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受欢迎的三角函数 >

2tan^2(x)-tan(x)-6=0

解答

2 tan^{2} (x) - tan (x) - 6 = 0

解答

x = 1.10714 \dots + πn, x = - 0.98279 \dots + πn

+1

度数

x = 63.43494 \dots^{\circ} + 18 0^{\circ} n, x = - 56.30993 \dots^{\circ} + 18 0^{\circ} n

求解步骤

2 tan^{2} (x) - tan (x) - 6 = 0

用替代法求解

2 tan^{2} (x) - tan (x) - 6 = 0

令

: tan (x) = u

2 u^{2} - u - 6 = 0

2 u^{2} - u - 6 = 0 : u = 2, u = - \frac{3}{2}

2 u^{2} - u - 6 = 0

使用求根公式求解

2 u^{2} - u - 6 = 0

二次方程求根公式:

若

a = 2, b = - 1, c = - 6

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

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

(- 1)^{2} - 4 \cdot 2 (- 6) = 7

(- 1)^{2} - 4 \cdot 2 (- 6)

使用法则

- (- a) = a

= (- 1)^{2} + 4 \cdot 2 \cdot 6

(- 1)^{2} = 1

(- 1)^{2}

使用指数法则:

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

若

n

是偶数

(- 1)^{2} = 1^{2}

= 1^{2}

使用法则

1^{a} = 1

= 1

4 \cdot 2 \cdot 6 = 48

4 \cdot 2 \cdot 6

数字相乘:

4 \cdot 2 \cdot 6 = 48

= 48

= 1 + 48

数字相加:

1 + 48 = 49

= 49

因式分解数字:

49 = 7^{2}

= 7^{2}

使用根式运算法则:

n a^{n} = a

7^{2} = 7

= 7

u_{1, 2} = \frac{- ( - 1 ) \pm 7}{2 \cdot 2}

将解分隔开

u_{1} = \frac{- ( - 1 ) + 7}{2 \cdot 2}, u_{2} = \frac{- ( - 1 ) - 7}{2 \cdot 2}

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

\frac{- ( - 1 ) + 7}{2 \cdot 2}

使用法则

- (- a) = a

= \frac{1 + 7}{2 \cdot 2}

数字相加:

1 + 7 = 8

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

数字相乘:

2 \cdot 2 = 4

= \frac{8}{4}

数字相除:

\frac{8}{4} = 2

= 2

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

\frac{- ( - 1 ) - 7}{2 \cdot 2}

使用法则

- (- a) = a

= \frac{1 - 7}{2 \cdot 2}

数字相减:

1 - 7 = - 6

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

数字相乘:

2 \cdot 2 = 4

= \frac{- 6}{4}

使用分式法则:

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

= - \frac{6}{4}

约分:

2

= - \frac{3}{2}

二次方程组的解是:

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

u = tan (x)

代回

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

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

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) = - \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

合并所有解

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

以小数形式表示解

x = 1.10714 \dots + πn, x = - 0.98279 \dots + πn

作图

流行的例子

15cos(x)+8=-cos(x)

15 cos (x) + 8 = - cos (x)

cos(2x+pi/6)=(sqrt(3))/2

cos (2 x + \frac{π}{6}) = \frac{3}{2}

4 sin (x) - 2 = 0

cos (2 x) = 3

tan (3 x) + 1 = 0