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受欢迎的三角函数 >

tan^2(x)+tan(x)-12=2

解答

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

解答

x = 1.27443 \dots + πn, x = - 1.34100 \dots + πn

+1

度数

x = 73.01988 \dots^{\circ} + 18 0^{\circ} n, x = - 76.83395 \dots^{\circ} + 18 0^{\circ} n

求解步骤

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

用替代法求解

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

令

: tan (x) = u

u^{2} + u - 12 = 2

u^{2} + u - 12 = 2 : u = \frac{- 1 + 57}{2}, u = \frac{- 1 - 57}{2}

u^{2} + u - 12 = 2

将

2

para o lado esquerdo

u^{2} + u - 12 = 2

两边减去

2

u^{2} + u - 12 - 2 = 2 - 2

化简

u^{2} + u - 14 = 0

u^{2} + u - 14 = 0

使用求根公式求解

u^{2} + u - 14 = 0

二次方程求根公式:

若

a = 1, b = 1, c = - 14

u_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot ( - 14 )}{2 \cdot 1}

u_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot ( - 14 )}{2 \cdot 1}

1^{2} - 4 \cdot 1 \cdot (- 14) = 57

1^{2} - 4 \cdot 1 \cdot (- 14)

使用法则

1^{a} = 1

1^{2} = 1

= 1 - 4 \cdot 1 \cdot (- 14)

使用法则

- (- a) = a

= 1 + 4 \cdot 1 \cdot 14

数字相乘:

4 \cdot 1 \cdot 14 = 56

= 1 + 56

数字相加:

1 + 56 = 57

= 57

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

将解分隔开

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

u = \frac{- 1 + 57}{2 \cdot 1} : \frac{- 1 + 57}{2}

\frac{- 1 + 57}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{- 1 + 57}{2}

u = \frac{- 1 - 57}{2 \cdot 1} : \frac{- 1 - 57}{2}

\frac{- 1 - 57}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{- 1 - 57}{2}

二次方程组的解是:

u = \frac{- 1 + 57}{2}, u = \frac{- 1 - 57}{2}

u = tan (x)

代回

tan (x) = \frac{- 1 + 57}{2}, tan (x) = \frac{- 1 - 57}{2}

tan (x) = \frac{- 1 + 57}{2}, tan (x) = \frac{- 1 - 57}{2}

tan (x) = \frac{- 1 + 57}{2} : x = arctan (\frac{- 1 + 57}{2}) + πn

tan (x) = \frac{- 1 + 57}{2}

使用反三角函数性质

tan (x) = \frac{- 1 + 57}{2}

tan (x) = \frac{- 1 + 57}{2}

的通解

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

x = arctan (\frac{- 1 + 57}{2}) + πn

x = arctan (\frac{- 1 + 57}{2}) + πn

tan (x) = \frac{- 1 - 57}{2} : x = arctan (\frac{- 1 - 57}{2}) + πn

tan (x) = \frac{- 1 - 57}{2}

使用反三角函数性质

tan (x) = \frac{- 1 - 57}{2}

tan (x) = \frac{- 1 - 57}{2}

的通解

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

x = arctan (\frac{- 1 - 57}{2}) + πn

x = arctan (\frac{- 1 - 57}{2}) + πn

合并所有解

x = arctan (\frac{- 1 + 57}{2}) + πn, x = arctan (\frac{- 1 - 57}{2}) + πn

以小数形式表示解

x = 1.27443 \dots + πn, x = - 1.34100 \dots + πn

作图

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