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受欢迎的三角函数 >

tan^2(θ)+9tan(θ)+18=0

解答

tan^{2} (θ) + 9 tan (θ) + 18 = 0

解答

θ = - 1.24904 \dots + πn, θ = - 1.40564 \dots + πn

+1

度数

θ = - 71.56505 \dots^{\circ} + 18 0^{\circ} n, θ = - 80.53767 \dots^{\circ} + 18 0^{\circ} n

求解步骤

tan^{2} (θ) + 9 tan (θ) + 18 = 0

用替代法求解

tan^{2} (θ) + 9 tan (θ) + 18 = 0

令

: tan (θ) = u

u^{2} + 9 u + 18 = 0

u^{2} + 9 u + 18 = 0 : u = - 3, u = - 6

u^{2} + 9 u + 18 = 0

使用求根公式求解

u^{2} + 9 u + 18 = 0

二次方程求根公式:

若

a = 1, b = 9, c = 18

u_{1, 2} = \frac{- 9 \pm 9 ^{2} - 4 \cdot 1 \cdot 18}{2 \cdot 1}

u_{1, 2} = \frac{- 9 \pm 9 ^{2} - 4 \cdot 1 \cdot 18}{2 \cdot 1}

9^{2} - 4 \cdot 1 \cdot 18 = 3

9^{2} - 4 \cdot 1 \cdot 18

数字相乘:

4 \cdot 1 \cdot 18 = 72

= 9^{2} - 72

9^{2} = 81

= 81 - 72

数字相减:

81 - 72 = 9

= 9

因式分解数字:

9 = 3^{2}

= 3^{2}

使用根式运算法则:

n a^{n} = a

3^{2} = 3

= 3

u_{1, 2} = \frac{- 9 \pm 3}{2 \cdot 1}

将解分隔开

u_{1} = \frac{- 9 + 3}{2 \cdot 1}, u_{2} = \frac{- 9 - 3}{2 \cdot 1}

u = \frac{- 9 + 3}{2 \cdot 1} : - 3

\frac{- 9 + 3}{2 \cdot 1}

数字相加/相减:

- 9 + 3 = - 6

= \frac{- 6}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{- 6}{2}

使用分式法则:

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

= - \frac{6}{2}

数字相除:

\frac{6}{2} = 3

= - 3

u = \frac{- 9 - 3}{2 \cdot 1} : - 6

\frac{- 9 - 3}{2 \cdot 1}

数字相减:

- 9 - 3 = - 12

= \frac{- 12}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{- 12}{2}

使用分式法则:

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

= - \frac{12}{2}

数字相除:

\frac{12}{2} = 6

= - 6

二次方程组的解是:

u = - 3, u = - 6

u = tan (θ)

代回

tan (θ) = - 3, tan (θ) = - 6

tan (θ) = - 3, tan (θ) = - 6

tan (θ) = - 3 : θ = arctan (- 3) + πn

tan (θ) = - 3

使用反三角函数性质

tan (θ) = - 3

tan (θ) = - 3

的通解

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

θ = arctan (- 3) + πn

θ = arctan (- 3) + πn

tan (θ) = - 6 : θ = arctan (- 6) + πn

tan (θ) = - 6

使用反三角函数性质

tan (θ) = - 6

tan (θ) = - 6

的通解

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

θ = arctan (- 6) + πn

θ = arctan (- 6) + πn

合并所有解

θ = arctan (- 3) + πn, θ = arctan (- 6) + πn

以小数形式表示解

θ = - 1.24904 \dots + πn, θ = - 1.40564 \dots + πn

作图

流行的例子

cos^2(θ)-sin^2(θ)=-sin(θ)+1

cos^{2} (θ) - sin^{2} (θ) = - sin (θ) + 1

2 sin (θ) + 6 = 7

8 cos (12 x) + 4 = - 4

12tan^3(x)=4tan(x)

12 tan^{3} (x) = 4 tan (x)

cos(2θ)=3sin(θ)-1

cos (2 θ) = 3 sin (θ) - 1