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受欢迎的三角函数 >

tan^2(x)+3tan(x)=-1

解答

tan^{2} (x) + 3 tan (x) = - 1

解答

x = - 0.36486 \dots + πn, x = - 1.20593 \dots + πn

+1

度数

x = - 20.90515 \dots^{\circ} + 18 0^{\circ} n, x = - 69.09484 \dots^{\circ} + 18 0^{\circ} n

求解步骤

tan^{2} (x) + 3 tan (x) = - 1

用替代法求解

tan^{2} (x) + 3 tan (x) = - 1

令

: tan (x) = u

u^{2} + 3 u = - 1

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

u^{2} + 3 u = - 1

将

1

para o lado esquerdo

u^{2} + 3 u = - 1

两边加上

1

u^{2} + 3 u + 1 = - 1 + 1

化简

u^{2} + 3 u + 1 = 0

u^{2} + 3 u + 1 = 0

使用求根公式求解

u^{2} + 3 u + 1 = 0

二次方程求根公式:

若

a = 1, b = 3, c = 1

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

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

3^{2} - 4 \cdot 1 \cdot 1 = 5

3^{2} - 4 \cdot 1 \cdot 1

数字相乘:

4 \cdot 1 \cdot 1 = 4

= 3^{2} - 4

3^{2} = 9

= 9 - 4

数字相减:

9 - 4 = 5

= 5

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

将解分隔开

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

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

\frac{- 3 + 5}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{- 3 + 5}{2}

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

\frac{- 3 - 5}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{- 3 - 5}{2}

二次方程组的解是:

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

u = tan (x)

代回

tan (x) = \frac{- 3 + 5}{2}, tan (x) = \frac{- 3 - 5}{2}

tan (x) = \frac{- 3 + 5}{2}, tan (x) = \frac{- 3 - 5}{2}

tan (x) = \frac{- 3 + 5}{2} : x = arctan (\frac{- 3 + 5}{2}) + πn

tan (x) = \frac{- 3 + 5}{2}

使用反三角函数性质

tan (x) = \frac{- 3 + 5}{2}

tan (x) = \frac{- 3 + 5}{2}

的通解

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

x = arctan (\frac{- 3 + 5}{2}) + πn

x = arctan (\frac{- 3 + 5}{2}) + πn

tan (x) = \frac{- 3 - 5}{2} : x = arctan (\frac{- 3 - 5}{2}) + πn

tan (x) = \frac{- 3 - 5}{2}

使用反三角函数性质

tan (x) = \frac{- 3 - 5}{2}

tan (x) = \frac{- 3 - 5}{2}

的通解

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

x = arctan (\frac{- 3 - 5}{2}) + πn

x = arctan (\frac{- 3 - 5}{2}) + πn

合并所有解

x = arctan (\frac{- 3 + 5}{2}) + πn, x = arctan (\frac{- 3 - 5}{2}) + πn

以小数形式表示解

x = - 0.36486 \dots + πn, x = - 1.20593 \dots + πn

作图

流行的例子

7 sin (x) - 4 = 0

(sin(x)-2)(cos(x)+7)=0

(sin (x) - 2) (cos (x) + 7) = 0

-4tan(θ)-10=4tan(θ)-7

- 4 tan (θ) - 10 = 4 tan (θ) - 7

sin(x)=sin(x^2)

sin (x) = sin (x^{2})

sin (x) = - 0.23