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人気のある三角関数 >

18sin^2(x)-9sin(x)=0

解

18 sin^{2} (x) - 9 sin (x) = 0

解

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = 2 πn, x = π + 2 πn

+1

度

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n, x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

解答ステップ

18 sin^{2} (x) - 9 sin (x) = 0

置換で解く

18 sin^{2} (x) - 9 sin (x) = 0

仮定:

sin (x) = u

18 u^{2} - 9 u = 0

18 u^{2} - 9 u = 0 : u = \frac{1}{2}, u = 0

18 u^{2} - 9 u = 0

解くとthe二次式

18 u^{2} - 9 u = 0

二次Equationの公式:

次の場合:

a = 18, b = - 9, c = 0

u_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 \cdot 18 \cdot 0}{2 \cdot 18}

u_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 \cdot 18 \cdot 0}{2 \cdot 18}

(- 9)^{2} - 4 \cdot 18 \cdot 0 = 9

(- 9)^{2} - 4 \cdot 18 \cdot 0

指数の規則を適用する:

n

が偶数であれば

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

(- 9)^{2} = 9^{2}

= 9^{2} - 4 \cdot 18 \cdot 0

規則を適用

0 \cdot a = 0

= 9^{2} - 0

9^{2} - 0 = 9^{2}

= 9^{2}

累乗根の規則を適用する:

n a^{n} = a,

, 以下を想定

a \geq 0

= 9

u_{1, 2} = \frac{- ( - 9 ) \pm 9}{2 \cdot 18}

解を分離する

u_{1} = \frac{- ( - 9 ) + 9}{2 \cdot 18}, u_{2} = \frac{- ( - 9 ) - 9}{2 \cdot 18}

u = \frac{- ( - 9 ) + 9}{2 \cdot 18} : \frac{1}{2}

\frac{- ( - 9 ) + 9}{2 \cdot 18}

規則を適用

- (- a) = a

= \frac{9 + 9}{2 \cdot 18}

数を足す:

9 + 9 = 18

= \frac{18}{2 \cdot 18}

数を乗じる:

2 \cdot 18 = 36

= \frac{18}{36}

共通因数を約分する:

18

= \frac{1}{2}

u = \frac{- ( - 9 ) - 9}{2 \cdot 18} : 0

\frac{- ( - 9 ) - 9}{2 \cdot 18}

規則を適用

- (- a) = a

= \frac{9 - 9}{2 \cdot 18}

数を引く:

9 - 9 = 0

= \frac{0}{2 \cdot 18}

数を乗じる:

2 \cdot 18 = 36

= \frac{0}{36}

規則を適用

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

= 0

二次equationの解:

u = \frac{1}{2}, u = 0

代用を戻す

u = sin (x)

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

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

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = \frac{1}{2}

以下の一般解

sin (x) = \frac{1}{2}

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 = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

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 = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = 2 πn, x = π + 2 πn

グラフ

人気の例

cos (\frac{π x}{2}) = 0

arccot(x)= pi/2

arccot (x) = \frac{π}{2}

cos(2θ)+cos(4θ)=0

cos (2 θ) + cos (4 θ) = 0

6cos(2x)+cos(2x)=1

6 cos (2 x) + cos (2 x) = 1

3sec(θ)+1=7,0<= θ<2pi

3 sec (θ) + 1 = 7, 0 \leq θ < 2 π