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受欢迎的三角函数 >

2sin(4x)+sqrt(3)=0

解答

2 sin (4 x) + 3 = 0

解答

x = \frac{π}{3} + \frac{πn}{2}, x = \frac{5 π}{12} + \frac{πn}{2}

+1

度数

x = 6 0^{\circ} + 9 0^{\circ} n, x = 7 5^{\circ} + 9 0^{\circ} n

求解步骤

2 sin (4 x) + 3 = 0

将

3

到右边

2 sin (4 x) + 3 = 0

两边减去

3

2 sin (4 x) + 3 - 3 = 0 - 3

化简

2 sin (4 x) = - 3

2 sin (4 x) = - 3

两边除以

2

2 sin (4 x) = - 3

两边除以

2

\frac{2 sin ( 4 x )}{2} = \frac{- 3}{2}

化简

sin (4 x) = - \frac{3}{2}

sin (4 x) = - \frac{3}{2}

sin (4 x) = - \frac{3}{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}

4 x = \frac{4 π}{3} + 2 πn, 4 x = \frac{5 π}{3} + 2 πn

4 x = \frac{4 π}{3} + 2 πn, 4 x = \frac{5 π}{3} + 2 πn

解

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

4 x = \frac{4 π}{3} + 2 πn

两边除以

4

4 x = \frac{4 π}{3} + 2 πn

两边除以

4

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

化简

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

化简

\frac{4 x}{4} : x

\frac{4 x}{4}

数字相除:

\frac{4}{4} = 1

= x

化简

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

\frac{\frac{4 π}{3}}{4} + \frac{2 πn}{4}

\frac{\frac{4 π}{3}}{4} = \frac{π}{3}

\frac{\frac{4 π}{3}}{4}

使用分式法则:

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

= \frac{4 π}{3 \cdot 4}

数字相乘:

3 \cdot 4 = 12

= \frac{4 π}{12}

约分:

4

= \frac{π}{3}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

约分:

2

= \frac{πn}{2}

= \frac{π}{3} + \frac{πn}{2}

x = \frac{π}{3} + \frac{πn}{2}

x = \frac{π}{3} + \frac{πn}{2}

x = \frac{π}{3} + \frac{πn}{2}

解

4 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{12} + \frac{πn}{2}

4 x = \frac{5 π}{3} + 2 πn

两边除以

4

4 x = \frac{5 π}{3} + 2 πn

两边除以

4

\frac{4 x}{4} = \frac{\frac{5 π}{3}}{4} + \frac{2 πn}{4}

化简

\frac{4 x}{4} = \frac{\frac{5 π}{3}}{4} + \frac{2 πn}{4}

化简

\frac{4 x}{4} : x

\frac{4 x}{4}

数字相除:

\frac{4}{4} = 1

= x

化简

\frac{\frac{5 π}{3}}{4} + \frac{2 πn}{4} : \frac{5 π}{12} + \frac{πn}{2}

\frac{\frac{5 π}{3}}{4} + \frac{2 πn}{4}

\frac{\frac{5 π}{3}}{4} = \frac{5 π}{12}

\frac{\frac{5 π}{3}}{4}

使用分式法则:

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

= \frac{5 π}{3 \cdot 4}

数字相乘:

3 \cdot 4 = 12

= \frac{5 π}{12}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

约分:

2

= \frac{πn}{2}

= \frac{5 π}{12} + \frac{πn}{2}

x = \frac{5 π}{12} + \frac{πn}{2}

x = \frac{5 π}{12} + \frac{πn}{2}

x = \frac{5 π}{12} + \frac{πn}{2}

x = \frac{π}{3} + \frac{πn}{2}, x = \frac{5 π}{12} + \frac{πn}{2}

作图

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