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受欢迎的三角函数 >

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

解答

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

解答

x \in R 无解

求解步骤

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

用替代法求解

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

令

: sin (x) = u

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

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

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

使用求根公式求解

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

二次方程求根公式:

若

a = 1, b = 5, c = 5

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

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

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

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

数字相乘:

4 \cdot 1 \cdot 5 = 20

= 5^{2} - 20

5^{2} = 25

= 25 - 20

数字相减:

25 - 20 = 5

= 5

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

将解分隔开

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

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

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

数字相乘:

2 \cdot 1 = 2

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

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

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

数字相乘:

2 \cdot 1 = 2

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

二次方程组的解是:

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

u = sin (x)

代回

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

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

sin (x) = \frac{- 5 + 5}{2} :

无解

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

- 1 \leq sin (x) \leq 1

无解

sin (x) = \frac{- 5 - 5}{2} :

无解

sin (x) = \frac{- 5 - 5}{2}

- 1 \leq sin (x) \leq 1

无解

合并所有解

x \in R 无解

作图

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