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受欢迎的三角函数 >

-3tan^2(θ)-4tan(θ)=-4

解答

- 3 tan^{2} (θ) - 4 tan (θ) = - 4

解答

θ = - 1.10714 \dots + πn, θ = 0.58800 \dots + πn

+1

度数

θ = - 63.43494 \dots^{\circ} + 18 0^{\circ} n, θ = 33.69006 \dots^{\circ} + 18 0^{\circ} n

求解步骤

- 3 tan^{2} (θ) - 4 tan (θ) = - 4

用替代法求解

- 3 tan^{2} (θ) - 4 tan (θ) = - 4

令

: tan (θ) = u

- 3 u^{2} - 4 u = - 4

- 3 u^{2} - 4 u = - 4 : u = - 2, u = \frac{2}{3}

- 3 u^{2} - 4 u = - 4

将

4

para o lado esquerdo

- 3 u^{2} - 4 u = - 4

两边加上

4

- 3 u^{2} - 4 u + 4 = - 4 + 4

化简

- 3 u^{2} - 4 u + 4 = 0

- 3 u^{2} - 4 u + 4 = 0

使用求根公式求解

- 3 u^{2} - 4 u + 4 = 0

二次方程求根公式:

若

a = - 3, b = - 4, c = 4

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

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

(- 4)^{2} - 4 (- 3) \cdot 4 = 8

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

使用法则

- (- a) = a

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

使用指数法则:

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

若

n

是偶数

(- 4)^{2} = 4^{2}

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

数字相乘:

4 \cdot 3 \cdot 4 = 48

= 4^{2} + 48

4^{2} = 16

= 16 + 48

数字相加:

16 + 48 = 64

= 64

因式分解数字:

64 = 8^{2}

= 8^{2}

使用根式运算法则:

n a^{n} = a

8^{2} = 8

= 8

u_{1, 2} = \frac{- ( - 4 ) \pm 8}{2 ( - 3 )}

将解分隔开

u_{1} = \frac{- ( - 4 ) + 8}{2 ( - 3 )}, u_{2} = \frac{- ( - 4 ) - 8}{2 ( - 3 )}

u = \frac{- ( - 4 ) + 8}{2 ( - 3 )} : - 2

\frac{- ( - 4 ) + 8}{2 ( - 3 )}

去除括号:

(- a) = - a, - (- a) = a

= \frac{4 + 8}{- 2 \cdot 3}

数字相加:

4 + 8 = 12

= \frac{12}{- 2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{12}{- 6}

使用分式法则:

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

= - \frac{12}{6}

数字相除:

\frac{12}{6} = 2

= - 2

u = \frac{- ( - 4 ) - 8}{2 ( - 3 )} : \frac{2}{3}

\frac{- ( - 4 ) - 8}{2 ( - 3 )}

去除括号:

(- a) = - a, - (- a) = a

= \frac{4 - 8}{- 2 \cdot 3}

数字相减:

4 - 8 = - 4

= \frac{- 4}{- 2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{- 4}{- 6}

使用分式法则:

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

= \frac{4}{6}

约分:

2

= \frac{2}{3}

二次方程组的解是:

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

u = tan (θ)

代回

tan (θ) = - 2, tan (θ) = \frac{2}{3}

tan (θ) = - 2, tan (θ) = \frac{2}{3}

tan (θ) = - 2 : θ = arctan (- 2) + πn

tan (θ) = - 2

使用反三角函数性质

tan (θ) = - 2

tan (θ) = - 2

的通解

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

θ = arctan (- 2) + πn

θ = arctan (- 2) + πn

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

tan (θ) = \frac{2}{3}

使用反三角函数性质

tan (θ) = \frac{2}{3}

tan (θ) = \frac{2}{3}

的通解

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

θ = arctan (\frac{2}{3}) + πn

θ = arctan (\frac{2}{3}) + πn

合并所有解

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

以小数形式表示解

θ = - 1.10714 \dots + πn, θ = 0.58800 \dots + πn

作图

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