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人気のある三角関数 >

2tan^2(x)-3sec(x)+3=0

解

2 tan^{2} (x) - 3 sec (x) + 3 = 0

解

x = 2 πn

+1

度

x = 0^{\circ} + 36 0^{\circ} n

解答ステップ

2 tan^{2} (x) - 3 sec (x) + 3 = 0

三角関数の公式を使用して書き換える

3 + 2 tan^{2} (x) - 3 sec (x)

ピタゴラスの公式を使用する:

tan^{2} (x) + 1 = sec^{2} (x)

tan^{2} (x) = sec^{2} (x) - 1

= 3 + 2 (sec^{2} (x) - 1) - 3 sec (x)

簡素化

3 + 2 (sec^{2} (x) - 1) - 3 sec (x) : 2 sec^{2} (x) - 3 sec (x) + 1

3 + 2 (sec^{2} (x) - 1) - 3 sec (x)

拡張

2 (sec^{2} (x) - 1) : 2 sec^{2} (x) - 2

2 (sec^{2} (x) - 1)

分配法則を適用する:

a (b - c) = ab - a c

a = 2, b = sec^{2} (x), c = 1

= 2 sec^{2} (x) - 2 \cdot 1

数を乗じる:

2 \cdot 1 = 2

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

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

簡素化

3 + 2 sec^{2} (x) - 2 - 3 sec (x) : 2 sec^{2} (x) - 3 sec (x) + 1

3 + 2 sec^{2} (x) - 2 - 3 sec (x)

条件のようなグループ

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

数を足す/引く:

3 - 2 = 1

= 2 sec^{2} (x) - 3 sec (x) + 1

= 2 sec^{2} (x) - 3 sec (x) + 1

= 2 sec^{2} (x) - 3 sec (x) + 1

1 + 2 sec^{2} (x) - 3 sec (x) = 0

置換で解く

1 + 2 sec^{2} (x) - 3 sec (x) = 0

仮定:

sec (x) = u

1 + 2 u^{2} - 3 u = 0

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

1 + 2 u^{2} - 3 u = 0

標準的な形式で書く

a x^{2} + b x + c = 0

2 u^{2} - 3 u + 1 = 0

解くとthe二次式

2 u^{2} - 3 u + 1 = 0

二次Equationの公式:

次の場合:

a = 2, b = - 3, c = 1

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

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

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

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

指数の規則を適用する:

n

が偶数であれば

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

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

= 3^{2} - 4 \cdot 2 \cdot 1

数を乗じる:

4 \cdot 2 \cdot 1 = 8

= 3^{2} - 8

3^{2} = 9

= 9 - 8

数を引く:

9 - 8 = 1

= 1

規則を適用

1 = 1

= 1

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

解を分離する

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

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

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

規則を適用

- (- a) = a

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

数を足す:

3 + 1 = 4

= \frac{4}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{4}{4}

規則を適用

\frac{a}{a} = 1

= 1

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

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

規則を適用

- (- a) = a

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

数を引く:

3 - 1 = 2

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

数を乗じる:

2 \cdot 2 = 4

= \frac{2}{4}

共通因数を約分する:

2

= \frac{1}{2}

二次equationの解:

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

代用を戻す

u = sec (x)

sec (x) = 1, sec (x) = \frac{1}{2}

sec (x) = 1, sec (x) = \frac{1}{2}

sec (x) = 1 : x = 2 πn

sec (x) = 1

以下の一般解

sec (x) = 1

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 = 0 + 2 πn

x = 0 + 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

sec (x) = \frac{1}{2} :

解なし

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

sec (x) \leq - 1 or sec (x) \geq 1

解なし

すべての解を組み合わせる

x = 2 πn

グラフ

人気の例

cos(x)=sin(x/2)

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

tan (θ) = 0.5

-sqrt(3)tan(θ)-6=-3

- 3 tan (θ) - 6 = - 3

tan (θ) = 2.5

arccos(1-x)+arccos(x)=arccos(-x)

arccos (1 - x) + arccos (x) = arccos (- x)