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人気のある >

solvefor x,z=arcsin((xy)/(x^2+y^2))

解

解く

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

解

x = \frac{y + y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}, x = \frac{y - y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}

解答ステップ

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

辺を交換する

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

三角関数の逆数プロパティを適用する

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

arcsin (x) = a \Rightarrow x = sin (a)

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

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

解く

\frac{x y}{x ^{2} + y ^{2}} = sin (z) : x = \frac{y + y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}, x = \frac{y - y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}; sin (z) \neq = 0

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

以下で両辺を乗じる:

x^{2} + y^{2}

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

以下で両辺を乗じる:

x^{2} + y^{2}

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

簡素化

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

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

解く

x y = sin (z) (x^{2} + y^{2}) : x = \frac{y + y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}, x = \frac{y - y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}; sin (z) \neq = 0

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

拡張

sin (z) (x^{2} + y^{2}) : x^{2} sin (z) + y^{2} sin (z)

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

分配法則を適用する:

a (b + c) = ab + a c

a = sin (z), b = x^{2}, c = y^{2}

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

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

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

辺を交換する

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

x y

を左側に移動します

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

両辺から

x y

を引く

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

簡素化

x^{2} sin (z) + y^{2} sin (z) - x y = 0

x^{2} sin (z) + y^{2} sin (z) - x y = 0

標準的な形式で書く

a x^{2} + b x + c = 0

sin (z) x^{2} - y x + y^{2} sin (z) = 0

解くとthe二次式

sin (z) x^{2} - y x + y^{2} sin (z) = 0

二次Equationの公式:

次の場合:

a = sin (z), b = - y, c = y^{2} sin (z)

x_{1, 2} = \frac{- ( - y ) \pm ( - y ) ^{2} - 4 sin ( z ) y ^{2} sin ( z )}{2 sin ( z )}

x_{1, 2} = \frac{- ( - y ) \pm ( - y ) ^{2} - 4 sin ( z ) y ^{2} sin ( z )}{2 sin ( z )}

簡素化

(- y)^{2} - 4 sin (z) y^{2} sin (z) : y 1 - 4 sin^{2} (z)

(- y)^{2} - 4 sin (z) y^{2} sin (z)

(- y)^{2} = y^{2}

(- y)^{2}

指数の規則を適用する:

n

が偶数であれば

(- a)^{n} = a^{n}

(- y)^{2} = y^{2}

= y^{2}

4 sin (z) y^{2} sin (z) = 4 y^{2} sin^{2} (z)

4 sin (z) y^{2} sin (z)

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

sin (z) sin (z) = sin^{1 + 1} (z)

= 4 y^{2} sin^{1 + 1} (z)

数を足す:

1 + 1 = 2

= 4 y^{2} sin^{2} (z)

= y^{2} - 4 y^{2} sin^{2} (z)

共通項をくくり出す

y^{2}

= y^{2} (1 - 4 sin^{2} (z))

累乗根の規則を適用する:

n ab = n a n b,

, 以下を想定

a \geq 0, b \geq 0

= y^{2} - 4 sin^{2} (z) + 1

累乗根の規則を適用する:

n a^{n} = a,

, 以下を想定

a \geq 0

y^{2} = y

= y - 4 sin^{2} (z) + 1

x_{1, 2} = \frac{- ( - y ) \pm y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}; sin (z) \neq = 0

解を分離する

x_{1} = \frac{- ( - y ) + y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}, x_{2} = \frac{- ( - y ) - y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}

x = \frac{- ( - y ) + y 1 - 4 sin ^{2} ( z )}{2 sin ( z )} : \frac{y + y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}

\frac{- ( - y ) + y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}

規則を適用

- (- a) = a

= \frac{y + y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}

x = \frac{- ( - y ) - y 1 - 4 sin ^{2} ( z )}{2 sin ( z )} : \frac{y - y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}

\frac{- ( - y ) - y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}

規則を適用

- (- a) = a

= \frac{y - y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}

二次equationの解:

x = \frac{y + y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}, x = \frac{y - y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}; sin (z) \neq = 0

x = \frac{y + y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}, x = \frac{y - y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}; sin (z) \neq = 0

x = \frac{y + y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}, x = \frac{y - y 1 - 4 sin ^{2} ( z )}{2 sin ( z )}

グラフ

人気の例

(tan(x)+cos(x))/((1+sin(x)))= 1/(cos(x))

\frac{tan ( x ) + cos ( x )}{( 1 + sin ( x ) )} = \frac{1}{cos ( x )}

sin(θ)= 4/5 ,0<= θ<= pi/2

sin (θ) = \frac{4}{5}, 0 \leq θ \leq \frac{π}{2}

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- cos^{2} (x) + cos (x) + 2 = 0

2-cos^2(x)=4sin^2(1/2 x)

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\frac{( tan ( x ) + 2 sin ( x ) )}{( tan ( x ) - 2 sin ( x ) )} = 3