : x^{2} (- arccos (f g) + 2 πn)

- arccos (f g) x^{2} + 2 πn x^{2}

Fatorar o termo comum

x^{2}

= x^{2} (- arccos (f g) + 2 πn)

x^{2} (- arccos (f g) + 2 πn) = 1

Dividir ambos os lados por

- arccos (f g) + 2 πn; f \neq = \frac{cos ( 2 πn )}{g}

x^{2} (- arccos (f g) + 2 πn) = 1

Dividir ambos os lados por

- arccos (f g) + 2 πn; f \neq = \frac{cos ( 2 πn )}{g}

\frac{x ^{2} ( - arccos ( f g ) + 2 πn )}{- arccos ( f g ) + 2 πn} = \frac{1}{- arccos ( f g ) + 2 πn}; f \neq = \frac{cos ( 2 πn )}{g}

Simplificar

x^{2} = \frac{1}{- arccos ( f g ) + 2 πn}; f \neq = \frac{cos ( 2 πn )}{g}

x^{2} = \frac{1}{- arccos ( f g ) + 2 πn}; f \neq = \frac{cos ( 2 πn )}{g}

Para

x^{2} = f (a)

as soluções são

x = f (a), - f (a)

x = \frac{1}{- arccos ( f g ) + 2 πn}, x = - \frac{1}{- arccos ( f g ) + 2 πn}; f \neq = \frac{cos ( 2 πn )}{g}

x = \frac{1}{- arccos ( f g ) + 2 πn}, x = - \frac{1}{- arccos ( f g ) + 2 πn}; f \neq = \frac{cos ( 2 πn )}{g}

x = \frac{1}{arccos ( f g ) + 2 πn}, x = - \frac{1}{arccos ( f g ) + 2 πn}, x = \frac{1}{- arccos ( f g ) + 2 πn}, x = - \frac{1}{- arccos ( f g ) + 2 πn}

Gráfico

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