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受欢迎的三角函数 >

3cos^2(θ)-cos(θ)-4=0

解答

3 cos^{2} (θ) - cos (θ) - 4 = 0

解答

θ = π + 2 πn

+1

度数

θ = 18 0^{\circ} + 36 0^{\circ} n

求解步骤

3 cos^{2} (θ) - cos (θ) - 4 = 0

用替代法求解

3 cos^{2} (θ) - cos (θ) - 4 = 0

令

: cos (θ) = u

3 u^{2} - u - 4 = 0

3 u^{2} - u - 4 = 0 : u = \frac{4}{3}, u = - 1

3 u^{2} - u - 4 = 0

使用求根公式求解

3 u^{2} - u - 4 = 0

二次方程求根公式:

若

a = 3, b = - 1, c = - 4

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

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

(- 1)^{2} - 4 \cdot 3 (- 4) = 7

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

使用法则

- (- a) = a

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

(- 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 3 \cdot 4 = 48

4 \cdot 3 \cdot 4

数字相乘:

4 \cdot 3 \cdot 4 = 48

= 48

= 1 + 48

数字相加:

1 + 48 = 49

= 49

因式分解数字:

49 = 7^{2}

= 7^{2}

使用根式运算法则:

n a^{n} = a

7^{2} = 7

= 7

u_{1, 2} = \frac{- ( - 1 ) \pm 7}{2 \cdot 3}

将解分隔开

u_{1} = \frac{- ( - 1 ) + 7}{2 \cdot 3}, u_{2} = \frac{- ( - 1 ) - 7}{2 \cdot 3}

u = \frac{- ( - 1 ) + 7}{2 \cdot 3} : \frac{4}{3}

\frac{- ( - 1 ) + 7}{2 \cdot 3}

使用法则

- (- a) = a

= \frac{1 + 7}{2 \cdot 3}

数字相加:

1 + 7 = 8

= \frac{8}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{8}{6}

约分:

2

= \frac{4}{3}

u = \frac{- ( - 1 ) - 7}{2 \cdot 3} : - 1

\frac{- ( - 1 ) - 7}{2 \cdot 3}

使用法则

- (- a) = a

= \frac{1 - 7}{2 \cdot 3}

数字相减:

1 - 7 = - 6

= \frac{- 6}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{- 6}{6}

使用分式法则:

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

= - \frac{6}{6}

使用法则

\frac{a}{a} = 1

= - 1

二次方程组的解是:

u = \frac{4}{3}, u = - 1

u = cos (θ)

代回

cos (θ) = \frac{4}{3}, cos (θ) = - 1

cos (θ) = \frac{4}{3}, cos (θ) = - 1

cos (θ) = \frac{4}{3} :

无解

cos (θ) = \frac{4}{3}

- 1 \leq cos (x) \leq 1

无解

cos (θ) = - 1 : θ = π + 2 πn

cos (θ) = - 1

cos (θ) = - 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}

θ = π + 2 πn

θ = π + 2 πn

合并所有解

θ = π + 2 πn

作图

流行的例子

tan(4x)=tan(2x)

tan (4 x) = tan (2 x)

- 2 sin (2 y) = 0

1/(sqrt(3))=tan(x)

\frac{1}{3} = tan (x)

0.9 = cos (x)

cos (x) = \frac{8}{9}