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受欢迎的三角函数 >

sqrt(2)sin(4x)-1=0

解答

2 sin (4 x) - 1 = 0

解答

x = \frac{π}{16} + \frac{πn}{2}, x = \frac{3 π}{16} + \frac{πn}{2}

+1

度数

x = 11.2 5^{\circ} + 9 0^{\circ} n, x = 33.7 5^{\circ} + 9 0^{\circ} n

求解步骤

2 sin (4 x) - 1 = 0

将

1

到右边

2 sin (4 x) - 1 = 0

两边加上

1

2 sin (4 x) - 1 + 1 = 0 + 1

化简

2 sin (4 x) = 1

2 sin (4 x) = 1

两边除以

2

2 sin (4 x) = 1

两边除以

2

\frac{2 sin ( 4 x )}{2} = \frac{1}{2}

化简

\frac{2 sin ( 4 x )}{2} = \frac{1}{2}

化简

\frac{2 sin ( 4 x )}{2} : sin (4 x)

\frac{2 sin ( 4 x )}{2}

约分:

2

= sin (4 x)

化简

\frac{1}{2} : \frac{2}{2}

\frac{1}{2}

乘以共轭根式

\frac{2}{2}

= \frac{1 \cdot 2}{2 2}

1 \cdot 2 = 2

22 = 2

22

使用根式运算法则:

a a = a

22 = 2

= 2

= \frac{2}{2}

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

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

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

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

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

解

4 x = \frac{π}{4} + 2 πn : x = \frac{π}{16} + \frac{πn}{2}

4 x = \frac{π}{4} + 2 πn

两边除以

4

4 x = \frac{π}{4} + 2 πn

两边除以

4

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

化简

\frac{4 x}{4} = \frac{\frac{π}{4}}{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{π}{4}}{4} + \frac{2 πn}{4} : \frac{π}{16} + \frac{πn}{2}

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

\frac{\frac{π}{4}}{4} = \frac{π}{16}

\frac{\frac{π}{4}}{4}

使用分式法则:

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

= \frac{π}{4 \cdot 4}

数字相乘:

4 \cdot 4 = 16

= \frac{π}{16}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

约分:

2

= \frac{πn}{2}

= \frac{π}{16} + \frac{πn}{2}

x = \frac{π}{16} + \frac{πn}{2}

x = \frac{π}{16} + \frac{πn}{2}

x = \frac{π}{16} + \frac{πn}{2}

解

4 x = \frac{3 π}{4} + 2 πn : x = \frac{3 π}{16} + \frac{πn}{2}

4 x = \frac{3 π}{4} + 2 πn

两边除以

4

4 x = \frac{3 π}{4} + 2 πn

两边除以

4

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

化简

\frac{4 x}{4} = \frac{\frac{3 π}{4}}{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{3 π}{4}}{4} + \frac{2 πn}{4} : \frac{3 π}{16} + \frac{πn}{2}

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

\frac{\frac{3 π}{4}}{4} = \frac{3 π}{16}

\frac{\frac{3 π}{4}}{4}

使用分式法则:

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

= \frac{3 π}{4 \cdot 4}

数字相乘:

4 \cdot 4 = 16

= \frac{3 π}{16}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

约分:

2

= \frac{πn}{2}

= \frac{3 π}{16} + \frac{πn}{2}

x = \frac{3 π}{16} + \frac{πn}{2}

x = \frac{3 π}{16} + \frac{πn}{2}

x = \frac{3 π}{16} + \frac{πn}{2}

x = \frac{π}{16} + \frac{πn}{2}, x = \frac{3 π}{16} + \frac{πn}{2}

作图

流行的例子

sqrt(6)sin(x)-sqrt(2)cos(x)=sqrt(2)

3-3sin(x)=6cos^2(x)

cos(x)= 60/61 ,tan(x)= 11/60

3sqrt(2)cos(x)+2=-1