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受欢迎的三角函数 >

3tan^2(θ)+5tan(θ)=2

解答

3 tan^{2} (θ) + 5 tan (θ) = 2

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) + 5 tan (θ) = 2

用替代法求解

3 tan^{2} (θ) + 5 tan (θ) = 2

令

: tan (θ) = u

3 u^{2} + 5 u = 2

3 u^{2} + 5 u = 2 : u = \frac{1}{3}, u = - 2

3 u^{2} + 5 u = 2

将

2

para o lado esquerdo

3 u^{2} + 5 u = 2

两边减去

2

3 u^{2} + 5 u - 2 = 2 - 2

化简

3 u^{2} + 5 u - 2 = 0

3 u^{2} + 5 u - 2 = 0

使用求根公式求解

3 u^{2} + 5 u - 2 = 0

二次方程求根公式:

若

a = 3, b = 5, c = - 2

u_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 3 ( - 2 )}{2 \cdot 3}

u_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 3 ( - 2 )}{2 \cdot 3}

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

5^{2} - 4 \cdot 3 (- 2)

使用法则

- (- a) = a

= 5^{2} + 4 \cdot 3 \cdot 2

数字相乘:

4 \cdot 3 \cdot 2 = 24

= 5^{2} + 24

5^{2} = 25

= 25 + 24

数字相加:

25 + 24 = 49

= 49

因式分解数字:

49 = 7^{2}

= 7^{2}

使用根式运算法则:

n a^{n} = a

7^{2} = 7

= 7

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

将解分隔开

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

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

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

数字相加/相减:

- 5 + 7 = 2

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

数字相乘:

2 \cdot 3 = 6

= \frac{2}{6}

约分:

2

= \frac{1}{3}

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

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

数字相减:

- 5 - 7 = - 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

流行的例子

cos^2(x)+4cos(x)=-3

cos^{2} (x) + 4 cos (x) = - 3

tan (θ) = \frac{11}{9}

tan (θ) = \frac{11}{5}

2(sin(x))^2-5cos(x)-4=0

2 (sin (x))^{2} - 5 cos (x) - 4 = 0

arctan(x)+arctan(2)=arctan(7)

arctan (x) + arctan (2) = arctan (7)