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受欢迎的三角函数 >

2tan^2(x)+9tan(x)+3=0

解答

2 tan^{2} (x) + 9 tan (x) + 3 = 0

解答

x = - 0.34780 \dots + πn, x = - 1.33364 \dots + πn

+1

度数

x = - 19.92767 \dots^{\circ} + 18 0^{\circ} n, x = - 76.41251 \dots^{\circ} + 18 0^{\circ} n

求解步骤

2 tan^{2} (x) + 9 tan (x) + 3 = 0

用替代法求解

2 tan^{2} (x) + 9 tan (x) + 3 = 0

令

: tan (x) = u

2 u^{2} + 9 u + 3 = 0

2 u^{2} + 9 u + 3 = 0 : u = \frac{- 9 + 57}{4}, u = \frac{- 9 - 57}{4}

2 u^{2} + 9 u + 3 = 0

使用求根公式求解

2 u^{2} + 9 u + 3 = 0

二次方程求根公式:

若

a = 2, b = 9, c = 3

u_{1, 2} = \frac{- 9 \pm 9 ^{2} - 4 \cdot 2 \cdot 3}{2 \cdot 2}

u_{1, 2} = \frac{- 9 \pm 9 ^{2} - 4 \cdot 2 \cdot 3}{2 \cdot 2}

9^{2} - 4 \cdot 2 \cdot 3 = 57

9^{2} - 4 \cdot 2 \cdot 3

数字相乘:

4 \cdot 2 \cdot 3 = 24

= 9^{2} - 24

9^{2} = 81

= 81 - 24

数字相减:

81 - 24 = 57

= 57

u_{1, 2} = \frac{- 9 \pm 57}{2 \cdot 2}

将解分隔开

u_{1} = \frac{- 9 + 57}{2 \cdot 2}, u_{2} = \frac{- 9 - 57}{2 \cdot 2}

u = \frac{- 9 + 57}{2 \cdot 2} : \frac{- 9 + 57}{4}

\frac{- 9 + 57}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{- 9 + 57}{4}

u = \frac{- 9 - 57}{2 \cdot 2} : \frac{- 9 - 57}{4}

\frac{- 9 - 57}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{- 9 - 57}{4}

二次方程组的解是:

u = \frac{- 9 + 57}{4}, u = \frac{- 9 - 57}{4}

u = tan (x)

代回

tan (x) = \frac{- 9 + 57}{4}, tan (x) = \frac{- 9 - 57}{4}

tan (x) = \frac{- 9 + 57}{4}, tan (x) = \frac{- 9 - 57}{4}

tan (x) = \frac{- 9 + 57}{4} : x = arctan (\frac{- 9 + 57}{4}) + πn

tan (x) = \frac{- 9 + 57}{4}

使用反三角函数性质

tan (x) = \frac{- 9 + 57}{4}

tan (x) = \frac{- 9 + 57}{4}

的通解

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

x = arctan (\frac{- 9 + 57}{4}) + πn

x = arctan (\frac{- 9 + 57}{4}) + πn

tan (x) = \frac{- 9 - 57}{4} : x = arctan (\frac{- 9 - 57}{4}) + πn

tan (x) = \frac{- 9 - 57}{4}

使用反三角函数性质

tan (x) = \frac{- 9 - 57}{4}

tan (x) = \frac{- 9 - 57}{4}

的通解

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

x = arctan (\frac{- 9 - 57}{4}) + πn

x = arctan (\frac{- 9 - 57}{4}) + πn

合并所有解

x = arctan (\frac{- 9 + 57}{4}) + πn, x = arctan (\frac{- 9 - 57}{4}) + πn

以小数形式表示解

x = - 0.34780 \dots + πn, x = - 1.33364 \dots + πn

作图

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