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受欢迎的三角函数 >

tan^2(x)-3tan(x)-28=0

解答

tan^{2} (x) - 3 tan (x) - 28 = 0

解答

x = 1.42889 \dots + πn, x = - 1.32581 \dots + πn

+1

度数

x = 81.86989 \dots^{\circ} + 18 0^{\circ} n, x = - 75.96375 \dots^{\circ} + 18 0^{\circ} n

求解步骤

tan^{2} (x) - 3 tan (x) - 28 = 0

用替代法求解

tan^{2} (x) - 3 tan (x) - 28 = 0

令

: tan (x) = u

u^{2} - 3 u - 28 = 0

u^{2} - 3 u - 28 = 0 : u = 7, u = - 4

u^{2} - 3 u - 28 = 0

使用求根公式求解

u^{2} - 3 u - 28 = 0

二次方程求根公式:

若

a = 1, b = - 3, c = - 28

u_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 1 \cdot ( - 28 )}{2 \cdot 1}

u_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 1 \cdot ( - 28 )}{2 \cdot 1}

(- 3)^{2} - 4 \cdot 1 \cdot (- 28) = 11

(- 3)^{2} - 4 \cdot 1 \cdot (- 28)

使用法则

- (- a) = a

= (- 3)^{2} + 4 \cdot 1 \cdot 28

使用指数法则:

(- a)^{n} = a^{n},

若

n

是偶数

(- 3)^{2} = 3^{2}

= 3^{2} + 4 \cdot 1 \cdot 28

数字相乘:

4 \cdot 1 \cdot 28 = 112

= 3^{2} + 112

3^{2} = 9

= 9 + 112

数字相加:

9 + 112 = 121

= 121

因式分解数字:

121 = 1 1^{2}

= 1 1^{2}

使用根式运算法则:

1 1^{2} = 11

= 11

u_{1, 2} = \frac{- ( - 3 ) \pm 11}{2 \cdot 1}

将解分隔开

u_{1} = \frac{- ( - 3 ) + 11}{2 \cdot 1}, u_{2} = \frac{- ( - 3 ) - 11}{2 \cdot 1}

u = \frac{- ( - 3 ) + 11}{2 \cdot 1} : 7

\frac{- ( - 3 ) + 11}{2 \cdot 1}

使用法则

- (- a) = a

= \frac{3 + 11}{2 \cdot 1}

数字相加:

3 + 11 = 14

= \frac{14}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{14}{2}

数字相除:

\frac{14}{2} = 7

= 7

u = \frac{- ( - 3 ) - 11}{2 \cdot 1} : - 4

\frac{- ( - 3 ) - 11}{2 \cdot 1}

使用法则

- (- a) = a

= \frac{3 - 11}{2 \cdot 1}

数字相减:

3 - 11 = - 8

= \frac{- 8}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{- 8}{2}

使用分式法则:

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

= - \frac{8}{2}

数字相除:

\frac{8}{2} = 4

= - 4

二次方程组的解是:

u = 7, u = - 4

u = tan (x)

代回

tan (x) = 7, tan (x) = - 4

tan (x) = 7, tan (x) = - 4

tan (x) = 7 : x = arctan (7) + πn

tan (x) = 7

使用反三角函数性质

tan (x) = 7

tan (x) = 7

的通解

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

x = arctan (7) + πn

x = arctan (7) + πn

tan (x) = - 4 : x = arctan (- 4) + πn

tan (x) = - 4

使用反三角函数性质

tan (x) = - 4

tan (x) = - 4

的通解

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

x = arctan (- 4) + πn

x = arctan (- 4) + πn

合并所有解

x = arctan (7) + πn, x = arctan (- 4) + πn

以小数形式表示解

x = 1.42889 \dots + πn, x = - 1.32581 \dots + πn

作图

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