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受欢迎的三角函数 >

2sin(x-pi/6)+1=0

解答

2 sin (x - \frac{π}{6}) + 1 = 0

解答

x = 2 πn + \frac{4 π}{3}, x = 2 πn + 2 π

+1

度数

x = 24 0^{\circ} + 36 0^{\circ} n, x = 36 0^{\circ} + 36 0^{\circ} n

求解步骤

2 sin (x - \frac{π}{6}) + 1 = 0

将

1

到右边

2 sin (x - \frac{π}{6}) + 1 = 0

两边减去

1

2 sin (x - \frac{π}{6}) + 1 - 1 = 0 - 1

化简

2 sin (x - \frac{π}{6}) = - 1

2 sin (x - \frac{π}{6}) = - 1

两边除以

2

2 sin (x - \frac{π}{6}) = - 1

两边除以

2

\frac{2 sin ( x - \frac{π}{6} )}{2} = \frac{- 1}{2}

化简

sin (x - \frac{π}{6}) = - \frac{1}{2}

sin (x - \frac{π}{6}) = - \frac{1}{2}

sin (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}

x - \frac{π}{6} = \frac{7 π}{6} + 2 πn, x - \frac{π}{6} = \frac{11 π}{6} + 2 πn

x - \frac{π}{6} = \frac{7 π}{6} + 2 πn, x - \frac{π}{6} = \frac{11 π}{6} + 2 πn

解

x - \frac{π}{6} = \frac{7 π}{6} + 2 πn : x = 2 πn + \frac{4 π}{3}

x - \frac{π}{6} = \frac{7 π}{6} + 2 πn

将

\frac{π}{6}

到右边

x - \frac{π}{6} = \frac{7 π}{6} + 2 πn

两边加上

\frac{π}{6}

x - \frac{π}{6} + \frac{π}{6} = \frac{7 π}{6} + 2 πn + \frac{π}{6}

化简

x - \frac{π}{6} + \frac{π}{6} = \frac{7 π}{6} + 2 πn + \frac{π}{6}

化简

x - \frac{π}{6} + \frac{π}{6} : x

x - \frac{π}{6} + \frac{π}{6}

同类项相加:

- \frac{π}{6} + \frac{π}{6} = 0

= x

化简

\frac{7 π}{6} + 2 πn + \frac{π}{6} : 2 πn + \frac{4 π}{3}

\frac{7 π}{6} + 2 πn + \frac{π}{6}

对同类项分组

= 2 πn + \frac{π}{6} + \frac{7 π}{6}

合并分式

\frac{π}{6} + \frac{7 π}{6} : \frac{4 π}{3}

使用法则

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

= \frac{π + 7 π}{6}

同类项相加:

π + 7 π = 8 π

= \frac{8 π}{6}

约分:

2

= \frac{4 π}{3}

= 2 πn + \frac{4 π}{3}

x = 2 πn + \frac{4 π}{3}

x = 2 πn + \frac{4 π}{3}

x = 2 πn + \frac{4 π}{3}

解

x - \frac{π}{6} = \frac{11 π}{6} + 2 πn : x = 2 πn + 2 π

x - \frac{π}{6} = \frac{11 π}{6} + 2 πn

将

\frac{π}{6}

到右边

x - \frac{π}{6} = \frac{11 π}{6} + 2 πn

两边加上

\frac{π}{6}

x - \frac{π}{6} + \frac{π}{6} = \frac{11 π}{6} + 2 πn + \frac{π}{6}

化简

x - \frac{π}{6} + \frac{π}{6} = \frac{11 π}{6} + 2 πn + \frac{π}{6}

化简

x - \frac{π}{6} + \frac{π}{6} : x

x - \frac{π}{6} + \frac{π}{6}

同类项相加:

- \frac{π}{6} + \frac{π}{6} = 0

= x

化简

\frac{11 π}{6} + 2 πn + \frac{π}{6} : 2 πn + 2 π

\frac{11 π}{6} + 2 πn + \frac{π}{6}

对同类项分组

= 2 πn + \frac{π}{6} + \frac{11 π}{6}

合并分式

\frac{π}{6} + \frac{11 π}{6} : 2 π

使用法则

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

= \frac{π + 11 π}{6}

同类项相加:

π + 11 π = 12 π

= \frac{12 π}{6}

数字相除:

\frac{12}{6} = 2

= 2 π

= 2 πn + 2 π

x = 2 πn + 2 π

x = 2 πn + 2 π

x = 2 πn + 2 π

x = 2 πn + \frac{4 π}{3}, x = 2 πn + 2 π

作图

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