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 >

sec^2(θ)-6sec(θ)+8=0

解

sec^{2} (θ) - 6 sec (θ) + 8 = 0

解

θ = 1.31811 \dots + 2 πn, θ = 2 π - 1.31811 \dots + 2 πn, θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

+1

度

θ = 75.52248 \dots^{\circ} + 36 0^{\circ} n, θ = 284.47751 \dots^{\circ} + 36 0^{\circ} n, θ = 6 0^{\circ} + 36 0^{\circ} n, θ = 30 0^{\circ} + 36 0^{\circ} n

解答ステップ

sec^{2} (θ) - 6 sec (θ) + 8 = 0

置換で解く

sec^{2} (θ) - 6 sec (θ) + 8 = 0

仮定:

sec (θ) = u

u^{2} - 6 u + 8 = 0

u^{2} - 6 u + 8 = 0 : u = 4, u = 2

u^{2} - 6 u + 8 = 0

解くとthe二次式

u^{2} - 6 u + 8 = 0

二次Equationの公式:

次の場合:

a = 1, b = - 6, c = 8

u_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 1 \cdot 8}{2 \cdot 1}

u_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 1 \cdot 8}{2 \cdot 1}

(- 6)^{2} - 4 \cdot 1 \cdot 8 = 2

(- 6)^{2} - 4 \cdot 1 \cdot 8

指数の規則を適用する:

n

が偶数であれば

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

(- 6)^{2} = 6^{2}

= 6^{2} - 4 \cdot 1 \cdot 8

数を乗じる:

4 \cdot 1 \cdot 8 = 32

= 6^{2} - 32

6^{2} = 36

= 36 - 32

数を引く:

36 - 32 = 4

= 4

数を因数に分解する:

4 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

n a^{n} = a

2^{2} = 2

= 2

u_{1, 2} = \frac{- ( - 6 ) \pm 2}{2 \cdot 1}

解を分離する

u_{1} = \frac{- ( - 6 ) + 2}{2 \cdot 1}, u_{2} = \frac{- ( - 6 ) - 2}{2 \cdot 1}

u = \frac{- ( - 6 ) + 2}{2 \cdot 1} : 4

\frac{- ( - 6 ) + 2}{2 \cdot 1}

規則を適用

- (- a) = a

= \frac{6 + 2}{2 \cdot 1}

数を足す:

6 + 2 = 8

= \frac{8}{2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{8}{2}

数を割る:

\frac{8}{2} = 4

= 4

u = \frac{- ( - 6 ) - 2}{2 \cdot 1} : 2

\frac{- ( - 6 ) - 2}{2 \cdot 1}

規則を適用

- (- a) = a

= \frac{6 - 2}{2 \cdot 1}

数を引く:

6 - 2 = 4

= \frac{4}{2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{4}{2}

数を割る:

\frac{4}{2} = 2

= 2

二次equationの解:

u = 4, u = 2

代用を戻す

u = sec (θ)

sec (θ) = 4, sec (θ) = 2

sec (θ) = 4, sec (θ) = 2

sec (θ) = 4 : θ = arcsec (4) + 2 πn, θ = 2 π - arcsec (4) + 2 πn

sec (θ) = 4

三角関数の逆数プロパティを適用する

sec (θ) = 4

以下の一般解

sec (θ) = 4

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = 2 π - arcsec (a) + 2 πn

θ = arcsec (4) + 2 πn, θ = 2 π - arcsec (4) + 2 πn

θ = arcsec (4) + 2 πn, θ = 2 π - arcsec (4) + 2 πn

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

sec (θ) = 2

以下の一般解

sec (θ) = 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}

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

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

すべての解を組み合わせる

θ = arcsec (4) + 2 πn, θ = 2 π - arcsec (4) + 2 πn, θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

10進法形式で解を証明する

θ = 1.31811 \dots + 2 πn, θ = 2 π - 1.31811 \dots + 2 πn, θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

グラフ

人気の例

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

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

10tan(x)sin(x)=sin(x)

10 tan (x) sin (x) = sin (x)

cos(2x)=2sin(x)cos(x)

cos (2 x) = 2 sin (x) cos (x)

sin (θ) = \frac{5}{6}

3tan^2(x)=sqrt(3)tan(x)

3 tan^{2} (x) = 3 tan (x)