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受欢迎的三角函数 >

4tan^2(x)+12tan(x)-27=0

解答

4 tan^{2} (x) + 12 tan (x) - 27 = 0

解答

x = 0.98279 \dots + πn, x = - 1.35212 \dots + πn

+1

度数

x = 56.30993 \dots^{\circ} + 18 0^{\circ} n, x = - 77.47119 \dots^{\circ} + 18 0^{\circ} n

求解步骤

4 tan^{2} (x) + 12 tan (x) - 27 = 0

用替代法求解

4 tan^{2} (x) + 12 tan (x) - 27 = 0

令

: tan (x) = u

4 u^{2} + 12 u - 27 = 0

4 u^{2} + 12 u - 27 = 0 : u = \frac{3}{2}, u = - \frac{9}{2}

4 u^{2} + 12 u - 27 = 0

使用求根公式求解

4 u^{2} + 12 u - 27 = 0

二次方程求根公式:

若

a = 4, b = 12, c = - 27

u_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 \cdot 4 ( - 27 )}{2 \cdot 4}

u_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 \cdot 4 ( - 27 )}{2 \cdot 4}

1 2^{2} - 4 \cdot 4 (- 27) = 24

1 2^{2} - 4 \cdot 4 (- 27)

使用法则

- (- a) = a

= 1 2^{2} + 4 \cdot 4 \cdot 27

数字相乘:

4 \cdot 4 \cdot 27 = 432

= 1 2^{2} + 432

1 2^{2} = 144

= 144 + 432

数字相加:

144 + 432 = 576

= 576

因式分解数字:

576 = 2 4^{2}

= 2 4^{2}

使用根式运算法则:

n a^{n} = a

2 4^{2} = 24

= 24

u_{1, 2} = \frac{- 12 \pm 24}{2 \cdot 4}

将解分隔开

u_{1} = \frac{- 12 + 24}{2 \cdot 4}, u_{2} = \frac{- 12 - 24}{2 \cdot 4}

u = \frac{- 12 + 24}{2 \cdot 4} : \frac{3}{2}

\frac{- 12 + 24}{2 \cdot 4}

数字相加/相减:

- 12 + 24 = 12

= \frac{12}{2 \cdot 4}

数字相乘:

2 \cdot 4 = 8

= \frac{12}{8}

约分:

4

= \frac{3}{2}

u = \frac{- 12 - 24}{2 \cdot 4} : - \frac{9}{2}

\frac{- 12 - 24}{2 \cdot 4}

数字相减:

- 12 - 24 = - 36

= \frac{- 36}{2 \cdot 4}

数字相乘:

2 \cdot 4 = 8

= \frac{- 36}{8}

使用分式法则:

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

= - \frac{36}{8}

约分:

4

= - \frac{9}{2}

二次方程组的解是:

u = \frac{3}{2}, u = - \frac{9}{2}

u = tan (x)

代回

tan (x) = \frac{3}{2}, tan (x) = - \frac{9}{2}

tan (x) = \frac{3}{2}, tan (x) = - \frac{9}{2}

tan (x) = \frac{3}{2} : x = arctan (\frac{3}{2}) + πn

tan (x) = \frac{3}{2}

使用反三角函数性质

tan (x) = \frac{3}{2}

tan (x) = \frac{3}{2}

的通解

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

x = arctan (\frac{3}{2}) + πn

x = arctan (\frac{3}{2}) + πn

tan (x) = - \frac{9}{2} : x = arctan (- \frac{9}{2}) + πn

tan (x) = - \frac{9}{2}

使用反三角函数性质

tan (x) = - \frac{9}{2}

tan (x) = - \frac{9}{2}

的通解

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

x = arctan (- \frac{9}{2}) + πn

x = arctan (- \frac{9}{2}) + πn

合并所有解

x = arctan (\frac{3}{2}) + πn, x = arctan (- \frac{9}{2}) + πn

以小数形式表示解

x = 0.98279 \dots + πn, x = - 1.35212 \dots + πn

作图

流行的例子

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