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人気のある三角関数 >

(4sec^2(x))/2 =-8sec(x)

解

\frac{4 sec ^{2} ( x )}{2} = - 8 sec (x)

解

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

+1

度

x = 104.47751 \dots^{\circ} + 36 0^{\circ} n, x = - 104.47751 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

\frac{4 sec ^{2} ( x )}{2} = - 8 sec (x)

置換で解く

\frac{4 sec ^{2} ( x )}{2} = - 8 sec (x)

仮定:

sec (x) = u

\frac{4 u ^{2}}{2} = - 8 u

\frac{4 u ^{2}}{2} = - 8 u : u = 0, u = - 4

\frac{4 u ^{2}}{2} = - 8 u

以下で両辺を乗じる:

2

\frac{4 u ^{2}}{2} = - 8 u

以下で両辺を乗じる:

2

\frac{4 u ^{2}}{2} \cdot 2 = - 8 u \cdot 2

簡素化

4 u^{2} = - 16 u

4 u^{2} = - 16 u

16 u

を左側に移動します

4 u^{2} = - 16 u

両辺に

16 u

を足す

4 u^{2} + 16 u = - 16 u + 16 u

簡素化

4 u^{2} + 16 u = 0

4 u^{2} + 16 u = 0

解くとthe二次式

4 u^{2} + 16 u = 0

二次Equationの公式:

次の場合:

a = 4, b = 16, c = 0

u_{1, 2} = \frac{- 16 \pm 1 6 ^{2} - 4 \cdot 4 \cdot 0}{2 \cdot 4}

u_{1, 2} = \frac{- 16 \pm 1 6 ^{2} - 4 \cdot 4 \cdot 0}{2 \cdot 4}

1 6^{2} - 4 \cdot 4 \cdot 0 = 16

1 6^{2} - 4 \cdot 4 \cdot 0

規則を適用

0 \cdot a = 0

= 1 6^{2} - 0

1 6^{2} - 0 = 1 6^{2}

= 1 6^{2}

累乗根の規則を適用する:

n a^{n} = a,

, 以下を想定

a \geq 0

= 16

u_{1, 2} = \frac{- 16 \pm 16}{2 \cdot 4}

解を分離する

u_{1} = \frac{- 16 + 16}{2 \cdot 4}, u_{2} = \frac{- 16 - 16}{2 \cdot 4}

u = \frac{- 16 + 16}{2 \cdot 4} : 0

\frac{- 16 + 16}{2 \cdot 4}

数を足す/引く:

- 16 + 16 = 0

= \frac{0}{2 \cdot 4}

数を乗じる:

2 \cdot 4 = 8

= \frac{0}{8}

規則を適用

\frac{0}{a} = 0, a \neq = 0

= 0

u = \frac{- 16 - 16}{2 \cdot 4} : - 4

\frac{- 16 - 16}{2 \cdot 4}

数を引く:

- 16 - 16 = - 32

= \frac{- 32}{2 \cdot 4}

数を乗じる:

2 \cdot 4 = 8

= \frac{- 32}{8}

分数の規則を適用する:

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

= - \frac{32}{8}

数を割る:

\frac{32}{8} = 4

= - 4

二次equationの解:

u = 0, u = - 4

代用を戻す

u = sec (x)

sec (x) = 0, sec (x) = - 4

sec (x) = 0, sec (x) = - 4

sec (x) = 0 :

解なし

sec (x) = 0

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

解なし

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

sec (x) = - 4

三角関数の逆数プロパティを適用する

sec (x) = - 4

以下の一般解

sec (x) = - 4

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

x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

すべての解を組み合わせる

x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

10進法形式で解を証明する

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

グラフ

人気の例

tan(x)+tan^3(x)=0

tan (x) + tan^{3} (x) = 0

sin^3(x)-2sin(x)=4cos^2(x)-3

sin^{3} (x) - 2 sin (x) = 4 cos^{2} (x) - 3

cos^2(x)+6sin(x)-6=0

cos^{2} (x) + 6 sin (x) - 6 = 0

(1-sin(x))*cos^3(x)=0

(1 - sin (x)) \cdot cos^{3} (x) = 0

- tan (x) = 3.465