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Popular Trigonometria >

solvefor y,sin(x^2y^2)=x

Solução

resolver para

y, sin (x^{2} y^{2}) = x

Solução

y = \frac{arcsin ( x ) + 2 πn}{x}, y = - \frac{arcsin ( x ) + 2 πn}{x}, y = \frac{π + arcsin ( - x ) + 2 πn}{x}, y = - \frac{π + arcsin ( - x ) + 2 πn}{x}

Passos da solução

sin (x^{2} y^{2}) = x

Aplique as propriedades trigonométricas inversas

sin (x^{2} y^{2}) = x

Soluções gerais para

sin (x^{2} y^{2}) = x

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x^{2} y^{2} = arcsin (x) + 2 πn, x^{2} y^{2} = π + arcsin (- x) + 2 πn

x^{2} y^{2} = arcsin (x) + 2 πn, x^{2} y^{2} = π + arcsin (- x) + 2 πn

Resolver

x^{2} y^{2} = arcsin (x) + 2 πn : y = \frac{arcsin ( x ) + 2 πn}{x}, y = - \frac{arcsin ( x ) + 2 πn}{x}; x \neq = 0

x^{2} y^{2} = arcsin (x) + 2 πn

Dividir ambos os lados por

x^{2}; x \neq = 0

x^{2} y^{2} = arcsin (x) + 2 πn

Dividir ambos os lados por

x^{2}; x \neq = 0

\frac{x ^{2} y ^{2}}{x ^{2}} = \frac{arcsin ( x )}{x ^{2}} + \frac{2 πn}{x ^{2}}; x \neq = 0

Simplificar

y^{2} = \frac{arcsin ( x )}{x ^{2}} + \frac{2 πn}{x ^{2}}; x \neq = 0

y^{2} = \frac{arcsin ( x )}{x ^{2}} + \frac{2 πn}{x ^{2}}; x \neq = 0

Para

x^{2} = f (a)

as soluções são

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

y = \frac{arcsin ( x )}{x ^{2}} + \frac{2 πn}{x ^{2}}, y = - \frac{arcsin ( x )}{x ^{2}} + \frac{2 πn}{x ^{2}}; x \neq = 0

Simplificar

\frac{arcsin ( x )}{x ^{2}} + \frac{2 πn}{x ^{2}} : \frac{arcsin ( x ) + 2 πn}{x}

\frac{arcsin ( x )}{x ^{2}} + \frac{2 πn}{x ^{2}}

Combinar as frações usando o mínimo múltiplo comum:

\frac{arcsin ( x ) + 2 πn}{x ^{2}}

Aplicar a regra

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

= \frac{arcsin ( x ) + 2 πn}{x ^{2}}

= \frac{arcsin ( x ) + 2 πn}{x ^{2}}

Aplicar a seguinte propriedade dos radicais:

n \frac{a}{b} = \frac{n a}{n b},

assumindo que

a \geq 0, b \geq 0

= \frac{arcsin ( x ) + 2 πn}{x ^{2}}

Aplicar a seguinte propriedade dos radicais:

n a^{n} = a,

assumindo que

a \geq 0

x^{2} = x

= \frac{arcsin ( x ) + 2 πn}{x}

Simplificar

- \frac{arcsin ( x )}{x ^{2}} + \frac{2 πn}{x ^{2}} : - \frac{arcsin ( x ) + 2 πn}{x}

- \frac{arcsin ( x )}{x ^{2}} + \frac{2 πn}{x ^{2}}

Combinar as frações usando o mínimo múltiplo comum:

\frac{arcsin ( x ) + 2 πn}{x ^{2}}

Aplicar a regra

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

= \frac{arcsin ( x ) + 2 πn}{x ^{2}}

= - \frac{2 πn + arcsin ( x )}{x ^{2}}

Simplificar

\frac{arcsin ( x ) + 2 πn}{x ^{2}} : \frac{arcsin ( x ) + 2 πn}{x}

\frac{arcsin ( x ) + 2 πn}{x ^{2}}

Aplicar a seguinte propriedade dos radicais:

n \frac{a}{b} = \frac{n a}{n b},

assumindo que

a \geq 0, b \geq 0

= \frac{arcsin ( x ) + 2 πn}{x ^{2}}

Aplicar a seguinte propriedade dos radicais:

n a^{n} = a,

assumindo que

a \geq 0

x^{2} = x

= \frac{arcsin ( x ) + 2 πn}{x}

= - \frac{2 πn + arcsin ( x )}{x}

= - \frac{arcsin ( x ) + 2 πn}{x}

y = \frac{arcsin ( x ) + 2 πn}{x}, y = - \frac{arcsin ( x ) + 2 πn}{x}; x \neq = 0

Resolver

x^{2} y^{2} = π + arcsin (- x) + 2 πn : y = \frac{π + arcsin ( - x ) + 2 πn}{x}, y = - \frac{π + arcsin ( - x ) + 2 πn}{x}; x \neq = 0

x^{2} y^{2} = π + arcsin (- x) + 2 πn

Dividir ambos os lados por

x^{2}; x \neq = 0

x^{2} y^{2} = π + arcsin (- x) + 2 πn

Dividir ambos os lados por

x^{2}; x \neq = 0

\frac{x ^{2} y ^{2}}{x ^{2}} = \frac{π}{x ^{2}} + \frac{arcsin ( - x )}{x ^{2}} + \frac{2 πn}{x ^{2}}; x \neq = 0

Simplificar

y^{2} = \frac{π}{x ^{2}} + \frac{arcsin ( - x )}{x ^{2}} + \frac{2 πn}{x ^{2}}; x \neq = 0

y^{2} = \frac{π}{x ^{2}} + \frac{arcsin ( - x )}{x ^{2}} + \frac{2 πn}{x ^{2}}; x \neq = 0

Para

x^{2} = f (a)

as soluções são

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

y = \frac{π}{x ^{2}} + \frac{arcsin ( - x )}{x ^{2}} + \frac{2 πn}{x ^{2}}, y = - \frac{π}{x ^{2}} + \frac{arcsin ( - x )}{x ^{2}} + \frac{2 πn}{x ^{2}}; x \neq = 0

Simplificar

\frac{π}{x ^{2}} + \frac{arcsin ( - x )}{x ^{2}} + \frac{2 πn}{x ^{2}} : \frac{π + arcsin ( - x ) + 2 πn}{x}

\frac{π}{x ^{2}} + \frac{arcsin ( - x )}{x ^{2}} + \frac{2 πn}{x ^{2}}

Combinar as frações usando o mínimo múltiplo comum:

\frac{π + arcsin ( - x ) + 2 πn}{x ^{2}}

Aplicar a regra

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

= \frac{π + arcsin ( - x ) + 2 πn}{x ^{2}}

= \frac{π + arcsin ( - x ) + 2 πn}{x ^{2}}

Aplicar a seguinte propriedade dos radicais:

n \frac{a}{b} = \frac{n a}{n b},

assumindo que

a \geq 0, b \geq 0

= \frac{π + arcsin ( - x ) + 2 πn}{x ^{2}}

Aplicar a seguinte propriedade dos radicais:

n a^{n} = a,

assumindo que

a \geq 0

x^{2} = x

= \frac{π + arcsin ( - x ) + 2 πn}{x}

Simplificar

- \frac{π}{x ^{2}} + \frac{arcsin ( - x )}{x ^{2}} + \frac{2 πn}{x ^{2}} : - \frac{π + arcsin ( - x ) + 2 πn}{x}

- \frac{π}{x ^{2}} + \frac{arcsin ( - x )}{x ^{2}} + \frac{2 πn}{x ^{2}}

Combinar as frações usando o mínimo múltiplo comum:

\frac{π + arcsin ( - x ) + 2 πn}{x ^{2}}

Aplicar a regra

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

= \frac{π + arcsin ( - x ) + 2 πn}{x ^{2}}

= - \frac{π + 2 πn + arcsin ( - x )}{x ^{2}}

Simplificar

\frac{π + arcsin ( - x ) + 2 πn}{x ^{2}} : \frac{π + arcsin ( - x ) + 2 πn}{x}

\frac{π + arcsin ( - x ) + 2 πn}{x ^{2}}

Aplicar a seguinte propriedade dos radicais:

n \frac{a}{b} = \frac{n a}{n b},

assumindo que

a \geq 0, b \geq 0

= \frac{π + arcsin ( - x ) + 2 πn}{x ^{2}}

Aplicar a seguinte propriedade dos radicais:

n a^{n} = a,

assumindo que

a \geq 0

x^{2} = x

= \frac{π + arcsin ( - x ) + 2 πn}{x}

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

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

y = \frac{π + arcsin ( - x ) + 2 πn}{x}, y = - \frac{π + arcsin ( - x ) + 2 πn}{x}; x \neq = 0

y = \frac{arcsin ( x ) + 2 πn}{x}, y = - \frac{arcsin ( x ) + 2 πn}{x}, y = \frac{π + arcsin ( - x ) + 2 πn}{x}, y = - \frac{π + arcsin ( - x ) + 2 πn}{x}

Gráfico

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