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 >

3cot^2(x)-14csc(x)-2=0

解

3 cot^{2} (x) - 14 csc (x) - 2 = 0

解

x = 0.20135 \dots + 2 πn, x = π - 0.20135 \dots + 2 πn

+1

度

x = 11.53695 \dots^{\circ} + 36 0^{\circ} n, x = 168.46304 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

3 cot^{2} (x) - 14 csc (x) - 2 = 0

三角関数の公式を使用して書き換える

- 2 - 14 csc (x) + 3 cot^{2} (x)

ピタゴラスの公式を使用する:

1 + cot^{2} (x) = csc^{2} (x)

cot^{2} (x) = csc^{2} (x) - 1

= - 2 - 14 csc (x) + 3 (csc^{2} (x) - 1)

簡素化

- 2 - 14 csc (x) + 3 (csc^{2} (x) - 1) : 3 csc^{2} (x) - 14 csc (x) - 5

- 2 - 14 csc (x) + 3 (csc^{2} (x) - 1)

拡張

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

3 (csc^{2} (x) - 1)

分配法則を適用する:

a (b - c) = ab - a c

a = 3, b = csc^{2} (x), c = 1

= 3 csc^{2} (x) - 3 \cdot 1

数を乗じる:

3 \cdot 1 = 3

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

= - 2 - 14 csc (x) + 3 csc^{2} (x) - 3

簡素化

- 2 - 14 csc (x) + 3 csc^{2} (x) - 3 : 3 csc^{2} (x) - 14 csc (x) - 5

- 2 - 14 csc (x) + 3 csc^{2} (x) - 3

条件のようなグループ

= - 14 csc (x) + 3 csc^{2} (x) - 2 - 3

数を引く:

- 2 - 3 = - 5

= 3 csc^{2} (x) - 14 csc (x) - 5

= 3 csc^{2} (x) - 14 csc (x) - 5

= 3 csc^{2} (x) - 14 csc (x) - 5

- 5 - 14 csc (x) + 3 csc^{2} (x) = 0

置換で解く

- 5 - 14 csc (x) + 3 csc^{2} (x) = 0

仮定:

csc (x) = u

- 5 - 14 u + 3 u^{2} = 0

- 5 - 14 u + 3 u^{2} = 0 : u = 5, u = - \frac{1}{3}

- 5 - 14 u + 3 u^{2} = 0

標準的な形式で書く

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

3 u^{2} - 14 u - 5 = 0

解くとthe二次式

3 u^{2} - 14 u - 5 = 0

二次Equationの公式:

次の場合:

a = 3, b = - 14, c = - 5

u_{1, 2} = \frac{- ( - 14 ) \pm ( - 14 ) ^{2} - 4 \cdot 3 ( - 5 )}{2 \cdot 3}

u_{1, 2} = \frac{- ( - 14 ) \pm ( - 14 ) ^{2} - 4 \cdot 3 ( - 5 )}{2 \cdot 3}

(- 14)^{2} - 4 \cdot 3 (- 5) = 16

(- 14)^{2} - 4 \cdot 3 (- 5)

規則を適用

- (- a) = a

= (- 14)^{2} + 4 \cdot 3 \cdot 5

指数の規則を適用する:

n

が偶数であれば

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

(- 14)^{2} = 1 4^{2}

= 1 4^{2} + 4 \cdot 3 \cdot 5

数を乗じる:

4 \cdot 3 \cdot 5 = 60

= 1 4^{2} + 60

1 4^{2} = 196

= 196 + 60

数を足す:

196 + 60 = 256

= 256

数を因数に分解する:

256 = 1 6^{2}

= 1 6^{2}

累乗根の規則を適用する:

n a^{n} = a

1 6^{2} = 16

= 16

u_{1, 2} = \frac{- ( - 14 ) \pm 16}{2 \cdot 3}

解を分離する

u_{1} = \frac{- ( - 14 ) + 16}{2 \cdot 3}, u_{2} = \frac{- ( - 14 ) - 16}{2 \cdot 3}

u = \frac{- ( - 14 ) + 16}{2 \cdot 3} : 5

\frac{- ( - 14 ) + 16}{2 \cdot 3}

規則を適用

- (- a) = a

= \frac{14 + 16}{2 \cdot 3}

数を足す:

14 + 16 = 30

= \frac{30}{2 \cdot 3}

数を乗じる:

2 \cdot 3 = 6

= \frac{30}{6}

数を割る:

\frac{30}{6} = 5

= 5

u = \frac{- ( - 14 ) - 16}{2 \cdot 3} : - \frac{1}{3}

\frac{- ( - 14 ) - 16}{2 \cdot 3}

規則を適用

- (- a) = a

= \frac{14 - 16}{2 \cdot 3}

数を引く:

14 - 16 = - 2

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

数を乗じる:

2 \cdot 3 = 6

= \frac{- 2}{6}

分数の規則を適用する:

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

= - \frac{2}{6}

共通因数を約分する:

2

= - \frac{1}{3}

二次equationの解:

u = 5, u = - \frac{1}{3}

代用を戻す

u = csc (x)

csc (x) = 5, csc (x) = - \frac{1}{3}

csc (x) = 5, csc (x) = - \frac{1}{3}

csc (x) = 5 : x = arccsc (5) + 2 πn, x = π - arccsc (5) + 2 πn

csc (x) = 5

三角関数の逆数プロパティを適用する

csc (x) = 5

以下の一般解

csc (x) = 5

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π - arccsc (a) + 2 πn

x = arccsc (5) + 2 πn, x = π - arccsc (5) + 2 πn

x = arccsc (5) + 2 πn, x = π - arccsc (5) + 2 πn

csc (x) = - \frac{1}{3} :

解なし

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

csc (x) \leq - 1 or csc (x) \geq 1

解なし

すべての解を組み合わせる

x = arccsc (5) + 2 πn, x = π - arccsc (5) + 2 πn

10進法形式で解を証明する

x = 0.20135 \dots + 2 πn, x = π - 0.20135 \dots + 2 πn

グラフ

人気の例

250=100*5*cos(x)

250 = 100 \cdot 5 \cdot cos (x)

tan(x)= 1/(sin(2x)),0<= x<= pi

tan (x) = \frac{1}{sin ( 2 x )}, 0 \leq x \leq π

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

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

cos(x)= 1/4-sin^2(x)

cos (x) = \frac{1}{4} - sin^{2} (x)

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

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