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受欢迎的三角函数 >

tan^2(x)+5tan(x)+6=0

解答

tan^{2} (x) + 5 tan (x) + 6 = 0

解答

x = - 1.10714 \dots + πn, x = - 1.24904 \dots + πn

+1

度数

x = - 63.43494 \dots^{\circ} + 18 0^{\circ} n, x = - 71.56505 \dots^{\circ} + 18 0^{\circ} n

求解步骤

tan^{2} (x) + 5 tan (x) + 6 = 0

用替代法求解

tan^{2} (x) + 5 tan (x) + 6 = 0

令

: tan (x) = u

u^{2} + 5 u + 6 = 0

u^{2} + 5 u + 6 = 0 : u = - 2, u = - 3

u^{2} + 5 u + 6 = 0

使用求根公式求解

u^{2} + 5 u + 6 = 0

二次方程求根公式:

若

a = 1, b = 5, c = 6

u_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 1 \cdot 6}{2 \cdot 1}

u_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 1 \cdot 6}{2 \cdot 1}

5^{2} - 4 \cdot 1 \cdot 6 = 1

5^{2} - 4 \cdot 1 \cdot 6

数字相乘:

4 \cdot 1 \cdot 6 = 24

= 5^{2} - 24

5^{2} = 25

= 25 - 24

数字相减:

25 - 24 = 1

= 1

使用法则

1 = 1

= 1

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

将解分隔开

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

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

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

数字相加/相减:

- 5 + 1 = - 4

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

数字相乘:

2 \cdot 1 = 2

= \frac{- 4}{2}

使用分式法则:

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

= - \frac{4}{2}

数字相除:

\frac{4}{2} = 2

= - 2

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

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

数字相减:

- 5 - 1 = - 6

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

数字相乘:

2 \cdot 1 = 2

= \frac{- 6}{2}

使用分式法则:

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

= - \frac{6}{2}

数字相除:

\frac{6}{2} = 3

= - 3

二次方程组的解是:

u = - 2, u = - 3

u = tan (x)

代回

tan (x) = - 2, tan (x) = - 3

tan (x) = - 2, tan (x) = - 3

tan (x) = - 2 : x = arctan (- 2) + πn

tan (x) = - 2

使用反三角函数性质

tan (x) = - 2

tan (x) = - 2

的通解

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

x = arctan (- 2) + πn

x = arctan (- 2) + πn

tan (x) = - 3 : x = arctan (- 3) + πn

tan (x) = - 3

使用反三角函数性质

tan (x) = - 3

tan (x) = - 3

的通解

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

x = arctan (- 3) + πn

x = arctan (- 3) + πn

合并所有解

x = arctan (- 2) + πn, x = arctan (- 3) + πn

以小数形式表示解

x = - 1.10714 \dots + πn, x = - 1.24904 \dots + πn

作图

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