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受欢迎的三角函数 >

3tan^2(x)+5tan(x)-4=0

解答

3 tan^{2} (x) + 5 tan (x) - 4 = 0

解答

x = 0.53352 \dots + πn, x = - 1.15377 \dots + πn

+1

度数

x = 30.56895 \dots^{\circ} + 18 0^{\circ} n, x = - 66.10663 \dots^{\circ} + 18 0^{\circ} n

求解步骤

3 tan^{2} (x) + 5 tan (x) - 4 = 0

用替代法求解

3 tan^{2} (x) + 5 tan (x) - 4 = 0

令

: tan (x) = u

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

3 u^{2} + 5 u - 4 = 0 : u = \frac{- 5 + 73}{6}, u = \frac{- 5 - 73}{6}

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

使用求根公式求解

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

二次方程求根公式:

若

a = 3, b = 5, c = - 4

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

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

5^{2} - 4 \cdot 3 (- 4) = 73

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

使用法则

- (- a) = a

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

数字相乘:

4 \cdot 3 \cdot 4 = 48

= 5^{2} + 48

5^{2} = 25

= 25 + 48

数字相加:

25 + 48 = 73

= 73

u_{1, 2} = \frac{- 5 \pm 73}{2 \cdot 3}

将解分隔开

u_{1} = \frac{- 5 + 73}{2 \cdot 3}, u_{2} = \frac{- 5 - 73}{2 \cdot 3}

u = \frac{- 5 + 73}{2 \cdot 3} : \frac{- 5 + 73}{6}

\frac{- 5 + 73}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{- 5 + 73}{6}

u = \frac{- 5 - 73}{2 \cdot 3} : \frac{- 5 - 73}{6}

\frac{- 5 - 73}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{- 5 - 73}{6}

二次方程组的解是:

u = \frac{- 5 + 73}{6}, u = \frac{- 5 - 73}{6}

u = tan (x)

代回

tan (x) = \frac{- 5 + 73}{6}, tan (x) = \frac{- 5 - 73}{6}

tan (x) = \frac{- 5 + 73}{6}, tan (x) = \frac{- 5 - 73}{6}

tan (x) = \frac{- 5 + 73}{6} : x = arctan (\frac{- 5 + 73}{6}) + πn

tan (x) = \frac{- 5 + 73}{6}

使用反三角函数性质

tan (x) = \frac{- 5 + 73}{6}

tan (x) = \frac{- 5 + 73}{6}

的通解

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

x = arctan (\frac{- 5 + 73}{6}) + πn

x = arctan (\frac{- 5 + 73}{6}) + πn

tan (x) = \frac{- 5 - 73}{6} : x = arctan (\frac{- 5 - 73}{6}) + πn

tan (x) = \frac{- 5 - 73}{6}

使用反三角函数性质

tan (x) = \frac{- 5 - 73}{6}

tan (x) = \frac{- 5 - 73}{6}

的通解

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

x = arctan (\frac{- 5 - 73}{6}) + πn

x = arctan (\frac{- 5 - 73}{6}) + πn

合并所有解

x = arctan (\frac{- 5 + 73}{6}) + πn, x = arctan (\frac{- 5 - 73}{6}) + πn

以小数形式表示解

x = 0.53352 \dots + πn, x = - 1.15377 \dots + πn

作图

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