zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

4cos^2(x)-3cos(x)-2=0

解答

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

解答

x = 2.01018 \dots + 2 πn, x = - 2.01018 \dots + 2 πn

+1

度数

x = 115.17538 \dots^{\circ} + 36 0^{\circ} n, x = - 115.17538 \dots^{\circ} + 36 0^{\circ} n

求解步骤

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

用替代法求解

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

令

: cos (x) = u

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

4 u^{2} - 3 u - 2 = 0 : u = \frac{3 + 41}{8}, u = \frac{3 - 41}{8}

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

使用求根公式求解

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

二次方程求根公式:

若

a = 4, b = - 3, c = - 2

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

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

(- 3)^{2} - 4 \cdot 4 (- 2) = 41

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

使用法则

- (- a) = a

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

使用指数法则:

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

若

n

是偶数

(- 3)^{2} = 3^{2}

= 3^{2} + 4 \cdot 4 \cdot 2

数字相乘:

4 \cdot 4 \cdot 2 = 32

= 3^{2} + 32

3^{2} = 9

= 9 + 32

数字相加:

9 + 32 = 41

= 41

u_{1, 2} = \frac{- ( - 3 ) \pm 41}{2 \cdot 4}

将解分隔开

u_{1} = \frac{- ( - 3 ) + 41}{2 \cdot 4}, u_{2} = \frac{- ( - 3 ) - 41}{2 \cdot 4}

u = \frac{- ( - 3 ) + 41}{2 \cdot 4} : \frac{3 + 41}{8}

\frac{- ( - 3 ) + 41}{2 \cdot 4}

使用法则

- (- a) = a

= \frac{3 + 41}{2 \cdot 4}

数字相乘:

2 \cdot 4 = 8

= \frac{3 + 41}{8}

u = \frac{- ( - 3 ) - 41}{2 \cdot 4} : \frac{3 - 41}{8}

\frac{- ( - 3 ) - 41}{2 \cdot 4}

使用法则

- (- a) = a

= \frac{3 - 41}{2 \cdot 4}

数字相乘:

2 \cdot 4 = 8

= \frac{3 - 41}{8}

二次方程组的解是:

u = \frac{3 + 41}{8}, u = \frac{3 - 41}{8}

u = cos (x)

代回

cos (x) = \frac{3 + 41}{8}, cos (x) = \frac{3 - 41}{8}

cos (x) = \frac{3 + 41}{8}, cos (x) = \frac{3 - 41}{8}

cos (x) = \frac{3 + 41}{8} :

无解

cos (x) = \frac{3 + 41}{8}

- 1 \leq cos (x) \leq 1

无解

cos (x) = \frac{3 - 41}{8} : x = arccos (\frac{3 - 41}{8}) + 2 πn, x = - arccos (\frac{3 - 41}{8}) + 2 πn

cos (x) = \frac{3 - 41}{8}

使用反三角函数性质

cos (x) = \frac{3 - 41}{8}

cos (x) = \frac{3 - 41}{8}

的通解

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

x = arccos (\frac{3 - 41}{8}) + 2 πn, x = - arccos (\frac{3 - 41}{8}) + 2 πn

x = arccos (\frac{3 - 41}{8}) + 2 πn, x = - arccos (\frac{3 - 41}{8}) + 2 πn

合并所有解

x = arccos (\frac{3 - 41}{8}) + 2 πn, x = - arccos (\frac{3 - 41}{8}) + 2 πn

以小数形式表示解

x = 2.01018 \dots + 2 πn, x = - 2.01018 \dots + 2 πn

作图

流行的例子

sin (x) = cos (3 x)

solvefor x,y=5sin(x/4)

so l v e f or x, y = 5 sin (\frac{x}{4})

3 sin (\frac{π}{3} x) = 2

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

4cos(θ)=1+2cos(θ)

4 cos (θ) = 1 + 2 cos (θ)