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人気のある三角関数 >

6sec^2(x)tan(x)=12tan(x)

解

6 sec^{2} (x) tan (x) = 12 tan (x)

解

x = πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

+1

度

x = 0^{\circ} + 18 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n, x = 22 5^{\circ} + 36 0^{\circ} n, x = 4 5^{\circ} + 36 0^{\circ} n, x = 31 5^{\circ} + 36 0^{\circ} n

解答ステップ

6 sec^{2} (x) tan (x) = 12 tan (x)

両辺から

12 tan (x)

を引く

6 sec^{2} (x) tan (x) - 12 tan (x) = 0

因数

6 sec^{2} (x) tan (x) - 12 tan (x) : 6 tan (x) (sec (x) + 2) (sec (x) - 2)

6 sec^{2} (x) tan (x) - 12 tan (x)

- 12

を書き換え

2 \cdot 6

= 6 sec^{2} (x) tan (x) + 2 \cdot 6 tan (x)

共通項をくくり出す

6 tan (x)

= 6 tan (x) (sec^{2} (x) - 2)

因数

sec^{2} (x) - 2 : (sec (x) + 2) (sec (x) - 2)

sec^{2} (x) - 2

累乗根の規則を適用する:

a = (a)^{2}

2 = (2)^{2}

= sec^{2} (x) - (2)^{2}

2乗の差の公式を適用する:

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

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

= (sec (x) + 2) (sec (x) - 2)

= 6 tan (x) (sec (x) + 2) (sec (x) - 2)

6 tan (x) (sec (x) + 2) (sec (x) - 2) = 0

各部分を別個に解く

tan (x) = 0 or sec (x) + 2 = 0 or sec (x) - 2 = 0

tan (x) = 0 : x = πn

tan (x) = 0

以下の一般解

tan (x) = 0

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 0 + πn

x = 0 + πn

解く

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

sec (x) + 2 = 0 : x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

sec (x) + 2 = 0

2

を右側に移動します

sec (x) + 2 = 0

両辺から

2

を引く

sec (x) + 2 - 2 = 0 - 2

簡素化

sec (x) = - 2

sec (x) = - 2

以下の一般解

sec (x) = - 2

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

sec (x) - 2 = 0 : x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

sec (x) - 2 = 0

2

を右側に移動します

sec (x) - 2 = 0

両辺に

2

を足す

sec (x) - 2 + 2 = 0 + 2

簡素化

sec (x) = 2

sec (x) = 2

以下の一般解

sec (x) = 2

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

すべての解を組み合わせる

x = πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

グラフ

人気の例

cos(θ)+cos(2θ)=0

cos (θ) + cos (2 θ) = 0

sin (2 x) = 2

sin(2x)=sin(4x)

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sin(2x)=sin(3x)

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