ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある三角関数 >

8sec^2(x)-8sec(x)=16

解

8 sec^{2} (x) - 8 sec (x) = 16

解

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

+1

度

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

解答ステップ

8 sec^{2} (x) - 8 sec (x) = 16

置換で解く

8 sec^{2} (x) - 8 sec (x) = 16

仮定:

sec (x) = u

8 u^{2} - 8 u = 16

8 u^{2} - 8 u = 16 : u = 2, u = - 1

8 u^{2} - 8 u = 16

16

を左側に移動します

8 u^{2} - 8 u = 16

両辺から

16

を引く

8 u^{2} - 8 u - 16 = 16 - 16

簡素化

8 u^{2} - 8 u - 16 = 0

8 u^{2} - 8 u - 16 = 0

解くとthe二次式

8 u^{2} - 8 u - 16 = 0

二次Equationの公式:

次の場合:

a = 8, b = - 8, c = - 16

u_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 8 ( - 16 )}{2 \cdot 8}

u_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 8 ( - 16 )}{2 \cdot 8}

(- 8)^{2} - 4 \cdot 8 (- 16) = 24

(- 8)^{2} - 4 \cdot 8 (- 16)

規則を適用

- (- a) = a

= (- 8)^{2} + 4 \cdot 8 \cdot 16

指数の規則を適用する:

n

が偶数であれば

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

(- 8)^{2} = 8^{2}

= 8^{2} + 4 \cdot 8 \cdot 16

数を乗じる:

4 \cdot 8 \cdot 16 = 512

= 8^{2} + 512

8^{2} = 64

= 64 + 512

数を足す:

64 + 512 = 576

= 576

数を因数に分解する:

576 = 2 4^{2}

= 2 4^{2}

累乗根の規則を適用する:

n a^{n} = a

2 4^{2} = 24

= 24

u_{1, 2} = \frac{- ( - 8 ) \pm 24}{2 \cdot 8}

解を分離する

u_{1} = \frac{- ( - 8 ) + 24}{2 \cdot 8}, u_{2} = \frac{- ( - 8 ) - 24}{2 \cdot 8}

u = \frac{- ( - 8 ) + 24}{2 \cdot 8} : 2

\frac{- ( - 8 ) + 24}{2 \cdot 8}

規則を適用

- (- a) = a

= \frac{8 + 24}{2 \cdot 8}

数を足す:

8 + 24 = 32

= \frac{32}{2 \cdot 8}

数を乗じる:

2 \cdot 8 = 16

= \frac{32}{16}

数を割る:

\frac{32}{16} = 2

= 2

u = \frac{- ( - 8 ) - 24}{2 \cdot 8} : - 1

\frac{- ( - 8 ) - 24}{2 \cdot 8}

規則を適用

- (- a) = a

= \frac{8 - 24}{2 \cdot 8}

数を引く:

8 - 24 = - 16

= \frac{- 16}{2 \cdot 8}

数を乗じる:

2 \cdot 8 = 16

= \frac{- 16}{16}

分数の規則を適用する:

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

= - \frac{16}{16}

規則を適用

\frac{a}{a} = 1

= - 1

二次equationの解:

u = 2, u = - 1

代用を戻す

u = sec (x)

sec (x) = 2, sec (x) = - 1

sec (x) = 2, sec (x) = - 1

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

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}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

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

sec (x) = - 1 : x = π + 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 = π + 2 πn

x = π + 2 πn

すべての解を組み合わせる

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

グラフ

人気の例

50=36sin((2pi)/(365)(t-101))+14

50 = 36 sin (\frac{2 π}{365} (t - 101)) + 14

sin(2θ-pi/3)=-1/2

sin (2 θ - \frac{π}{3}) = - \frac{1}{2}

7cos(θ)+sqrt(20)=0

7 cos (θ) + 20 = 0

sec^2(x)= 1/2 csc^2(x)+tan^2(x)

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

4cos(2θ)-3cos(θ)+4=-cos(θ)+3

4 cos (2 θ) - 3 cos (θ) + 4 = - cos (θ) + 3