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受欢迎的三角函数 >

2cos^2(x)-cos(x)-3=0

解答

2 cos^{2} (x) - cos (x) - 3 = 0

解答

x = π + 2 πn

+1

度数

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

求解步骤

2 cos^{2} (x) - cos (x) - 3 = 0

用替代法求解

2 cos^{2} (x) - cos (x) - 3 = 0

令

: cos (x) = u

2 u^{2} - u - 3 = 0

2 u^{2} - u - 3 = 0 : u = \frac{3}{2}, u = - 1

2 u^{2} - u - 3 = 0

使用求根公式求解

2 u^{2} - u - 3 = 0

二次方程求根公式:

若

a = 2, b = - 1, c = - 3

u_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 2 ( - 3 )}{2 \cdot 2}

u_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 2 ( - 3 )}{2 \cdot 2}

(- 1)^{2} - 4 \cdot 2 (- 3) = 5

(- 1)^{2} - 4 \cdot 2 (- 3)

使用法则

- (- a) = a

= (- 1)^{2} + 4 \cdot 2 \cdot 3

(- 1)^{2} = 1

(- 1)^{2}

使用指数法则:

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

若

n

是偶数

(- 1)^{2} = 1^{2}

= 1^{2}

使用法则

1^{a} = 1

= 1

4 \cdot 2 \cdot 3 = 24

4 \cdot 2 \cdot 3

数字相乘:

4 \cdot 2 \cdot 3 = 24

= 24

= 1 + 24

数字相加:

1 + 24 = 25

= 25

因式分解数字:

25 = 5^{2}

= 5^{2}

使用根式运算法则:

n a^{n} = a

5^{2} = 5

= 5

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

将解分隔开

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

u = \frac{- ( - 1 ) + 5}{2 \cdot 2} : \frac{3}{2}

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

使用法则

- (- a) = a

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

数字相加:

1 + 5 = 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{- ( - 1 ) - 5}{2 \cdot 2} : - 1

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

使用法则

- (- a) = a

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

数字相减:

1 - 5 = - 4

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

数字相乘:

2 \cdot 2 = 4

= \frac{- 4}{4}

使用分式法则:

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

= - \frac{4}{4}

使用法则

\frac{a}{a} = 1

= - 1

二次方程组的解是:

u = \frac{3}{2}, u = - 1

u = cos (x)

代回

cos (x) = \frac{3}{2}, cos (x) = - 1

cos (x) = \frac{3}{2}, cos (x) = - 1

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

无解

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

- 1 \leq cos (x) \leq 1

无解

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

合并所有解

x = π + 2 πn

作图

流行的例子

arcsin(x)= pi/7

arcsin (x) = \frac{π}{7}

2 sin (2 θ) = - 1

sin(4θ)=-(2sqrt(3))/3

sin (4 θ) = - \frac{2 3}{3}

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

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

cot (θ) = \frac{1}{3}