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人気のある三角関数 >

cos(x)cot^2(x)-3cos(x)=0

解

cos (x) cot^{2} (x) - 3 cos (x) = 0

解

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{5 π}{6} + πn, x = \frac{π}{6} + πn

+1

度

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 18 0^{\circ} n, x = 3 0^{\circ} + 18 0^{\circ} n

解答ステップ

cos (x) cot^{2} (x) - 3 cos (x) = 0

因数

cos (x) cot^{2} (x) - 3 cos (x) : cos (x) (cot (x) + 3) (cot (x) - 3)

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

共通項をくくり出す

cos (x)

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

因数

cot^{2} (x) - 3 : (cot (x) + 3) (cot (x) - 3)

cot^{2} (x) - 3

累乗根の規則を適用する:

a = (a)^{2}

3 = (3)^{2}

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

2乗の差の公式を適用する:

x^{2} - y^{2} = (x + y) (x - y)

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

= (cot (x) + 3) (cot (x) - 3)

= cos (x) (cot (x) + 3) (cot (x) - 3)

cos (x) (cot (x) + 3) (cot (x) - 3) = 0

各部分を別個に解く

cos (x) = 0 or cot (x) + 3 = 0 or cot (x) - 3 = 0

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 0

以下の一般解

cos (x) = 0

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cot (x) + 3 = 0 : x = \frac{5 π}{6} + πn

cot (x) + 3 = 0

3

を右側に移動します

cot (x) + 3 = 0

両辺から

3

を引く

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

簡素化

cot (x) = - 3

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

cot (x) - 3 = 0 : x = \frac{π}{6} + πn

cot (x) - 3 = 0

3

を右側に移動します

cot (x) - 3 = 0

両辺に

3

を足す

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

簡素化

cot (x) = 3

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{π}{6} + πn

x = \frac{π}{6} + πn

すべての解を組み合わせる

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{5 π}{6} + πn, x = \frac{π}{6} + πn

グラフ

人気の例

-3cos^2(θ)-6cos(θ)+3=-cos(θ)+5

- 3 cos^{2} (θ) - 6 cos (θ) + 3 = - cos (θ) + 5

cos(x)-1=cos(2x)

cos (x) - 1 = cos (2 x)

sin(x+pi/4)=(sqrt(2))/2

sin (x + \frac{π}{4}) = \frac{2}{2}

tan (θ) = 2.4

sin(x)(2sin(x)-1)=0

sin (x) (2 sin (x) - 1) = 0