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人気のある三角関数 >

3sin^2(x)-6sin(x)=0

解

3 sin^{2} (x) - 6 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

3 sin^{2} (x) - 6 sin (x) = 0

置換で解く

3 sin^{2} (x) - 6 sin (x) = 0

仮定:

sin (x) = u

3 u^{2} - 6 u = 0

3 u^{2} - 6 u = 0 : u = 2, u = 0

3 u^{2} - 6 u = 0

解くとthe二次式

3 u^{2} - 6 u = 0

二次Equationの公式:

次の場合:

a = 3, b = - 6, c = 0

u_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 3 \cdot 0}{2 \cdot 3}

u_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 3 \cdot 0}{2 \cdot 3}

(- 6)^{2} - 4 \cdot 3 \cdot 0 = 6

(- 6)^{2} - 4 \cdot 3 \cdot 0

指数の規則を適用する:

n

が偶数であれば

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

(- 6)^{2} = 6^{2}

= 6^{2} - 4 \cdot 3 \cdot 0

規則を適用

0 \cdot a = 0

= 6^{2} - 0

6^{2} - 0 = 6^{2}

= 6^{2}

累乗根の規則を適用する:

n a^{n} = a,

, 以下を想定

a \geq 0

= 6

u_{1, 2} = \frac{- ( - 6 ) \pm 6}{2 \cdot 3}

解を分離する

u_{1} = \frac{- ( - 6 ) + 6}{2 \cdot 3}, u_{2} = \frac{- ( - 6 ) - 6}{2 \cdot 3}

u = \frac{- ( - 6 ) + 6}{2 \cdot 3} : 2

\frac{- ( - 6 ) + 6}{2 \cdot 3}

規則を適用

- (- a) = a

= \frac{6 + 6}{2 \cdot 3}

数を足す:

6 + 6 = 12

= \frac{12}{2 \cdot 3}

数を乗じる:

2 \cdot 3 = 6

= \frac{12}{6}

数を割る:

\frac{12}{6} = 2

= 2

u = \frac{- ( - 6 ) - 6}{2 \cdot 3} : 0

\frac{- ( - 6 ) - 6}{2 \cdot 3}

規則を適用

- (- a) = a

= \frac{6 - 6}{2 \cdot 3}

数を引く:

6 - 6 = 0

= \frac{0}{2 \cdot 3}

数を乗じる:

2 \cdot 3 = 6

= \frac{0}{6}

規則を適用

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

= 0

二次equationの解:

u = 2, u = 0

代用を戻す

u = sin (x)

sin (x) = 2, sin (x) = 0

sin (x) = 2, sin (x) = 0

sin (x) = 2 :

解なし

sin (x) = 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

sin^2(θ)=8sin(θ)+9

sin^{2} (θ) = 8 sin (θ) + 9

10 sin (3 x) = 5

40^2=28^2+15^2-2(28)(15)*cos(x)

4 0^{2} = 2 8^{2} + 1 5^{2} - 2 (28) (15) \cdot cos (x)

5sin(2x)+8cos(x)=0

5 sin (2 x) + 8 cos (x) = 0

15cos((2pi)/(365)t)+43=30

15 cos (\frac{2 π}{365} t) + 43 = 30