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受欢迎的三角函数 >

cos^2(x)+6cos(x)+5=0

解答

cos^{2} (x) + 6 cos (x) + 5 = 0

解答

x = π + 2 πn

+1

度数

x = 18 0^{\circ} + 36 0^{\circ} n

求解步骤

cos^{2} (x) + 6 cos (x) + 5 = 0

用替代法求解

cos^{2} (x) + 6 cos (x) + 5 = 0

令

: cos (x) = u

u^{2} + 6 u + 5 = 0

u^{2} + 6 u + 5 = 0 : u = - 1, u = - 5

u^{2} + 6 u + 5 = 0

使用求根公式求解

u^{2} + 6 u + 5 = 0

二次方程求根公式:

若

a = 1, b = 6, c = 5

u_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 \cdot 1 \cdot 5}{2 \cdot 1}

u_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 \cdot 1 \cdot 5}{2 \cdot 1}

6^{2} - 4 \cdot 1 \cdot 5 = 4

6^{2} - 4 \cdot 1 \cdot 5

数字相乘:

4 \cdot 1 \cdot 5 = 20

= 6^{2} - 20

6^{2} = 36

= 36 - 20

数字相减:

36 - 20 = 16

= 16

因式分解数字:

16 = 4^{2}

= 4^{2}

使用根式运算法则:

n a^{n} = a

4^{2} = 4

= 4

u_{1, 2} = \frac{- 6 \pm 4}{2 \cdot 1}

将解分隔开

u_{1} = \frac{- 6 + 4}{2 \cdot 1}, u_{2} = \frac{- 6 - 4}{2 \cdot 1}

u = \frac{- 6 + 4}{2 \cdot 1} : - 1

\frac{- 6 + 4}{2 \cdot 1}

数字相加/相减:

- 6 + 4 = - 2

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

数字相乘:

2 \cdot 1 = 2

= \frac{- 2}{2}

使用分式法则:

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

= - \frac{2}{2}

使用法则

\frac{a}{a} = 1

= - 1

u = \frac{- 6 - 4}{2 \cdot 1} : - 5

\frac{- 6 - 4}{2 \cdot 1}

数字相减:

- 6 - 4 = - 10

= \frac{- 10}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{- 10}{2}

使用分式法则:

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

= - \frac{10}{2}

数字相除:

\frac{10}{2} = 5

= - 5

二次方程组的解是:

u = - 1, u = - 5

u = cos (x)

代回

cos (x) = - 1, cos (x) = - 5

cos (x) = - 1, cos (x) = - 5

cos (x) = - 1 : x = π + 2 πn

cos (x) = - 1

cos (x) = - 1

的通解

cos (x)

周期表（周期为

2 πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = π + 2 πn

x = π + 2 πn

cos (x) = - 5 :

无解

cos (x) = - 5

- 1 \leq cos (x) \leq 1

无解

合并所有解

x = π + 2 πn

作图

流行的例子

sin (t) = - 0.9397

tan^2(x)=2sec^2(x)-3

tan^{2} (x) = 2 sec^{2} (x) - 3

sinh(x)+4=4cosh(x)

sinh (x) + 4 = 4 cosh (x)

sin (18 x) = - 1

solvefor x,y+sin(xy)=1

so l v e f or x, y + sin (x y) = 1