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solvefor x,ysin(xy)=y^2+2

Solução

resolver para

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

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

Passos da solução

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

Dividir ambos os lados por

y; y \neq = 0

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

Dividir ambos os lados por

y; y \neq = 0

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

Simplificar

\frac{y sin ( x y )}{y} = \frac{y ^{2}}{y} + \frac{2}{y}

Simplificar

\frac{y sin ( x y )}{y} : sin (x y)

\frac{y sin ( x y )}{y}

Eliminar o fator comum:

y

= sin (x y)

Simplificar

\frac{y ^{2}}{y} + \frac{2}{y} : \frac{y ^{2} + 2}{y}

\frac{y ^{2}}{y} + \frac{2}{y}

Aplicar a regra

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

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

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

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

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

Aplique as propriedades trigonométricas inversas

sin (x y) = \frac{y ^{2} + 2}{y}

Soluções gerais para

sin (x y) = \frac{y ^{2} + 2}{y}

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

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

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

Resolver

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

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

Dividir ambos os lados por

y; y \neq = 0

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

Dividir ambos os lados por

y; y \neq = 0

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

Simplificar

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

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

Resolver

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

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

Dividir ambos os lados por

y; y \neq = 0

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

Dividir ambos os lados por

y; y \neq = 0

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

Simplificar

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

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

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

3 sin (x) + 1 = 2 csc (x)

cos (x) = a

3 sin (x) + 3 cos (2 x) = 2

tan (3 x + 2 5^{\circ}) \cdot 16 0^{\circ} - 1 = 0

5 cos (x) = 1