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受欢迎的三角函数 >

sin(2x+pi/3)=0

解答

sin (2 x + \frac{π}{3}) = 0

解答

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

+1

度数

x = - 3 0^{\circ} + 18 0^{\circ} n, x = 6 0^{\circ} + 18 0^{\circ} n

求解步骤

sin (2 x + \frac{π}{3}) = 0

sin (2 x + \frac{π}{3}) = 0

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}{3} = 0 + 2 πn, 2 x + \frac{π}{3} = π + 2 πn

2 x + \frac{π}{3} = 0 + 2 πn, 2 x + \frac{π}{3} = π + 2 πn

解

2 x + \frac{π}{3} = 0 + 2 πn : x = πn - \frac{π}{6}

2 x + \frac{π}{3} = 0 + 2 πn

0 + 2 πn = 2 πn

2 x + \frac{π}{3} = 2 πn

将

\frac{π}{3}

到右边

2 x + \frac{π}{3} = 2 πn

两边减去

\frac{π}{3}

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

化简

2 x = 2 πn - \frac{π}{3}

2 x = 2 πn - \frac{π}{3}

两边除以

2

2 x = 2 πn - \frac{π}{3}

两边除以

2

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

化简

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

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

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

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

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

\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}

= πn - \frac{π}{6}

x = πn - \frac{π}{6}

x = πn - \frac{π}{6}

x = πn - \frac{π}{6}

解

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

2 x + \frac{π}{3} = π + 2 πn

将

\frac{π}{3}

到右边

2 x + \frac{π}{3} = π + 2 πn

两边减去

\frac{π}{3}

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

化简

2 x = π + 2 πn - \frac{π}{3}

2 x = π + 2 πn - \frac{π}{3}

两边除以

2

2 x = π + 2 πn - \frac{π}{3}

两边除以

2

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

化简

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

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

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

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

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

\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{π}{2} + πn - \frac{π}{6}

对同类项分组

= πn + \frac{π}{2} - \frac{π}{6}

x = πn + \frac{π}{2} - \frac{π}{6}

x = πn + \frac{π}{2} - \frac{π}{6}

x = πn + \frac{π}{2} - \frac{π}{6}

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

作图

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