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 >

12sin^2(x)+sin(x)-1=0

解

12 sin^{2} (x) + sin (x) - 1 = 0

解

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn, x = - 0.33983 \dots + 2 πn, x = π + 0.33983 \dots + 2 πn

+1

度

x = 14.47751 \dots^{\circ} + 36 0^{\circ} n, x = 165.52248 \dots^{\circ} + 36 0^{\circ} n, x = - 19.47122 \dots^{\circ} + 36 0^{\circ} n, x = 199.47122 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

12 sin^{2} (x) + sin (x) - 1 = 0

置換で解く

12 sin^{2} (x) + sin (x) - 1 = 0

仮定:

sin (x) = u

12 u^{2} + u - 1 = 0

12 u^{2} + u - 1 = 0 : u = \frac{1}{4}, u = - \frac{1}{3}

12 u^{2} + u - 1 = 0

解くとthe二次式

12 u^{2} + u - 1 = 0

二次Equationの公式:

次の場合:

a = 12, b = 1, c = - 1

u_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 12 ( - 1 )}{2 \cdot 12}

u_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 12 ( - 1 )}{2 \cdot 12}

1^{2} - 4 \cdot 12 (- 1) = 7

1^{2} - 4 \cdot 12 (- 1)

規則を適用

1^{a} = 1

1^{2} = 1

= 1 - 4 \cdot 12 (- 1)

規則を適用

- (- a) = a

= 1 + 4 \cdot 12 \cdot 1

数を乗じる:

4 \cdot 12 \cdot 1 = 48

= 1 + 48

数を足す:

1 + 48 = 49

= 49

数を因数に分解する:

49 = 7^{2}

= 7^{2}

累乗根の規則を適用する:

n a^{n} = a

7^{2} = 7

= 7

u_{1, 2} = \frac{- 1 \pm 7}{2 \cdot 12}

解を分離する

u_{1} = \frac{- 1 + 7}{2 \cdot 12}, u_{2} = \frac{- 1 - 7}{2 \cdot 12}

u = \frac{- 1 + 7}{2 \cdot 12} : \frac{1}{4}

\frac{- 1 + 7}{2 \cdot 12}

数を足す/引く:

- 1 + 7 = 6

= \frac{6}{2 \cdot 12}

数を乗じる:

2 \cdot 12 = 24

= \frac{6}{24}

共通因数を約分する:

6

= \frac{1}{4}

u = \frac{- 1 - 7}{2 \cdot 12} : - \frac{1}{3}

\frac{- 1 - 7}{2 \cdot 12}

数を引く:

- 1 - 7 = - 8

= \frac{- 8}{2 \cdot 12}

数を乗じる:

2 \cdot 12 = 24

= \frac{- 8}{24}

分数の規則を適用する:

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

= - \frac{8}{24}

共通因数を約分する:

8

= - \frac{1}{3}

二次equationの解:

u = \frac{1}{4}, u = - \frac{1}{3}

代用を戻す

u = sin (x)

sin (x) = \frac{1}{4}, sin (x) = - \frac{1}{3}

sin (x) = \frac{1}{4}, sin (x) = - \frac{1}{3}

sin (x) = \frac{1}{4} : x = arcsin (\frac{1}{4}) + 2 πn, x = π - arcsin (\frac{1}{4}) + 2 πn

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

三角関数の逆数プロパティを適用する

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

以下の一般解

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

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{1}{4}) + 2 πn, x = π - arcsin (\frac{1}{4}) + 2 πn

x = arcsin (\frac{1}{4}) + 2 πn, x = π - arcsin (\frac{1}{4}) + 2 πn

sin (x) = - \frac{1}{3} : x = arcsin (- \frac{1}{3}) + 2 πn, x = π + arcsin (\frac{1}{3}) + 2 πn

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

三角関数の逆数プロパティを適用する

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

以下の一般解

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

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{1}{3}) + 2 πn, x = π + arcsin (\frac{1}{3}) + 2 πn

x = arcsin (- \frac{1}{3}) + 2 πn, x = π + arcsin (\frac{1}{3}) + 2 πn

すべての解を組み合わせる

x = arcsin (\frac{1}{4}) + 2 πn, x = π - arcsin (\frac{1}{4}) + 2 πn, x = arcsin (- \frac{1}{3}) + 2 πn, x = π + arcsin (\frac{1}{3}) + 2 πn

10進法形式で解を証明する

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn, x = - 0.33983 \dots + 2 πn, x = π + 0.33983 \dots + 2 πn

グラフ

人気の例

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

-5(sec(x)-sqrt(2))(2sin(x)+sqrt(3))=0

- 5 (sec (x) - 2) (2 sin (x) + 3) = 0

5 sec^{2} (x) - 5 = 0

cos (3 θ) = - \frac{1}{2}

cos (x) = \frac{5}{6}