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 >

cos^2(x)+5cos(x)-2=0

解

cos^{2} (x) + 5 cos (x) - 2 = 0

解

x = 1.18933 \dots + 2 πn, x = 2 π - 1.18933 \dots + 2 πn

+1

度

x = 68.14361 \dots^{\circ} + 36 0^{\circ} n, x = 291.85638 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

cos^{2} (x) + 5 cos (x) - 2 = 0

置換で解く

cos^{2} (x) + 5 cos (x) - 2 = 0

仮定:

cos (x) = u

u^{2} + 5 u - 2 = 0

u^{2} + 5 u - 2 = 0 : u = \frac{- 5 + 33}{2}, u = \frac{- 5 - 33}{2}

u^{2} + 5 u - 2 = 0

解くとthe二次式

u^{2} + 5 u - 2 = 0

二次Equationの公式:

次の場合:

a = 1, b = 5, c = - 2

u_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 1 \cdot ( - 2 )}{2 \cdot 1}

u_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 1 \cdot ( - 2 )}{2 \cdot 1}

5^{2} - 4 \cdot 1 \cdot (- 2) = 33

5^{2} - 4 \cdot 1 \cdot (- 2)

規則を適用

- (- a) = a

= 5^{2} + 4 \cdot 1 \cdot 2

数を乗じる:

4 \cdot 1 \cdot 2 = 8

= 5^{2} + 8

5^{2} = 25

= 25 + 8

数を足す:

25 + 8 = 33

= 33

u_{1, 2} = \frac{- 5 \pm 33}{2 \cdot 1}

解を分離する

u_{1} = \frac{- 5 + 33}{2 \cdot 1}, u_{2} = \frac{- 5 - 33}{2 \cdot 1}

u = \frac{- 5 + 33}{2 \cdot 1} : \frac{- 5 + 33}{2}

\frac{- 5 + 33}{2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{- 5 + 33}{2}

u = \frac{- 5 - 33}{2 \cdot 1} : \frac{- 5 - 33}{2}

\frac{- 5 - 33}{2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{- 5 - 33}{2}

二次equationの解:

u = \frac{- 5 + 33}{2}, u = \frac{- 5 - 33}{2}

代用を戻す

u = cos (x)

cos (x) = \frac{- 5 + 33}{2}, cos (x) = \frac{- 5 - 33}{2}

cos (x) = \frac{- 5 + 33}{2}, cos (x) = \frac{- 5 - 33}{2}

cos (x) = \frac{- 5 + 33}{2} : x = arccos (\frac{- 5 + 33}{2}) + 2 πn, x = 2 π - arccos (\frac{- 5 + 33}{2}) + 2 πn

cos (x) = \frac{- 5 + 33}{2}

三角関数の逆数プロパティを適用する

cos (x) = \frac{- 5 + 33}{2}

以下の一般解

cos (x) = \frac{- 5 + 33}{2}

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

x = arccos (\frac{- 5 + 33}{2}) + 2 πn, x = 2 π - arccos (\frac{- 5 + 33}{2}) + 2 πn

x = arccos (\frac{- 5 + 33}{2}) + 2 πn, x = 2 π - arccos (\frac{- 5 + 33}{2}) + 2 πn

cos (x) = \frac{- 5 - 33}{2} :

解なし

cos (x) = \frac{- 5 - 33}{2}

- 1 \leq cos (x) \leq 1

解なし

すべての解を組み合わせる

x = arccos (\frac{- 5 + 33}{2}) + 2 πn, x = 2 π - arccos (\frac{- 5 + 33}{2}) + 2 πn

10進法形式で解を証明する

x = 1.18933 \dots + 2 πn, x = 2 π - 1.18933 \dots + 2 πn

グラフ

人気の例

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

(cos^2(x)+cos(x))*(sin(x)+sin^3(x))=0

arccos(x)-arcsin(x)=arcsin(1-x)

sin^2(x)=|sin(x)|

1-cos^2(x)-sin^{22}(x)=0