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受欢迎的三角函数 >

4tan^2(θ)+5tan(θ)=6

解答

4 tan^{2} (θ) + 5 tan (θ) = 6

解答

θ = 0.64350 \dots + πn, θ = - 1.10714 \dots + πn

+1

度数

θ = 36.86989 \dots^{\circ} + 18 0^{\circ} n, θ = - 63.43494 \dots^{\circ} + 18 0^{\circ} n

求解步骤

4 tan^{2} (θ) + 5 tan (θ) = 6

用替代法求解

4 tan^{2} (θ) + 5 tan (θ) = 6

令

: tan (θ) = u

4 u^{2} + 5 u = 6

4 u^{2} + 5 u = 6 : u = \frac{3}{4}, u = - 2

4 u^{2} + 5 u = 6

将

6

para o lado esquerdo

4 u^{2} + 5 u = 6

两边减去

6

4 u^{2} + 5 u - 6 = 6 - 6

化简

4 u^{2} + 5 u - 6 = 0

4 u^{2} + 5 u - 6 = 0

使用求根公式求解

4 u^{2} + 5 u - 6 = 0

二次方程求根公式:

若

a = 4, b = 5, c = - 6

u_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 4 ( - 6 )}{2 \cdot 4}

u_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 4 ( - 6 )}{2 \cdot 4}

5^{2} - 4 \cdot 4 (- 6) = 11

5^{2} - 4 \cdot 4 (- 6)

使用法则

- (- a) = a

= 5^{2} + 4 \cdot 4 \cdot 6

数字相乘:

4 \cdot 4 \cdot 6 = 96

= 5^{2} + 96

5^{2} = 25

= 25 + 96

数字相加:

25 + 96 = 121

= 121

因式分解数字:

121 = 1 1^{2}

= 1 1^{2}

使用根式运算法则:

n a^{n} = a

1 1^{2} = 11

= 11

u_{1, 2} = \frac{- 5 \pm 11}{2 \cdot 4}

将解分隔开

u_{1} = \frac{- 5 + 11}{2 \cdot 4}, u_{2} = \frac{- 5 - 11}{2 \cdot 4}

u = \frac{- 5 + 11}{2 \cdot 4} : \frac{3}{4}

\frac{- 5 + 11}{2 \cdot 4}

数字相加/相减:

- 5 + 11 = 6

= \frac{6}{2 \cdot 4}

数字相乘:

2 \cdot 4 = 8

= \frac{6}{8}

约分:

2

= \frac{3}{4}

u = \frac{- 5 - 11}{2 \cdot 4} : - 2

\frac{- 5 - 11}{2 \cdot 4}

数字相减:

- 5 - 11 = - 16

= \frac{- 16}{2 \cdot 4}

数字相乘:

2 \cdot 4 = 8

= \frac{- 16}{8}

使用分式法则:

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

= - \frac{16}{8}

数字相除:

\frac{16}{8} = 2

= - 2

二次方程组的解是:

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

u = tan (θ)

代回

tan (θ) = \frac{3}{4}, tan (θ) = - 2

tan (θ) = \frac{3}{4}, tan (θ) = - 2

tan (θ) = \frac{3}{4} : θ = arctan (\frac{3}{4}) + πn

tan (θ) = \frac{3}{4}

使用反三角函数性质

tan (θ) = \frac{3}{4}

tan (θ) = \frac{3}{4}

的通解

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

θ = arctan (\frac{3}{4}) + πn

θ = arctan (\frac{3}{4}) + 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{3}{4}) + πn, θ = arctan (- 2) + πn

以小数形式表示解

θ = 0.64350 \dots + πn, θ = - 1.10714 \dots + πn

作图

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