ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある三角関数 >

3sin^2(X)-cos(X)=0

解

3 sin^{2} (X) - cos (X) = 0

解

X = 0.56024 \dots + 2 πn, X = 2 π - 0.56024 \dots + 2 πn

+1

度

X = 32.09944 \dots^{\circ} + 36 0^{\circ} n, X = 327.90055 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

3 sin^{2} (X) - cos (X) = 0

三角関数の公式を使用して書き換える

- cos (X) + 3 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)

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

- cos (X) + (1 - cos^{2} (X)) \cdot 3 = 0

置換で解く

- cos (X) + (1 - cos^{2} (X)) \cdot 3 = 0

仮定:

cos (X) = u

- u + (1 - u^{2}) \cdot 3 = 0

- u + (1 - u^{2}) \cdot 3 = 0 : u = - \frac{1 + 37}{6}, u = \frac{37 - 1}{6}

- u + (1 - u^{2}) \cdot 3 = 0

拡張

- u + (1 - u^{2}) \cdot 3 : - u + 3 - 3 u^{2}

- u + (1 - u^{2}) \cdot 3

= - u + 3 (1 - u^{2})

拡張

3 (1 - u^{2}) : 3 - 3 u^{2}

3 (1 - u^{2})

分配法則を適用する:

a (b - c) = ab - a c

a = 3, b = 1, c = u^{2}

= 3 \cdot 1 - 3 u^{2}

数を乗じる:

3 \cdot 1 = 3

= 3 - 3 u^{2}

= - u + 3 - 3 u^{2}

- u + 3 - 3 u^{2} = 0

標準的な形式で書く

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

- 3 u^{2} - u + 3 = 0

解くとthe二次式

- 3 u^{2} - u + 3 = 0

二次Equationの公式:

次の場合:

a = - 3, b = - 1, c = 3

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

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

(- 1)^{2} - 4 (- 3) \cdot 3 = 37

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

規則を適用

- (- a) = a

= (- 1)^{2} + 4 \cdot 3 \cdot 3

(- 1)^{2} = 1

(- 1)^{2}

指数の規則を適用する:

n

が偶数であれば

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

(- 1)^{2} = 1^{2}

= 1^{2}

規則を適用

1^{a} = 1

= 1

4 \cdot 3 \cdot 3 = 36

4 \cdot 3 \cdot 3

数を乗じる:

4 \cdot 3 \cdot 3 = 36

= 36

= 1 + 36

数を足す:

1 + 36 = 37

= 37

u_{1, 2} = \frac{- ( - 1 ) \pm 37}{2 ( - 3 )}

解を分離する

u_{1} = \frac{- ( - 1 ) + 37}{2 ( - 3 )}, u_{2} = \frac{- ( - 1 ) - 37}{2 ( - 3 )}

u = \frac{- ( - 1 ) + 37}{2 ( - 3 )} : - \frac{1 + 37}{6}

\frac{- ( - 1 ) + 37}{2 ( - 3 )}

括弧を削除する:

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

= \frac{1 + 37}{- 2 \cdot 3}

数を乗じる:

2 \cdot 3 = 6

= \frac{1 + 37}{- 6}

分数の規則を適用する:

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

= - \frac{1 + 37}{6}

u = \frac{- ( - 1 ) - 37}{2 ( - 3 )} : \frac{37 - 1}{6}

\frac{- ( - 1 ) - 37}{2 ( - 3 )}

括弧を削除する:

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

= \frac{1 - 37}{- 2 \cdot 3}

数を乗じる:

2 \cdot 3 = 6

= \frac{1 - 37}{- 6}

分数の規則を適用する:

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

1 - 37 = - (37 - 1)

= \frac{37 - 1}{6}

二次equationの解:

u = - \frac{1 + 37}{6}, u = \frac{37 - 1}{6}

代用を戻す

u = cos (X)

cos (X) = - \frac{1 + 37}{6}, cos (X) = \frac{37 - 1}{6}

cos (X) = - \frac{1 + 37}{6}, cos (X) = \frac{37 - 1}{6}

cos (X) = - \frac{1 + 37}{6} :

解なし

cos (X) = - \frac{1 + 37}{6}

- 1 \leq cos (x) \leq 1

解なし

cos (X) = \frac{37 - 1}{6} : X = arccos (\frac{37 - 1}{6}) + 2 πn, X = 2 π - arccos (\frac{37 - 1}{6}) + 2 πn

cos (X) = \frac{37 - 1}{6}

三角関数の逆数プロパティを適用する

cos (X) = \frac{37 - 1}{6}

以下の一般解

cos (X) = \frac{37 - 1}{6}

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

X = arccos (\frac{37 - 1}{6}) + 2 πn, X = 2 π - arccos (\frac{37 - 1}{6}) + 2 πn

X = arccos (\frac{37 - 1}{6}) + 2 πn, X = 2 π - arccos (\frac{37 - 1}{6}) + 2 πn

すべての解を組み合わせる

X = arccos (\frac{37 - 1}{6}) + 2 πn, X = 2 π - arccos (\frac{37 - 1}{6}) + 2 πn

10進法形式で解を証明する

X = 0.56024 \dots + 2 πn, X = 2 π - 0.56024 \dots + 2 πn

グラフ

人気の例

4sin(θ)=csc(θ)

4 sin (θ) = csc (θ)

- \frac{1}{3} = sin (x)

6sin^2(a)+cos(2a)=2

6 sin^{2} (a) + cos (2 a) = 2

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

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

sin (2 q) = 0