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)+sqrt(3)=2(sqrt(3)+1)

解答

4 cos^{2} (x) + 3 = 2 (3 + 1)

解答

x = 0.26179 \dots + 2 πn, x = 2 π - 0.26179 \dots + 2 πn, x = 2.87979 \dots + 2 πn, x = - 2.87979 \dots + 2 πn

+1

度数

x = 1 5^{\circ} + 36 0^{\circ} n, x = 34 5^{\circ} + 36 0^{\circ} n, x = 16 5^{\circ} + 36 0^{\circ} n, x = - 16 5^{\circ} + 36 0^{\circ} n

求解步骤

4 cos^{2} (x) + 3 = 2 (3 + 1)

用替代法求解

4 cos^{2} (x) + 3 = 2 (3 + 1)

令

: cos (x) = u

4 u^{2} + 3 = 2 (3 + 1)

4 u^{2} + 3 = 2 (3 + 1) : u = \frac{3 + 2}{2}, u = - \frac{3 + 2}{2}

4 u^{2} + 3 = 2 (3 + 1)

将

3

到右边

4 u^{2} + 3 = 2 (3 + 1)

两边减去

3

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

化简

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

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

两边除以

4

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

两边除以

4

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

化简

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

化简

\frac{4 u ^{2}}{4} : u^{2}

\frac{4 u ^{2}}{4}

数字相除:

\frac{4}{4} = 1

= u^{2}

化简

\frac{2 ( 3 + 1 )}{4} - \frac{3}{4} : \frac{3 + 2}{4}

\frac{2 ( 3 + 1 )}{4} - \frac{3}{4}

使用法则

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

乘开

2 (3 + 1) - 3 : 3 + 2

2 (3 + 1) - 3

乘开

2 (3 + 1) : 23 + 2

2 (3 + 1)

使用分配律:

a (b + c) = ab + a c

a = 2, b = 3, c = 1

= 23 + 2 \cdot 1

数字相乘:

2 \cdot 1 = 2

= 23 + 2

= 23 + 2 - 3

同类项相加:

23 - 3 = 3

= 3 + 2

= \frac{3 + 2}{4}

u^{2} = \frac{3 + 2}{4}

u^{2} = \frac{3 + 2}{4}

u^{2} = \frac{3 + 2}{4}

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = \frac{3 + 2}{4}, u = - \frac{3 + 2}{4}

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

\frac{3 + 2}{4}

使用根式运算法则:

假定

a \geq 0, b \geq 0

= \frac{3 + 2}{4}

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

2^{2} = 2

= 2

= \frac{3 + 2}{2}

- \frac{3 + 2}{4} = - \frac{3 + 2}{2}

- \frac{3 + 2}{4}

化简

\frac{3 + 2}{4} : \frac{3 + 2}{2}

\frac{3 + 2}{4}

使用根式运算法则:

假定

a \geq 0, b \geq 0

= \frac{3 + 2}{4}

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

2^{2} = 2

= 2

= \frac{3 + 2}{2}

= - \frac{2 + 3}{2}

= - \frac{3 + 2}{2}

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

u = cos (x)

代回

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

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

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

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

使用反三角函数性质

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

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

的通解

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

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

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

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

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

使用反三角函数性质

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

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

的通解

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

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

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

合并所有解

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

以小数形式表示解

x = 0.26179 \dots + 2 πn, x = 2 π - 0.26179 \dots + 2 πn, x = 2.87979 \dots + 2 πn, x = - 2.87979 \dots + 2 πn

作图

流行的例子

2tan^2(x)+cot^2(x)-3=0

((2sin(x)-1))/((sin(x)+5))=0

sec^2(b)=2+tan(b)

cos^{23}(x)+cos^2(x)=0