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 >

tan^2(x)+5tan(x)-1=0

解

tan^{2} (x) + 5 tan (x) - 1 = 0

解

x = 0.19025 \dots + πn, x = - 1.38054 \dots + πn

+1

度

x = 10.90070 \dots^{\circ} + 18 0^{\circ} n, x = - 79.09929 \dots^{\circ} + 18 0^{\circ} n

解答ステップ

tan^{2} (x) + 5 tan (x) - 1 = 0

置換で解く

tan^{2} (x) + 5 tan (x) - 1 = 0

仮定:

tan (x) = u

u^{2} + 5 u - 1 = 0

u^{2} + 5 u - 1 = 0 : u = \frac{- 5 + 29}{2}, u = \frac{- 5 - 29}{2}

u^{2} + 5 u - 1 = 0

解くとthe二次式

u^{2} + 5 u - 1 = 0

二次Equationの公式:

次の場合:

a = 1, b = 5, c = - 1

u_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 1 \cdot ( - 1 )}{2 \cdot 1}

u_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 1 \cdot ( - 1 )}{2 \cdot 1}

5^{2} - 4 \cdot 1 \cdot (- 1) = 29

5^{2} - 4 \cdot 1 \cdot (- 1)

規則を適用

- (- a) = a

= 5^{2} + 4 \cdot 1 \cdot 1

数を乗じる:

4 \cdot 1 \cdot 1 = 4

= 5^{2} + 4

5^{2} = 25

= 25 + 4

数を足す:

25 + 4 = 29

= 29

u_{1, 2} = \frac{- 5 \pm 29}{2 \cdot 1}

解を分離する

u_{1} = \frac{- 5 + 29}{2 \cdot 1}, u_{2} = \frac{- 5 - 29}{2 \cdot 1}

u = \frac{- 5 + 29}{2 \cdot 1} : \frac{- 5 + 29}{2}

\frac{- 5 + 29}{2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{- 5 + 29}{2}

u = \frac{- 5 - 29}{2 \cdot 1} : \frac{- 5 - 29}{2}

\frac{- 5 - 29}{2 \cdot 1}

数を乗じる:

2 \cdot 1 = 2

= \frac{- 5 - 29}{2}

二次equationの解:

u = \frac{- 5 + 29}{2}, u = \frac{- 5 - 29}{2}

代用を戻す

u = tan (x)

tan (x) = \frac{- 5 + 29}{2}, tan (x) = \frac{- 5 - 29}{2}

tan (x) = \frac{- 5 + 29}{2}, tan (x) = \frac{- 5 - 29}{2}

tan (x) = \frac{- 5 + 29}{2} : x = arctan (\frac{- 5 + 29}{2}) + πn

tan (x) = \frac{- 5 + 29}{2}

三角関数の逆数プロパティを適用する

tan (x) = \frac{- 5 + 29}{2}

以下の一般解

tan (x) = \frac{- 5 + 29}{2}

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (\frac{- 5 + 29}{2}) + πn

x = arctan (\frac{- 5 + 29}{2}) + πn

tan (x) = \frac{- 5 - 29}{2} : x = arctan (\frac{- 5 - 29}{2}) + πn

tan (x) = \frac{- 5 - 29}{2}

三角関数の逆数プロパティを適用する

tan (x) = \frac{- 5 - 29}{2}

以下の一般解

tan (x) = \frac{- 5 - 29}{2}

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (\frac{- 5 - 29}{2}) + πn

x = arctan (\frac{- 5 - 29}{2}) + πn

すべての解を組み合わせる

x = arctan (\frac{- 5 + 29}{2}) + πn, x = arctan (\frac{- 5 - 29}{2}) + πn

10進法形式で解を証明する

x = 0.19025 \dots + πn, x = - 1.38054 \dots + πn

グラフ

人気の例

csc (θ) + 1 = 0

2sin^2(θ)-3sin(θ)+1=0,0<= θ<= 2pi

2 sin^{2} (θ) - 3 sin (θ) + 1 = 0, 0 \leq θ \leq 2 π

2sec(x)+2tan(x)=2

2 sec (x) + 2 tan (x) = 2

2sin^2(θ)+sqrt(3)sin(θ)=0

2 sin^{2} (θ) + 3 sin (θ) = 0

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

cos^{2} (x) = sin^{2} (\frac{x}{2})