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 >

sin(2x-pi/6)= 1/2

解答

sin (2 x - \frac{π}{6}) = \frac{1}{2}

解答

x = \frac{π}{6} + πn, x = πn + \frac{π}{2}

+1

度数

x = 3 0^{\circ} + 18 0^{\circ} n, x = 9 0^{\circ} + 18 0^{\circ} n

求解步骤

sin (2 x - \frac{π}{6}) = \frac{1}{2}

sin (2 x - \frac{π}{6}) = \frac{1}{2}

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}

2 x - \frac{π}{6} = \frac{π}{6} + 2 πn, 2 x - \frac{π}{6} = \frac{5 π}{6} + 2 πn

2 x - \frac{π}{6} = \frac{π}{6} + 2 πn, 2 x - \frac{π}{6} = \frac{5 π}{6} + 2 πn

解

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

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

将

\frac{π}{6}

到右边

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

两边加上

\frac{π}{6}

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

化简

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

化简

2 x - \frac{π}{6} + \frac{π}{6} : 2 x

2 x - \frac{π}{6} + \frac{π}{6}

同类项相加:

- \frac{π}{6} + \frac{π}{6} = 0

= 2 x

化简

\frac{π}{6} + 2 πn + \frac{π}{6} : \frac{π}{3} + 2 πn

\frac{π}{6} + 2 πn + \frac{π}{6}

对同类项分组

= \frac{π}{6} + \frac{π}{6} + 2 πn

合并分式

\frac{π}{6} + \frac{π}{6} : \frac{π}{3}

使用法则

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

= \frac{π + π}{6}

同类项相加:

π + π = 2 π

= \frac{2 π}{6}

约分:

2

= \frac{π}{3}

= \frac{π}{3} + 2 πn

2 x = \frac{π}{3} + 2 πn

2 x = \frac{π}{3} + 2 πn

2 x = \frac{π}{3} + 2 πn

两边除以

2

2 x = \frac{π}{3} + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{\frac{π}{3}}{2} + \frac{2 πn}{2}

化简

\frac{2 x}{2} = \frac{\frac{π}{3}}{2} + \frac{2 πn}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{\frac{π}{3}}{2} + \frac{2 πn}{2} : \frac{π}{6} + πn

\frac{\frac{π}{3}}{2} + \frac{2 πn}{2}

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\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}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

= \frac{π}{6} + πn

x = \frac{π}{6} + πn

x = \frac{π}{6} + πn

x = \frac{π}{6} + πn

解

2 x - \frac{π}{6} = \frac{5 π}{6} + 2 πn : x = πn + \frac{π}{2}

2 x - \frac{π}{6} = \frac{5 π}{6} + 2 πn

将

\frac{π}{6}

到右边

2 x - \frac{π}{6} = \frac{5 π}{6} + 2 πn

两边加上

\frac{π}{6}

2 x - \frac{π}{6} + \frac{π}{6} = \frac{5 π}{6} + 2 πn + \frac{π}{6}

化简

2 x - \frac{π}{6} + \frac{π}{6} = \frac{5 π}{6} + 2 πn + \frac{π}{6}

化简

2 x - \frac{π}{6} + \frac{π}{6} : 2 x

2 x - \frac{π}{6} + \frac{π}{6}

同类项相加:

- \frac{π}{6} + \frac{π}{6} = 0

= 2 x

化简

\frac{5 π}{6} + 2 πn + \frac{π}{6} : 2 πn + π

\frac{5 π}{6} + 2 πn + \frac{π}{6}

对同类项分组

= 2 πn + \frac{π}{6} + \frac{5 π}{6}

合并分式

\frac{π}{6} + \frac{5 π}{6} : π

使用法则

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

= \frac{π + 5 π}{6}

同类项相加:

π + 5 π = 6 π

= \frac{6 π}{6}

数字相除:

\frac{6}{6} = 1

= π

= 2 πn + π

2 x = 2 πn + π

2 x = 2 πn + π

2 x = 2 πn + π

两边除以

2

2 x = 2 πn + π

两边除以

2

\frac{2 x}{2} = \frac{2 πn}{2} + \frac{π}{2}

化简

x = πn + \frac{π}{2}

x = πn + \frac{π}{2}

x = \frac{π}{6} + πn, x = πn + \frac{π}{2}

作图

流行的例子

2cos(x)+1=3sec(x)

2 cos (x) + 1 = 3 sec (x)

csc (θ) = \frac{5}{4}

8sin^3(x)-4sin^2(x)-6sin(x)+3=0

8 sin^{3} (x) - 4 sin^{2} (x) - 6 sin (x) + 3 = 0

2cos(x)=1-sin(x)

2 cos (x) = 1 - sin (x)

tan(2θ)+tan(2θ)=tan(4θ)

tan (2 θ) + tan (2 θ) = tan (4 θ)