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 >

cos(x+pi/6)-cos(x-pi/6)=1

解答

cos (x + \frac{π}{6}) - cos (x - \frac{π}{6}) = 1

解答

x = \frac{3 π}{2} + 2 πn

+1

度数

x = 27 0^{\circ} + 36 0^{\circ} n

求解步骤

cos (x + \frac{π}{6}) - cos (x - \frac{π}{6}) = 1

使用三角恒等式改写

cos (x + \frac{π}{6}) - cos (x - \frac{π}{6})

使用和差化积恒等式:

cos (s) - cos (t) = - 2 sin (\frac{s + t}{2}) sin (\frac{s - t}{2})

= - 2 sin (\frac{x + \frac{π}{6} + x - \frac{π}{6}}{2}) sin (\frac{x + \frac{π}{6} - ( x - \frac{π}{6} )}{2})

化简

- 2 sin (\frac{x + \frac{π}{6} + x - \frac{π}{6}}{2}) sin (\frac{x + \frac{π}{6} - ( x - \frac{π}{6} )}{2}) : - sin (x)

- 2 sin (\frac{x + \frac{π}{6} + x - \frac{π}{6}}{2}) sin (\frac{x + \frac{π}{6} - ( x - \frac{π}{6} )}{2})

\frac{x + \frac{π}{6} + x - \frac{π}{6}}{2} = x

\frac{x + \frac{π}{6} + x - \frac{π}{6}}{2}

x + \frac{π}{6} + x - \frac{π}{6} = 2 x

x + \frac{π}{6} + x - \frac{π}{6}

对同类项分组

= x + x + \frac{π}{6} - \frac{π}{6}

同类项相加:

x + x = 2 x

= 2 x + \frac{π}{6} - \frac{π}{6}

同类项相加:

\frac{π}{6} - \frac{π}{6} = 0

= 2 x

= \frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

= - 2 sin (x) sin (\frac{x - ( x - \frac{π}{6} ) + \frac{π}{6}}{2})

\frac{x + \frac{π}{6} - ( x - \frac{π}{6} )}{2} = \frac{π}{6}

\frac{x + \frac{π}{6} - ( x - \frac{π}{6} )}{2}

化简

x + \frac{π}{6} - (x - \frac{π}{6}) : \frac{π}{3}

x + \frac{π}{6} - (x - \frac{π}{6})

将项转换为分式:

x = \frac{x 6}{6}, (x - \frac{π}{6}) = \frac{( x - \frac{π}{6} ) 6}{6}

= \frac{x \cdot 6}{6} + \frac{π}{6} - \frac{( x - \frac{π}{6} ) \cdot 6}{6}

因为分母相等，所以合并分式:

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

= \frac{x \cdot 6 + π - ( x - \frac{π}{6} ) \cdot 6}{6}

乘开

x \cdot 6 + π - (x - \frac{π}{6}) \cdot 6 : 2 π

x \cdot 6 + π - (x - \frac{π}{6}) \cdot 6

= 6 x + π - 6 (x - \frac{π}{6})

乘开

- 6 (x - \frac{π}{6}) : - 6 x + π

- 6 (x - \frac{π}{6})

使用分配律:

a (b - c) = ab - a c

a = - 6, b = x, c = \frac{π}{6}

= - 6 x - (- 6) \frac{π}{6}

使用加减运算法则

- (- a) = a

= - 6 x + 6 \cdot \frac{π}{6}

6 \cdot \frac{π}{6} = π

6 \cdot \frac{π}{6}

分式相乘:

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

= \frac{π 6}{6}

约分:

6

= π

= - 6 x + π

= x \cdot 6 + π - 6 x + π

化简

x \cdot 6 + π - 6 x + π : 2 π

x \cdot 6 + π - 6 x + π

对同类项分组

= 6 x - 6 x + π + π

同类项相加:

6 x - 6 x = 0

= π + π

同类项相加:

π + π = 2 π

= 2 π

= 2 π

= \frac{2 π}{6}

约分:

2

= \frac{π}{3}

= \frac{\frac{π}{3}}{2}

使用分式法则:

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

= \frac{π}{3 \cdot 2}

数字相乘:

3 \cdot 2 = 6

= \frac{π}{6}

= - 2 sin (\frac{π}{6}) sin (x)

化简

sin (\frac{π}{6}) : \frac{1}{2}

sin (\frac{π}{6})

使用以下普通恒等式:

sin (\frac{π}{6}) = \frac{1}{2}

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= - 2 \cdot \frac{1}{2} sin (x)

分式相乘:

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

= - \frac{1 \cdot 2}{2} sin (x)

约分:

2

= - sin (x) \cdot 1

乘以:

sin (x) \cdot 1 = sin (x)

= - sin (x)

= - sin (x)

- sin (x) = 1

两边除以

- 1

- sin (x) = 1

两边除以

- 1

\frac{- sin ( x )}{- 1} = \frac{1}{- 1}

化简

sin (x) = - 1

sin (x) = - 1

sin (x) = - 1

的通解

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

作图

流行的例子

tan(2θ)+2sin(θ)=0

tan (2 θ) + 2 sin (θ) = 0

2cos^2(x)+7sin(x)=5

2 cos^{2} (x) + 7 sin (x) = 5

tan^2(x)+sec(x)=1

tan^{2} (x) + sec (x) = 1

- 4 sin (2 x) = 0

(sin(2x))/(cos(x))=2

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