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人気のある三角関数 >

tan^2(x)+2sec(x)=-1

解

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

解

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

+1

度

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

解答ステップ

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

両辺から

- 1

を引く

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

三角関数の公式を使用して書き換える

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

ピタゴラスの公式を使用する:

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

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

sec^{2} (x) + 2 sec (x) = 0

置換で解く

sec^{2} (x) + 2 sec (x) = 0

仮定:

sec (x) = u

u^{2} + 2 u = 0

u^{2} + 2 u = 0 : u = 0, u = - 2

u^{2} + 2 u = 0

解くとthe二次式

u^{2} + 2 u = 0

二次Equationの公式:

次の場合:

a = 1, b = 2, c = 0

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

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

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

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

規則を適用

0 \cdot a = 0

= 2^{2} - 0

2^{2} - 0 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

n a^{n} = a,

, 以下を想定

a \geq 0

= 2

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

解を分離する

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

u = \frac{- 2 + 2}{2 \cdot 1} : 0

\frac{- 2 + 2}{2 \cdot 1}

数を足す/引く:

- 2 + 2 = 0

= \frac{0}{2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{0}{2}

規則を適用

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

= 0

u = \frac{- 2 - 2}{2 \cdot 1} : - 2

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

数を引く:

- 2 - 2 = - 4

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

数を乗じる:

2 \cdot 1 = 2

= \frac{- 4}{2}

分数の規則を適用する:

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

= - \frac{4}{2}

数を割る:

\frac{4}{2} = 2

= - 2

二次equationの解:

u = 0, u = - 2

代用を戻す

u = sec (x)

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

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

sec (x) = 0 :

解なし

sec (x) = 0

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

解なし

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

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

すべての解を組み合わせる

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

グラフ

人気の例

2cos^2(θ)+3cos(θ)+1=0

2 cos^{2} (θ) + 3 cos (θ) + 1 = 0

tan^2(x)sin(x)=-sin(x)

tan^{2} (x) sin (x) = - sin (x)

cos(4x)=sin(x),0<= x<= 2pi

cos (4 x) = sin (x), 0 \leq x \leq 2 π

sqrt(2)cos(x)=1

2 cos (x) = 1

sin(θ)=(-sqrt(3))/2

sin (θ) = \frac{- 3}{2}