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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

使用指数法则:

(- a)^{n} = a^{n},

若

n

是偶数

(- 4)^{2} = 4^{2}

= 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}

使用法则

- (- a) = a

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

数字相乘:

2 \cdot 1 = 2

= \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

csc(θ)=(sqrt(34))/3 ,cos(θ)>0

csc (θ) = \frac{34}{3}, cos (θ) > 0

sin^2(x)+4cos^2(x)=1

sin^{2} (x) + 4 cos^{2} (x) = 1

5sin^2(x)=9tan(x)

5 sin^{2} (x) = 9 tan (x)

cos (θ) = \frac{5}{4}

csc^2(x)=4cot^2(x)

csc^{2} (x) = 4 cot^{2} (x)