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人気のある三角関数 >

2tan^2(t)=-3sec(t)

解

2 tan^{2} (t) = - 3 sec (t)

解

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

+1

度

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

解答ステップ

2 tan^{2} (t) = - 3 sec (t)

両辺から

- 3 sec (t)

を引く

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

三角関数の公式を使用して書き換える

2 tan^{2} (t) + 3 sec (t)

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

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

(- 1 + sec^{2} (t)) \cdot 2 + 3 sec (t) = 0

置換で解く

(- 1 + sec^{2} (t)) \cdot 2 + 3 sec (t) = 0

仮定:

sec (t) = u

(- 1 + u^{2}) \cdot 2 + 3 u = 0

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

(- 1 + u^{2}) \cdot 2 + 3 u = 0

拡張

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

(- 1 + u^{2}) \cdot 2 + 3 u

= 2 (- 1 + u^{2}) + 3 u

拡張

2 (- 1 + u^{2}) : - 2 + 2 u^{2}

2 (- 1 + u^{2})

分配法則を適用する:

a (b + c) = ab + a c

a = 2, b = - 1, c = u^{2}

= 2 (- 1) + 2 u^{2}

マイナス・プラスの規則を適用する

+ (- a) = - a

= - 2 \cdot 1 + 2 u^{2}

数を乗じる:

2 \cdot 1 = 2

= - 2 + 2 u^{2}

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

- 2 + 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 - 2 = 0

解くとthe二次式

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

二次Equationの公式:

次の場合:

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

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

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

3^{2} - 4 \cdot 2 (- 2) = 5

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

規則を適用

- (- a) = a

= 3^{2} + 4 \cdot 2 \cdot 2

数を乗じる:

4 \cdot 2 \cdot 2 = 16

= 3^{2} + 16

3^{2} = 9

= 9 + 16

数を足す:

9 + 16 = 25

= 25

数を因数に分解する:

25 = 5^{2}

= 5^{2}

累乗根の規則を適用する:

n a^{n} = a

5^{2} = 5

= 5

u_{1, 2} = \frac{- 3 \pm 5}{2 \cdot 2}

解を分離する

u_{1} = \frac{- 3 + 5}{2 \cdot 2}, u_{2} = \frac{- 3 - 5}{2 \cdot 2}

u = \frac{- 3 + 5}{2 \cdot 2} : \frac{1}{2}

\frac{- 3 + 5}{2 \cdot 2}

数を足す/引く:

- 3 + 5 = 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}

u = \frac{- 3 - 5}{2 \cdot 2} : - 2

\frac{- 3 - 5}{2 \cdot 2}

数を引く:

- 3 - 5 = - 8

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

数を乗じる:

2 \cdot 2 = 4

= \frac{- 8}{4}

分数の規則を適用する:

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

= - \frac{8}{4}

数を割る:

\frac{8}{4} = 2

= - 2

二次equationの解:

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

代用を戻す

u = sec (t)

sec (t) = \frac{1}{2}, sec (t) = - 2

sec (t) = \frac{1}{2}, sec (t) = - 2

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

解なし

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

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

解なし

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

sec (t) = - 2

以下の一般解

sec (t) = - 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}

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

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

すべての解を組み合わせる

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

グラフ

人気の例

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

4 cos (θ) + 1 = 0

cos(a)= 3/(sqrt(-6))

cos (a) = \frac{3}{- 6}

cos(x+5)= 1/2 sqrt(3),0<= x<= 2pi

cos (x + 5) = \frac{1}{2} 3, 0 \leq x \leq 2 π

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

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