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受欢迎的三角函数 >

2sin^2(x)+5sin(x)-12=0

解答

2 sin^{2} (x) + 5 sin (x) - 12 = 0

解答

x \in R 无解

求解步骤

2 sin^{2} (x) + 5 sin (x) - 12 = 0

用替代法求解

2 sin^{2} (x) + 5 sin (x) - 12 = 0

令

: sin (x) = u

2 u^{2} + 5 u - 12 = 0

2 u^{2} + 5 u - 12 = 0 : u = \frac{3}{2}, u = - 4

2 u^{2} + 5 u - 12 = 0

使用求根公式求解

2 u^{2} + 5 u - 12 = 0

二次方程求根公式:

若

a = 2, b = 5, c = - 12

u_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 2 ( - 12 )}{2 \cdot 2}

u_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 2 ( - 12 )}{2 \cdot 2}

5^{2} - 4 \cdot 2 (- 12) = 11

5^{2} - 4 \cdot 2 (- 12)

使用法则

- (- a) = a

= 5^{2} + 4 \cdot 2 \cdot 12

数字相乘:

4 \cdot 2 \cdot 12 = 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 2}

将解分隔开

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

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

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

数字相加/相减:

- 5 + 11 = 6

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

数字相乘:

2 \cdot 2 = 4

= \frac{6}{4}

约分:

2

= \frac{3}{2}

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

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

数字相减:

- 5 - 11 = - 16

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

数字相乘:

2 \cdot 2 = 4

= \frac{- 16}{4}

使用分式法则:

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

= - \frac{16}{4}

数字相除:

\frac{16}{4} = 4

= - 4

二次方程组的解是:

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

u = sin (x)

代回

sin (x) = \frac{3}{2}, sin (x) = - 4

sin (x) = \frac{3}{2}, sin (x) = - 4

sin (x) = \frac{3}{2} :

无解

sin (x) = \frac{3}{2}

- 1 \leq sin (x) \leq 1

无解

sin (x) = - 4 :

无解

sin (x) = - 4

- 1 \leq sin (x) \leq 1

无解

合并所有解

x \in R 无解

作图

流行的例子

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3 tan (x - \frac{π}{5}) - 1 = 0

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tan (θ) = \frac{17}{12}

csc^2(θ)=2cot(θ)

csc^{2} (θ) = 2 cot (θ)

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