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人気のある三角関数 >

cos^3(x)=-1

解

cos^{3} (x) = - 1

解

x = π + 2 πn

+1

度

x = 18 0^{\circ} + 36 0^{\circ} n

解答ステップ

cos^{3} (x) = - 1

置換で解く

cos^{3} (x) = - 1

仮定:

cos (x) = u

u^{3} = - 1

u^{3} = - 1 : u = - 1, u = \frac{1}{2} - i \frac{3}{2}, u = \frac{1}{2} + i \frac{3}{2}

u^{3} = - 1

x^{3} = f (a)

では, 解は

x = 3 f (a), 3 f (a) \frac{- 1 - 3 i}{2}, 3 f (a) \frac{- 1 + 3 i}{2}

u = 3 - 1, u = 3 - 1 \frac{- 1 + 3 i}{2}, u = 3 - 1 \frac{- 1 - 3 i}{2}

3 - 1 = - 1

3 - 1

が奇数であれば,

s q r t [n] - 1 = - 1

3 - 1 = - 1

= - 1

簡素化

3 - 1 \frac{- 1 + 3 i}{2} : \frac{1}{2} - i \frac{3}{2}

3 - 1 \frac{- 1 + 3 i}{2}

3 - 1 = - 1

3 - 1

が奇数であれば,

s q r t [n] - 1 = - 1

3 - 1 = - 1

= - 1

= - 1 \cdot \frac{- 1 + 3 i}{2}

乗算:

1 \cdot \frac{- 1 + 3 i}{2} = \frac{- 1 + 3 i}{2}

= - \frac{- 1 + 3 i}{2}

標準的な複素数形式で

- \frac{- 1 + 3 i}{2}

を書き換える:

\frac{1}{2} - \frac{3}{2} i

- \frac{- 1 + 3 i}{2}

分数の規則を適用する:

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

\frac{- 1 + 3 i}{2} = - (- \frac{1}{2}) - (\frac{3 i}{2})

= - (- \frac{1}{2}) - (\frac{3 i}{2})

括弧を削除する:

(a) = a, - (- a) = a

= \frac{1}{2} - \frac{3 i}{2}

= \frac{1}{2} - \frac{3}{2} i

簡素化

3 - 1 \frac{- 1 - 3 i}{2} : \frac{1}{2} + i \frac{3}{2}

3 - 1 \frac{- 1 - 3 i}{2}

3 - 1 = - 1

3 - 1

が奇数であれば,

s q r t [n] - 1 = - 1

3 - 1 = - 1

= - 1

= - 1 \cdot \frac{- 1 - 3 i}{2}

乗算:

1 \cdot \frac{- 1 - 3 i}{2} = \frac{- 1 - 3 i}{2}

= - \frac{- 1 - 3 i}{2}

標準的な複素数形式で

- \frac{- 1 - 3 i}{2}

を書き換える:

\frac{1}{2} + \frac{3}{2} i

- \frac{- 1 - 3 i}{2}

分数の規則を適用する:

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

\frac{- 1 - 3 i}{2} = - (- \frac{1}{2}) - (- \frac{3 i}{2})

= - (- \frac{1}{2}) - (- \frac{3 i}{2})

規則を適用

- (- a) = a

= \frac{1}{2} + \frac{3 i}{2}

= \frac{1}{2} + \frac{3}{2} i

u = - 1, u = \frac{1}{2} - i \frac{3}{2}, u = \frac{1}{2} + i \frac{3}{2}

代用を戻す

u = cos (x)

cos (x) = - 1, cos (x) = \frac{1}{2} - i \frac{3}{2}, cos (x) = \frac{1}{2} + i \frac{3}{2}

cos (x) = - 1, cos (x) = \frac{1}{2} - i \frac{3}{2}, cos (x) = \frac{1}{2} + i \frac{3}{2}

cos (x) = - 1 : x = π + 2 πn

cos (x) = - 1

以下の一般解

cos (x) = - 1

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}

x = π + 2 πn

x = π + 2 πn

cos (x) = \frac{1}{2} - i \frac{3}{2} :

解なし

cos (x) = \frac{1}{2} - i \frac{3}{2}

解なし

cos (x) = \frac{1}{2} + i \frac{3}{2} :

解なし

cos (x) = \frac{1}{2} + i \frac{3}{2}

解なし

すべての解を組み合わせる

x = π + 2 πn

グラフ

人気の例

sin (θ) = \frac{35}{37}

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2 cos^{2} (x) - 7 cos (x) = - 3, 0 \leq x \leq 2 π

sin(x)=sin(90-x)

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