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受欢迎的三角函数 >

3tan^2(θ)+7tan(θ)-2=-4

解答

3 tan^{2} (θ) + 7 tan (θ) - 2 = - 4

解答

θ = - 0.32175 \dots + πn, θ = - 1.10714 \dots + πn

+1

度数

θ = - 18.43494 \dots^{\circ} + 18 0^{\circ} n, θ = - 63.43494 \dots^{\circ} + 18 0^{\circ} n

求解步骤

3 tan^{2} (θ) + 7 tan (θ) - 2 = - 4

用替代法求解

3 tan^{2} (θ) + 7 tan (θ) - 2 = - 4

令

: tan (θ) = u

3 u^{2} + 7 u - 2 = - 4

3 u^{2} + 7 u - 2 = - 4 : u = - \frac{1}{3}, u = - 2

3 u^{2} + 7 u - 2 = - 4

将

4

para o lado esquerdo

3 u^{2} + 7 u - 2 = - 4

两边加上

4

3 u^{2} + 7 u - 2 + 4 = - 4 + 4

化简

3 u^{2} + 7 u + 2 = 0

3 u^{2} + 7 u + 2 = 0

使用求根公式求解

3 u^{2} + 7 u + 2 = 0

二次方程求根公式:

若

a = 3, b = 7, c = 2

u_{1, 2} = \frac{- 7 \pm 7 ^{2} - 4 \cdot 3 \cdot 2}{2 \cdot 3}

u_{1, 2} = \frac{- 7 \pm 7 ^{2} - 4 \cdot 3 \cdot 2}{2 \cdot 3}

7^{2} - 4 \cdot 3 \cdot 2 = 5

7^{2} - 4 \cdot 3 \cdot 2

数字相乘:

4 \cdot 3 \cdot 2 = 24

= 7^{2} - 24

7^{2} = 49

= 49 - 24

数字相减:

49 - 24 = 25

= 25

因式分解数字:

25 = 5^{2}

= 5^{2}

使用根式运算法则:

n a^{n} = a

5^{2} = 5

= 5

u_{1, 2} = \frac{- 7 \pm 5}{2 \cdot 3}

将解分隔开

u_{1} = \frac{- 7 + 5}{2 \cdot 3}, u_{2} = \frac{- 7 - 5}{2 \cdot 3}

u = \frac{- 7 + 5}{2 \cdot 3} : - \frac{1}{3}

\frac{- 7 + 5}{2 \cdot 3}

数字相加/相减:

- 7 + 5 = - 2

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

数字相乘:

2 \cdot 3 = 6

= \frac{- 2}{6}

使用分式法则:

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

= - \frac{2}{6}

约分:

2

= - \frac{1}{3}

u = \frac{- 7 - 5}{2 \cdot 3} : - 2

\frac{- 7 - 5}{2 \cdot 3}

数字相减:

- 7 - 5 = - 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

二次方程组的解是:

u = - \frac{1}{3}, u = - 2

u = tan (θ)

代回

tan (θ) = - \frac{1}{3}, tan (θ) = - 2

tan (θ) = - \frac{1}{3}, tan (θ) = - 2

tan (θ) = - \frac{1}{3} : θ = arctan (- \frac{1}{3}) + πn

tan (θ) = - \frac{1}{3}

使用反三角函数性质

tan (θ) = - \frac{1}{3}

tan (θ) = - \frac{1}{3}

的通解

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

θ = arctan (- \frac{1}{3}) + πn

θ = arctan (- \frac{1}{3}) + πn

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

合并所有解

θ = arctan (- \frac{1}{3}) + πn, θ = arctan (- 2) + πn

以小数形式表示解

θ = - 0.32175 \dots + πn, θ = - 1.10714 \dots + πn

作图

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