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人気のある三角関数 >

sin(x)=sin(x^2)

解

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

解

x = \frac{- 1 + 1 - 4 ( - 4 πn - π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - π )}{2}, x = \frac{- 1 + 1 - 4 ( - 4 πn - 3 π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - 3 π )}{2}

+1

度

x = - 28.64788 \dots^{\circ} + 228.88185 \dots^{\circ} n, x = - 28.64788 \dots^{\circ} - 228.88185 \dots^{\circ} n, x = - 28.64788 \dots^{\circ} + 270.20988 \dots^{\circ} n, x = - 28.64788 \dots^{\circ} - 270.20988 \dots^{\circ} n

解答ステップ

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

両辺から

sin (x^{2})

を引く

sin (x) - sin (x^{2}) = 0

三角関数の公式を使用して書き換える

sin (x) - sin (x^{2})

和・積の公式を使用する:

sin (s) - sin (t) = 2 sin (\frac{s - t}{2}) cos (\frac{s + t}{2})

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

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

各部分を別個に解く

cos (\frac{x + x ^{2}}{2}) = 0 or sin (\frac{x - x ^{2}}{2}) = 0

cos (\frac{x + x ^{2}}{2}) = 0 : x = \frac{- 1 + 1 - 4 ( - 4 πn - π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - π )}{2}, x = \frac{- 1 + 1 - 4 ( - 4 πn - 3 π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - 3 π )}{2}

cos (\frac{x + x ^{2}}{2}) = 0

以下の一般解

cos (\frac{x + x ^{2}}{2}) = 0

cos (x)

2 πn

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

\frac{x + x ^{2}}{2} = \frac{π}{2} + 2 πn, \frac{x + x ^{2}}{2} = \frac{3 π}{2} + 2 πn

\frac{x + x ^{2}}{2} = \frac{π}{2} + 2 πn, \frac{x + x ^{2}}{2} = \frac{3 π}{2} + 2 πn

解く

\frac{x + x ^{2}}{2} = \frac{π}{2} + 2 πn : x = \frac{- 1 + 1 - 4 ( - 4 πn - π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - π )}{2}

\frac{x + x ^{2}}{2} = \frac{π}{2} + 2 πn

以下で両辺を乗じる:

2

\frac{x + x ^{2}}{2} = \frac{π}{2} + 2 πn

以下で両辺を乗じる:

2

\frac{x + x ^{2}}{2} \cdot 2 = \frac{π}{2} \cdot 2 + 2 πn \cdot 2

簡素化

x + x^{2} = π + 4 πn

x + x^{2} = π + 4 πn

4 πn

を左側に移動します

x + x^{2} = π + 4 πn

両辺から

4 πn

を引く

x + x^{2} - 4 πn = π + 4 πn - 4 πn

簡素化

x + x^{2} - 4 πn = π

x + x^{2} - 4 πn = π

π

を左側に移動します

x + x^{2} - 4 πn = π

両辺から

π

を引く

x + x^{2} - 4 πn - π = π - π

簡素化

x + x^{2} - 4 πn - π = 0

x + x^{2} - 4 πn - π = 0

標準的な形式で書く

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

x^{2} + x - 4 πn - π = 0

解くとthe二次式

x^{2} + x - 4 πn - π = 0

二次Equationの公式:

次の場合:

a = 1, b = 1, c = - 4 πn - π

x_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot ( - 4 πn - π )}{2 \cdot 1}

x_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot ( - 4 πn - π )}{2 \cdot 1}

簡素化

1^{2} - 4 \cdot 1 \cdot (- 4 πn - π) : 1 - 4 (- 4 πn - π)

1^{2} - 4 \cdot 1 \cdot (- 4 πn - π)

規則を適用

1^{a} = 1

1^{2} = 1

= 1 - 4 \cdot 1 \cdot (- 4 πn - π)

数を乗じる:

4 \cdot 1 = 4

= 1 - 4 (- 4 πn - π)

x_{1, 2} = \frac{- 1 \pm 1 - 4 ( - 4 πn - π )}{2 \cdot 1}

解を分離する

x_{1} = \frac{- 1 + 1 - 4 ( - 4 πn - π )}{2 \cdot 1}, x_{2} = \frac{- 1 - 1 - 4 ( - 4 πn - π )}{2 \cdot 1}

x = \frac{- 1 + 1 - 4 ( - 4 πn - π )}{2 \cdot 1} : \frac{- 1 + 1 - 4 ( - 4 πn - π )}{2}

\frac{- 1 + 1 - 4 ( - 4 πn - π )}{2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{- 1 + - 4 ( - 4 πn - π ) + 1}{2}

x = \frac{- 1 - 1 - 4 ( - 4 πn - π )}{2 \cdot 1} : \frac{- 1 - 1 - 4 ( - 4 πn - π )}{2}

\frac{- 1 - 1 - 4 ( - 4 πn - π )}{2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{- 1 - - 4 ( - 4 πn - π ) + 1}{2}

二次equationの解:

x = \frac{- 1 + 1 - 4 ( - 4 πn - π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - π )}{2}

解く

\frac{x + x ^{2}}{2} = \frac{3 π}{2} + 2 πn : x = \frac{- 1 + 1 - 4 ( - 4 πn - 3 π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - 3 π )}{2}

\frac{x + x ^{2}}{2} = \frac{3 π}{2} + 2 πn

以下で両辺を乗じる:

2

\frac{x + x ^{2}}{2} = \frac{3 π}{2} + 2 πn

以下で両辺を乗じる:

2

\frac{x + x ^{2}}{2} \cdot 2 = \frac{3 π}{2} \cdot 2 + 2 πn \cdot 2

簡素化

x + x^{2} = 3 π + 4 πn

x + x^{2} = 3 π + 4 πn

4 πn

を左側に移動します

x + x^{2} = 3 π + 4 πn

両辺から

4 πn

を引く

x + x^{2} - 4 πn = 3 π + 4 πn - 4 πn

簡素化

x + x^{2} - 4 πn = 3 π

x + x^{2} - 4 πn = 3 π

3 π

を左側に移動します

x + x^{2} - 4 πn = 3 π

両辺から

3 π

を引く

x + x^{2} - 4 πn - 3 π = 3 π - 3 π

簡素化

x + x^{2} - 4 πn - 3 π = 0

x + x^{2} - 4 πn - 3 π = 0

標準的な形式で書く

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

x^{2} + x - 4 πn - 3 π = 0

解くとthe二次式

x^{2} + x - 4 πn - 3 π = 0

二次Equationの公式:

次の場合:

a = 1, b = 1, c = - 4 πn - 3 π

x_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot ( - 4 πn - 3 π )}{2 \cdot 1}

x_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot ( - 4 πn - 3 π )}{2 \cdot 1}

簡素化

1^{2} - 4 \cdot 1 \cdot (- 4 πn - 3 π) : 1 - 4 (- 4 πn - 3 π)

1^{2} - 4 \cdot 1 \cdot (- 4 πn - 3 π)

規則を適用

1^{a} = 1

1^{2} = 1

= 1 - 4 \cdot 1 \cdot (- 4 πn - 3 π)

数を乗じる:

4 \cdot 1 = 4

= 1 - 4 (- 4 πn - 3 π)

x_{1, 2} = \frac{- 1 \pm 1 - 4 ( - 4 πn - 3 π )}{2 \cdot 1}

解を分離する

x_{1} = \frac{- 1 + 1 - 4 ( - 4 πn - 3 π )}{2 \cdot 1}, x_{2} = \frac{- 1 - 1 - 4 ( - 4 πn - 3 π )}{2 \cdot 1}

x = \frac{- 1 + 1 - 4 ( - 4 πn - 3 π )}{2 \cdot 1} : \frac{- 1 + 1 - 4 ( - 4 πn - 3 π )}{2}

\frac{- 1 + 1 - 4 ( - 4 πn - 3 π )}{2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{- 1 + - 4 ( - 4 πn - 3 π ) + 1}{2}

x = \frac{- 1 - 1 - 4 ( - 4 πn - 3 π )}{2 \cdot 1} : \frac{- 1 - 1 - 4 ( - 4 πn - 3 π )}{2}

\frac{- 1 - 1 - 4 ( - 4 πn - 3 π )}{2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{- 1 - - 4 ( - 4 πn - 3 π ) + 1}{2}

二次equationの解:

x = \frac{- 1 + 1 - 4 ( - 4 πn - 3 π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - 3 π )}{2}

x = \frac{- 1 + 1 - 4 ( - 4 πn - π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - π )}{2}, x = \frac{- 1 + 1 - 4 ( - 4 πn - 3 π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - 3 π )}{2}

sin (\frac{x - x ^{2}}{2}) = 0 :

解なし

sin (\frac{x - x ^{2}}{2}) = 0

以下の一般解

sin (\frac{x - x ^{2}}{2}) = 0

sin (x)

2 πn

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{x - x ^{2}}{2} = 0 + 2 πn, \frac{x - x ^{2}}{2} = π + 2 πn

\frac{x - x ^{2}}{2} = 0 + 2 πn, \frac{x - x ^{2}}{2} = π + 2 πn

解く

\frac{x - x ^{2}}{2} = 0 + 2 πn : x = - \frac{- 1 + 1 - 16 πn}{2}, x = - \frac{- 1 - 1 - 16 πn}{2}

\frac{x - x ^{2}}{2} = 0 + 2 πn

以下で両辺を乗じる:

2

\frac{x - x ^{2}}{2} = 0 + 2 πn

以下で両辺を乗じる:

2

\frac{x - x ^{2}}{2} \cdot 2 = 0 \cdot 2 + 2 πn \cdot 2

簡素化

x - x^{2} = 0 + 4 πn

x - x^{2} = 0 + 4 πn

x - x^{2} = 4 πn

4 πn

を左側に移動します

x - x^{2} = 4 πn

両辺から

4 πn

を引く

x - x^{2} - 4 πn = 4 πn - 4 πn

簡素化

x - x^{2} - 4 πn = 0

x - x^{2} - 4 πn = 0

標準的な形式で書く

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

- x^{2} + x - 4 πn = 0

解くとthe二次式

- x^{2} + x - 4 πn = 0

二次Equationの公式:

次の場合:

a = - 1, b = 1, c = - 4 πn

x_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 ( - 1 ) ( - 4 πn )}{2 ( - 1 )}

x_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 ( - 1 ) ( - 4 πn )}{2 ( - 1 )}

簡素化

1^{2} - 4 (- 1) (- 4 πn) : 1 - 16 πn

1^{2} - 4 (- 1) (- 4 πn)

規則を適用

1^{a} = 1

1^{2} = 1

= 1 - 4 (- 1) (- 4 πn)

規則を適用

- (- a) = a

= 1 - 4 \cdot 1 \cdot 4 πn

数を乗じる:

4 \cdot 1 \cdot 4 = 16

= 1 - 16 πn

x_{1, 2} = \frac{- 1 \pm 1 - 16 πn}{2 ( - 1 )}

解を分離する

x_{1} = \frac{- 1 + 1 - 16 πn}{2 ( - 1 )}, x_{2} = \frac{- 1 - 1 - 16 πn}{2 ( - 1 )}

x = \frac{- 1 + 1 - 16 πn}{2 ( - 1 )} : - \frac{- 1 + 1 - 16 πn}{2}

\frac{- 1 + 1 - 16 πn}{2 ( - 1 )}

括弧を削除する:

(- a) = - a

= \frac{- 1 + 1 - 16 πn}{- 2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{- 1 + - 16 πn + 1}{- 2}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{- 1 + 1 - 16 πn}{2}

x = \frac{- 1 - 1 - 16 πn}{2 ( - 1 )} : - \frac{- 1 - 1 - 16 πn}{2}

\frac{- 1 - 1 - 16 πn}{2 ( - 1 )}

括弧を削除する:

(- a) = - a

= \frac{- 1 - 1 - 16 πn}{- 2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{- 1 - - 16 πn + 1}{- 2}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{- 1 - 1 - 16 πn}{2}

二次equationの解:

x = - \frac{- 1 + 1 - 16 πn}{2}, x = - \frac{- 1 - 1 - 16 πn}{2}

解く

\frac{x - x ^{2}}{2} = π + 2 πn : x = - \frac{- 1 + 1 + 4 ( - 4 πn - 2 π )}{2}, x = - \frac{- 1 - 1 + 4 ( - 4 πn - 2 π )}{2}

\frac{x - x ^{2}}{2} = π + 2 πn

以下で両辺を乗じる:

2

\frac{x - x ^{2}}{2} = π + 2 πn

以下で両辺を乗じる:

2

\frac{x - x ^{2}}{2} \cdot 2 = π 2 + 2 πn \cdot 2

簡素化

x - x^{2} = 2 π + 4 πn

x - x^{2} = 2 π + 4 πn

4 πn

を左側に移動します

x - x^{2} = 2 π + 4 πn

両辺から

4 πn

を引く

x - x^{2} - 4 πn = 2 π + 4 πn - 4 πn

簡素化

x - x^{2} - 4 πn = 2 π

x - x^{2} - 4 πn = 2 π

2 π

を左側に移動します

x - x^{2} - 4 πn = 2 π

両辺から

2 π

を引く

x - x^{2} - 4 πn - 2 π = 2 π - 2 π

簡素化

x - x^{2} - 4 πn - 2 π = 0

x - x^{2} - 4 πn - 2 π = 0

標準的な形式で書く

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

- x^{2} + x - 4 πn - 2 π = 0

解くとthe二次式

- x^{2} + x - 4 πn - 2 π = 0

二次Equationの公式:

次の場合:

a = - 1, b = 1, c = - 4 πn - 2 π

x_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 ( - 1 ) ( - 4 πn - 2 π )}{2 ( - 1 )}

x_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 ( - 1 ) ( - 4 πn - 2 π )}{2 ( - 1 )}

簡素化

1^{2} - 4 (- 1) (- 4 πn - 2 π) : 1 + 4 (- 4 πn - 2 π)

1^{2} - 4 (- 1) (- 4 πn - 2 π)

規則を適用

1^{a} = 1

1^{2} = 1

= 1 - 4 (- 1) (- 4 πn - 2 π)

規則を適用

- (- a) = a

= 1 + 4 \cdot 1 \cdot (- 4 πn - 2 π)

数を乗じる:

4 \cdot 1 = 4

= 1 + 4 (- 4 πn - 2 π)

x_{1, 2} = \frac{- 1 \pm 1 + 4 ( - 4 πn - 2 π )}{2 ( - 1 )}

解を分離する

x_{1} = \frac{- 1 + 1 + 4 ( - 4 πn - 2 π )}{2 ( - 1 )}, x_{2} = \frac{- 1 - 1 + 4 ( - 4 πn - 2 π )}{2 ( - 1 )}

x = \frac{- 1 + 1 + 4 ( - 4 πn - 2 π )}{2 ( - 1 )} : - \frac{- 1 + 1 + 4 ( - 4 πn - 2 π )}{2}

\frac{- 1 + 1 + 4 ( - 4 πn - 2 π )}{2 ( - 1 )}

括弧を削除する:

(- a) = - a

= \frac{- 1 + 1 + 4 ( - 4 πn - 2 π )}{- 2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{- 1 + 4 ( - 4 πn - 2 π ) + 1}{- 2}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{- 1 + 1 + 4 ( - 4 πn - 2 π )}{2}

x = \frac{- 1 - 1 + 4 ( - 4 πn - 2 π )}{2 ( - 1 )} : - \frac{- 1 - 1 + 4 ( - 4 πn - 2 π )}{2}

\frac{- 1 - 1 + 4 ( - 4 πn - 2 π )}{2 ( - 1 )}

括弧を削除する:

(- a) = - a

= \frac{- 1 - 1 + 4 ( - 4 πn - 2 π )}{- 2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{- 1 - 4 ( - 4 πn - 2 π ) + 1}{- 2}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{- 1 - 1 + 4 ( - 4 πn - 2 π )}{2}

二次equationの解:

x = - \frac{- 1 + 1 + 4 ( - 4 πn - 2 π )}{2}, x = - \frac{- 1 - 1 + 4 ( - 4 πn - 2 π )}{2}

x = - \frac{- 1 + 1 - 16 πn}{2}, x = - \frac{- 1 - 1 - 16 πn}{2}, x = - \frac{- 1 + 1 + 4 ( - 4 πn - 2 π )}{2}, x = - \frac{- 1 - 1 + 4 ( - 4 πn - 2 π )}{2}

equationは以下で未定義のため:

- \frac{- 1 + 1 - 16 πn}{2}, - \frac{- 1 - 1 - 16 πn}{2}, - \frac{- 1 + 1 + 4 ( - 4 πn - 2 π )}{2}, - \frac{- 1 - 1 + 4 ( - 4 πn - 2 π )}{2}

解なし

すべての解を組み合わせる

x = \frac{- 1 + 1 - 4 ( - 4 πn - π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - π )}{2}, x = \frac{- 1 + 1 - 4 ( - 4 πn - 3 π )}{2}, x = \frac{- 1 - 1 - 4 ( - 4 πn - 3 π )}{2}

グラフ

人気の例

sin (x) = - 0.23

2sin^2(x)+3sin(x)+1=0,0<= x<= 2pi

2 sin^{2} (x) + 3 sin (x) + 1 = 0, 0 \leq x \leq 2 π

cos(3x)-1=sin(3x)

cos (3 x) - 1 = sin (3 x)

sin(x/3)=(sqrt(2))/2

sin (\frac{x}{3}) = \frac{2}{2}

2cos(3x)=-sqrt(3)

2 cos (3 x) = - 3