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 >

4tan^2(x)+15sec(x)=0

解

4 tan^{2} (x) + 15 sec (x) = 0

解

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

+1

度

x = 104.47751 \dots^{\circ} + 36 0^{\circ} n, x = - 104.47751 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

4 tan^{2} (x) + 15 sec (x) = 0

三角関数の公式を使用して書き換える

15 sec (x) + 4 tan^{2} (x)

ピタゴラスの公式を使用する:

tan^{2} (x) + 1 = sec^{2} (x)

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

= 15 sec (x) + 4 (sec^{2} (x) - 1)

(- 1 + sec^{2} (x)) \cdot 4 + 15 sec (x) = 0

置換で解く

(- 1 + sec^{2} (x)) \cdot 4 + 15 sec (x) = 0

仮定:

sec (x) = u

(- 1 + u^{2}) \cdot 4 + 15 u = 0

(- 1 + u^{2}) \cdot 4 + 15 u = 0 : u = \frac{1}{4}, u = - 4

(- 1 + u^{2}) \cdot 4 + 15 u = 0

拡張

(- 1 + u^{2}) \cdot 4 + 15 u : - 4 + 4 u^{2} + 15 u

(- 1 + u^{2}) \cdot 4 + 15 u

= 4 (- 1 + u^{2}) + 15 u

拡張

4 (- 1 + u^{2}) : - 4 + 4 u^{2}

4 (- 1 + u^{2})

分配法則を適用する:

a (b + c) = ab + a c

a = 4, b = - 1, c = u^{2}

= 4 (- 1) + 4 u^{2}

マイナス・プラスの規則を適用する

+ (- a) = - a

= - 4 \cdot 1 + 4 u^{2}

数を乗じる:

4 \cdot 1 = 4

= - 4 + 4 u^{2}

= - 4 + 4 u^{2} + 15 u

- 4 + 4 u^{2} + 15 u = 0

標準的な形式で書く

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

4 u^{2} + 15 u - 4 = 0

解くとthe二次式

4 u^{2} + 15 u - 4 = 0

二次Equationの公式:

次の場合:

a = 4, b = 15, c = - 4

u_{1, 2} = \frac{- 15 \pm 1 5 ^{2} - 4 \cdot 4 ( - 4 )}{2 \cdot 4}

u_{1, 2} = \frac{- 15 \pm 1 5 ^{2} - 4 \cdot 4 ( - 4 )}{2 \cdot 4}

1 5^{2} - 4 \cdot 4 (- 4) = 17

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

規則を適用

- (- a) = a

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

数を乗じる:

4 \cdot 4 \cdot 4 = 64

= 1 5^{2} + 64

1 5^{2} = 225

= 225 + 64

数を足す:

225 + 64 = 289

= 289

数を因数に分解する:

289 = 1 7^{2}

= 1 7^{2}

累乗根の規則を適用する:

n a^{n} = a

1 7^{2} = 17

= 17

u_{1, 2} = \frac{- 15 \pm 17}{2 \cdot 4}

解を分離する

u_{1} = \frac{- 15 + 17}{2 \cdot 4}, u_{2} = \frac{- 15 - 17}{2 \cdot 4}

u = \frac{- 15 + 17}{2 \cdot 4} : \frac{1}{4}

\frac{- 15 + 17}{2 \cdot 4}

数を足す/引く:

- 15 + 17 = 2

= \frac{2}{2 \cdot 4}

数を乗じる:

2 \cdot 4 = 8

= \frac{2}{8}

共通因数を約分する:

2

= \frac{1}{4}

u = \frac{- 15 - 17}{2 \cdot 4} : - 4

\frac{- 15 - 17}{2 \cdot 4}

数を引く:

- 15 - 17 = - 32

= \frac{- 32}{2 \cdot 4}

数を乗じる:

2 \cdot 4 = 8

= \frac{- 32}{8}

分数の規則を適用する:

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

= - \frac{32}{8}

数を割る:

\frac{32}{8} = 4

= - 4

二次equationの解:

u = \frac{1}{4}, u = - 4

代用を戻す

u = sec (x)

sec (x) = \frac{1}{4}, sec (x) = - 4

sec (x) = \frac{1}{4}, sec (x) = - 4

sec (x) = \frac{1}{4} :

解なし

sec (x) = \frac{1}{4}

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

解なし

sec (x) = - 4 : x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

sec (x) = - 4

三角関数の逆数プロパティを適用する

sec (x) = - 4

以下の一般解

sec (x) = - 4

sec (x) = - a \Rightarrow x = arcsec (- a) + 2 πn, x = - arcsec (- a) + 2 πn

x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

すべての解を組み合わせる

x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

10進法形式で解を証明する

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

グラフ

人気の例

sin^4(x)+cos^4(x)=cos^4(x)

sin^{4} (x) + cos^{4} (x) = cos^{4} (x)

cot (x) = \frac{40}{32}

tan (a) = \frac{3}{8}

sin(2x+10)=cos(3x-20)

sin (2 x + 10) = cos (3 x - 20)

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