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受欢迎的三角函数 >

cos^2(x)+4cos(x)+4=0

解答

cos^{2} (x) + 4 cos (x) + 4 = 0

解答

x \in R 无解

求解步骤

cos^{2} (x) + 4 cos (x) + 4 = 0

用替代法求解

cos^{2} (x) + 4 cos (x) + 4 = 0

令

: cos (x) = u

u^{2} + 4 u + 4 = 0

u^{2} + 4 u + 4 = 0 : u = - 2

u^{2} + 4 u + 4 = 0

使用求根公式求解

u^{2} + 4 u + 4 = 0

二次方程求根公式:

若

a = 1, b = 4, c = 4

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

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

4^{2} - 4 \cdot 1 \cdot 4 = 0

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

数字相乘:

4 \cdot 1 \cdot 4 = 16

= 4^{2} - 16

4^{2} = 16

= 16 - 16

数字相减:

16 - 16 = 0

= 0

u_{1, 2} = \frac{- 4 \pm 0}{2 \cdot 1}

u = \frac{- 4}{2 \cdot 1}

\frac{- 4}{2 \cdot 1} = - 2

\frac{- 4}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{- 4}{2}

使用分式法则:

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

= - \frac{4}{2}

数字相除:

\frac{4}{2} = 2

= - 2

u = - 2

二次方程组的解是:

u = - 2

u = cos (x)

代回

cos (x) = - 2

cos (x) = - 2

cos (x) = - 2 :

无解

cos (x) = - 2

- 1 \leq cos (x) \leq 1

无解

合并所有解

x \in R 无解

作图

流行的例子

2 cos (x) = tan (x)

sin^3(a)=3sin(a)-4sin^3(a)

sin^{3} (a) = 3 sin (a) - 4 sin^{3} (a)

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

solvefor x,arcsin(y)-arccos(x)=1

so l v e f or x, arcsin (y) - arccos (x) = 1

-6=-2+8sin(θ+pi/4)

- 6 = - 2 + 8 sin (θ + \frac{π}{4})