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人気のある三角関数 >

cos^3(x)+sin^2(x)*cos(x)=-1/2

解

cos^{3} (x) + sin^{2} (x) \cdot cos (x) = - \frac{1}{2}

解

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

+1

度

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

解答ステップ

cos^{3} (x) + sin^{2} (x) cos (x) = - \frac{1}{2}

両辺から

- \frac{1}{2}

を引く

cos^{3} (x) + sin^{2} (x) cos (x) + \frac{1}{2} = 0

簡素化

cos^{3} (x) + sin^{2} (x) cos (x) + \frac{1}{2} : \frac{2 cos ^{3} ( x ) + 2 sin ^{2} ( x ) cos ( x ) + 1}{2}

cos^{3} (x) + sin^{2} (x) cos (x) + \frac{1}{2}

元を分数に変換する:

cos^{3} (x) = \frac{cos ^{3} ( x ) 2}{2}, sin^{2} (x) cos (x) = \frac{sin ^{2} ( x ) cos ( x ) 2}{2}

= \frac{cos ^{3} ( x ) \cdot 2}{2} + \frac{sin ^{2} ( x ) cos ( x ) \cdot 2}{2} + \frac{1}{2}

分母が等しいので, 分数を組み合わせる:

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

= \frac{cos ^{3} ( x ) \cdot 2 + sin ^{2} ( x ) cos ( x ) \cdot 2 + 1}{2}

\frac{2 cos ^{3} ( x ) + 2 sin ^{2} ( x ) cos ( x ) + 1}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

2 cos^{3} (x) + 2 sin^{2} (x) cos (x) + 1 = 0

三角関数の公式を使用して書き換える

1 + 2 cos^{3} (x) + 2 cos (x) sin^{2} (x)

ピタゴラスの公式を使用する:

cos^{2} (x) + sin^{2} (x) = 1

sin^{2} (x) = 1 - cos^{2} (x)

= 1 + 2 cos^{3} (x) + 2 cos (x) (1 - cos^{2} (x))

簡素化

1 + 2 cos^{3} (x) + 2 cos (x) (1 - cos^{2} (x)) : 2 cos (x) + 1

1 + 2 cos^{3} (x) + 2 cos (x) (1 - cos^{2} (x))

拡張

2 cos (x) (1 - cos^{2} (x)) : 2 cos (x) - 2 cos^{3} (x)

2 cos (x) (1 - cos^{2} (x))

分配法則を適用する:

a (b - c) = ab - a c

a = 2 cos (x), b = 1, c = cos^{2} (x)

= 2 cos (x) \cdot 1 - 2 cos (x) cos^{2} (x)

= 2 \cdot 1 \cdot cos (x) - 2 cos^{2} (x) cos (x)

簡素化

2 \cdot 1 \cdot cos (x) - 2 cos^{2} (x) cos (x) : 2 cos (x) - 2 cos^{3} (x)

2 \cdot 1 \cdot cos (x) - 2 cos^{2} (x) cos (x)

2 \cdot 1 \cdot cos (x) = 2 cos (x)

2 \cdot 1 \cdot cos (x)

数を乗じる:

2 \cdot 1 = 2

= 2 cos (x)

2 cos^{2} (x) cos (x) = 2 cos^{3} (x)

2 cos^{2} (x) cos (x)

指数の規則を適用する:

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

cos^{2} (x) cos (x) = cos^{2 + 1} (x)

= 2 cos^{2 + 1} (x)

数を足す:

2 + 1 = 3

= 2 cos^{3} (x)

= 2 cos (x) - 2 cos^{3} (x)

= 2 cos (x) - 2 cos^{3} (x)

= 1 + 2 cos^{3} (x) + 2 cos (x) - 2 cos^{3} (x)

簡素化

1 + 2 cos^{3} (x) + 2 cos (x) - 2 cos^{3} (x) : 2 cos (x) + 1

1 + 2 cos^{3} (x) + 2 cos (x) - 2 cos^{3} (x)

条件のようなグループ

= 2 cos^{3} (x) + 2 cos (x) - 2 cos^{3} (x) + 1

類似した元を足す:

2 cos^{3} (x) - 2 cos^{3} (x) = 0

= 2 cos (x) + 1

= 2 cos (x) + 1

= 2 cos (x) + 1

1 + 2 cos (x) = 0

1

を右側に移動します

1 + 2 cos (x) = 0

両辺から

1

を引く

1 + 2 cos (x) - 1 = 0 - 1

簡素化

2 cos (x) = - 1

2 cos (x) = - 1

以下で両辺を割る

2

2 cos (x) = - 1

以下で両辺を割る

2

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

簡素化

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

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

以下の一般解

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

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 = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

グラフ

人気の例

cos(3A)+sin(A)=0

cos (3 A) + sin (A) = 0

0 = 1 - sec^{2} (x)

sin (θ) = 0.1

2/(sin(x))+10=6

\frac{2}{sin ( x )} + 10 = 6

sin(θ)-0.2cos(θ)=0.6377

sin (θ) - 0.2 cos (θ) = 0.6377