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 >

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

解

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

解

x = 2 πn, x = π + 2 πn

+1

度

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

解答ステップ

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

置換で解く

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

仮定:

sin (x) = u

2 u^{2} - 3 u = 0

2 u^{2} - 3 u = 0 : u = \frac{3}{2}, u = 0

2 u^{2} - 3 u = 0

解くとthe二次式

2 u^{2} - 3 u = 0

二次Equationの公式:

次の場合:

a = 2, b = - 3, c = 0

u_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 2 \cdot 0}{2 \cdot 2}

u_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 2 \cdot 0}{2 \cdot 2}

(- 3)^{2} - 4 \cdot 2 \cdot 0 = 3

(- 3)^{2} - 4 \cdot 2 \cdot 0

指数の規則を適用する:

n

が偶数であれば

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

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

= 3^{2} - 4 \cdot 2 \cdot 0

規則を適用

0 \cdot a = 0

= 3^{2} - 0

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

= 3^{2}

累乗根の規則を適用する:

n a^{n} = a,

, 以下を想定

a \geq 0

= 3

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

解を分離する

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

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

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

規則を適用

- (- a) = a

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

数を足す:

3 + 3 = 6

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

数を乗じる:

2 \cdot 2 = 4

= \frac{6}{4}

共通因数を約分する:

2

= \frac{3}{2}

u = \frac{- ( - 3 ) - 3}{2 \cdot 2} : 0

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

規則を適用

- (- a) = a

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

数を引く:

3 - 3 = 0

= \frac{0}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{0}{4}

規則を適用

\frac{0}{a} = 0, a \neq = 0

= 0

二次equationの解:

u = \frac{3}{2}, u = 0

代用を戻す

u = sin (x)

sin (x) = \frac{3}{2}, sin (x) = 0

sin (x) = \frac{3}{2}, sin (x) = 0

sin (x) = \frac{3}{2} :

解なし

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

- 1 \leq sin (x) \leq 1

解なし

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

以下の一般解

sin (x) = 0

sin (x)

2 πn

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

解く

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

すべての解を組み合わせる

x = 2 πn, x = π + 2 πn

グラフ

人気の例

0.32=0.59406cos(x)

0.32 = 0.59406 cos (x)

solvefor x,4cos(x)=0

so l v e f or x, 4 cos (x) = 0

sec(3x)=-(2sqrt(3))/3

sec (3 x) = - \frac{2 3}{3}

cos(x)+(1-cos^2(x))sqrt(2)=0

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

2 cos (3 θ) = 0