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人気のある三角関数 >

cot^2(x)=-sqrt(3)cot(x)

解

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

解

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

+1

度

x = 9 0^{\circ} + 18 0^{\circ} n, x = 15 0^{\circ} + 18 0^{\circ} n

解答ステップ

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

置換で解く

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

仮定:

cot (x) = u

u^{2} = - 3 u

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

u^{2} = - 3 u

3 u

を左側に移動します

u^{2} = - 3 u

両辺に

3 u

を足す

u^{2} + 3 u = - 3 u + 3 u

簡素化

u^{2} + 3 u = 0

u^{2} + 3 u = 0

解くとthe二次式

u^{2} + 3 u = 0

二次Equationの公式:

次の場合:

a = 1, b = 3, c = 0

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

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

(3)^{2} - 4 \cdot 1 \cdot 0 = 3

(3)^{2} - 4 \cdot 1 \cdot 0

(3)^{2} = 3

(3)^{2}

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2}

共通因数を約分する:

2

= 1

= 3

4 \cdot 1 \cdot 0 = 0

4 \cdot 1 \cdot 0

規則を適用

0 \cdot a = 0

= 0

= 3 - 0

数を引く:

3 - 0 = 3

= 3

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

解を分離する

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

u = \frac{- 3 + 3}{2 \cdot 1} : 0

\frac{- 3 + 3}{2 \cdot 1}

類似した元を足す:

- 3 + 3 = 0

= \frac{0}{2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{0}{2}

規則を適用

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

= 0

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

\frac{- 3 - 3}{2 \cdot 1}

類似した元を足す:

- 3 - 3 = - 23

= \frac{- 2 3}{2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{- 2 3}{2}

分数の規則を適用する:

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

= - \frac{2 3}{2}

数を割る:

\frac{2}{2} = 1

= - 3

二次equationの解:

u = 0, u = - 3

代用を戻す

u = cot (x)

cot (x) = 0, cot (x) = - 3

cot (x) = 0, cot (x) = - 3

cot (x) = 0 : x = \frac{π}{2} + πn

cot (x) = 0

以下の一般解

cot (x) = 0

cot (x)

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

cot (x) = - 3 : x = \frac{5 π}{6} + πn

cot (x) = - 3

以下の一般解

cot (x) = - 3

cot (x)

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

すべての解を組み合わせる

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

グラフ

人気の例

tan(θ)=(cos(θ))/(sin(θ))

tan (θ) = \frac{cos ( θ )}{sin ( θ )}

sin(θ)+2sin^2(θ)=0

sin (θ) + 2 sin^{2} (θ) = 0

(cot(x)+1)(sin(x)+1)=0

(cot (x) + 1) (sin (x) + 1) = 0

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

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

sin(x)cos(2x)+cos(x)sin(2x)= 1/2

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