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شائع علم المثلثات >

solvefor x,u=cos(x^2y)

الحلّ

solve for

x, u = cos (x^{2} y)

الحلّ

x = \frac{arccos ( u ) + 2 πn}{y}, x = - \frac{arccos ( u ) + 2 πn}{y}, x = \frac{- arccos ( u ) + 2 πn}{y}, x = - \frac{- arccos ( u ) + 2 πn}{y}

خطوات الحلّ

u = cos (x^{2} y)

بدّل الأطراف

cos (x^{2} y) = u

Apply trig inverse properties

cos (x^{2} y) = u

cos (x^{2} y) = u :

حلول عامّة لـ

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

x^{2} y = arccos (u) + 2 πn, x^{2} y = - arccos (u) + 2 πn

x^{2} y = arccos (u) + 2 πn, x^{2} y = - arccos (u) + 2 πn

x^{2} y = arccos (u) + 2 πn

حلّ:

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

x^{2} y = arccos (u) + 2 πn

y; y \neq = 0

اقسم الطرفين على

x^{2} y = arccos (u) + 2 πn

y; y \neq = 0

اقسم الطرفين على

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

بسّط

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

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

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

الحلول هي

x^{2} = f (a)

لـ

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

\frac{arccos ( u )}{y} + \frac{2 πn}{y}

بسّط:

\frac{arccos ( u ) + 2 πn}{y}

\frac{arccos ( u )}{y} + \frac{2 πn}{y}

\frac{arccos ( u )}{y} + \frac{2 πn}{y}

وحّد الكسور:

\frac{arccos ( u ) + 2 πn}{y}

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

فعّل القانون

= \frac{arccos ( u ) + 2 πn}{y}

= \frac{arccos ( u ) + 2 πn}{y}

- \frac{arccos ( u )}{y} + \frac{2 πn}{y}

بسّط:

- \frac{arccos ( u ) + 2 πn}{y}

- \frac{arccos ( u )}{y} + \frac{2 πn}{y}

\frac{arccos ( u )}{y} + \frac{2 πn}{y}

وحّد الكسور:

\frac{arccos ( u ) + 2 πn}{y}

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

فعّل القانون

= \frac{arccos ( u ) + 2 πn}{y}

= - \frac{2 πn + arccos ( u )}{y}

= - \frac{arccos ( u ) + 2 πn}{y}

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

x^{2} y = - arccos (u) + 2 πn

حلّ:

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

x^{2} y = - arccos (u) + 2 πn

y; y \neq = 0

اقسم الطرفين على

x^{2} y = - arccos (u) + 2 πn

y; y \neq = 0

اقسم الطرفين على

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

بسّط

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

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

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

الحلول هي

x^{2} = f (a)

لـ

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

- \frac{arccos ( u )}{y} + \frac{2 πn}{y}

بسّط:

\frac{- arccos ( u ) + 2 πn}{y}

- \frac{arccos ( u )}{y} + \frac{2 πn}{y}

- \frac{arccos ( u )}{y} + \frac{2 πn}{y}

وحّد الكسور:

\frac{- arccos ( u ) + 2 πn}{y}

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

فعّل القانون

= \frac{- arccos ( u ) + 2 πn}{y}

= \frac{- arccos ( u ) + 2 πn}{y}

- - \frac{arccos ( u )}{y} + \frac{2 πn}{y}

بسّط:

- \frac{- arccos ( u ) + 2 πn}{y}

- - \frac{arccos ( u )}{y} + \frac{2 πn}{y}

- \frac{arccos ( u )}{y} + \frac{2 πn}{y}

وحّد الكسور:

\frac{- arccos ( u ) + 2 πn}{y}

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

فعّل القانون

= \frac{- arccos ( u ) + 2 πn}{y}

= - \frac{2 πn - arccos ( u )}{y}

= - \frac{- arccos ( u ) + 2 πn}{y}

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

x = \frac{arccos ( u ) + 2 πn}{y}, x = - \frac{arccos ( u ) + 2 πn}{y}, x = \frac{- arccos ( u ) + 2 πn}{y}, x = - \frac{- arccos ( u ) + 2 πn}{y}

رسم

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