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شائع علم المثلثات >

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

الحلّ

solve for

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

الحلّ

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}

خطوات الحلّ

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

Apply trig inverse properties

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

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

حلول عامّة لـ

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

x^{2} y^{2} = arcsin (x) + 2 πn

حلّ:

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

x^{2}; x \neq = 0

اقسم الطرفين على

x^{2} y^{2} = arcsin (x) + 2 πn

x^{2}; x \neq = 0

اقسم الطرفين على

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

بسّط

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

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

الحلول هي

x^{2} = f (a)

لـ

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

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

بسّط:

\frac{arcsin ( x ) + 2 πn}{x}

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

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

وحّد الكسور:

\frac{arcsin ( x ) + 2 πn}{x ^{2}}

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

فعّل القانون

= \frac{arcsin ( x ) + 2 πn}{x ^{2}}

= \frac{arcsin ( x ) + 2 πn}{x ^{2}}

a \geq 0, b \geq 0

بافتراض أنّ

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

:فعّل قانون الجذور

= \frac{arcsin ( x ) + 2 πn}{x ^{2}}

a \geq 0

بافتراض أنّ

n a^{n} = a

:فعّل قانون الجذور

x^{2} = x

= \frac{arcsin ( x ) + 2 πn}{x}

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

بسّط:

- \frac{arcsin ( x ) + 2 πn}{x}

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

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

وحّد الكسور:

\frac{arcsin ( x ) + 2 πn}{x ^{2}}

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

فعّل القانون

= \frac{arcsin ( x ) + 2 πn}{x ^{2}}

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

\frac{arcsin ( x ) + 2 πn}{x ^{2}}

بسّط:

\frac{arcsin ( x ) + 2 πn}{x}

\frac{arcsin ( x ) + 2 πn}{x ^{2}}

a \geq 0, b \geq 0

بافتراض أنّ

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

:فعّل قانون الجذور

= \frac{arcsin ( x ) + 2 πn}{x ^{2}}

a \geq 0

بافتراض أنّ

n a^{n} = a

:فعّل قانون الجذور

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

x^{2} y^{2} = π + arcsin (- x) + 2 πn

حلّ:

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

x^{2}; x \neq = 0

اقسم الطرفين على

x^{2} y^{2} = π + arcsin (- x) + 2 πn

x^{2}; x \neq = 0

اقسم الطرفين على

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

بسّط

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

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

الحلول هي

x^{2} = f (a)

لـ

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

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

بسّط:

\frac{π + arcsin ( - x ) + 2 πn}{x}

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

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

وحّد الكسور:

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

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

فعّل القانون

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

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

a \geq 0, b \geq 0

بافتراض أنّ

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

:فعّل قانون الجذور

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

a \geq 0

بافتراض أنّ

n a^{n} = a

:فعّل قانون الجذور

x^{2} = x

= \frac{π + arcsin ( - x ) + 2 πn}{x}

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

بسّط:

- \frac{π + arcsin ( - x ) + 2 πn}{x}

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

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

وحّد الكسور:

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

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

فعّل القانون

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

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

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

بسّط:

\frac{π + arcsin ( - x ) + 2 πn}{x}

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

a \geq 0, b \geq 0

بافتراض أنّ

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

:فعّل قانون الجذور

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

a \geq 0

بافتراض أنّ

n a^{n} = a

:فعّل قانون الجذور

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}

رسم

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