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受欢迎的三角函数 >

sin(3x-pi/4)=(sqrt(2))/2

解答

sin (3 x - \frac{π}{4}) = \frac{2}{2}

解答

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

+1

度数

x = 3 0^{\circ} + 12 0^{\circ} n, x = 6 0^{\circ} + 12 0^{\circ} n

求解步骤

sin (3 x - \frac{π}{4}) = \frac{2}{2}

sin (3 x - \frac{π}{4}) = \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}

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

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

解

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

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

将

\frac{π}{4}

到右边

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

两边加上

\frac{π}{4}

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

化简

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

化简

3 x - \frac{π}{4} + \frac{π}{4} : 3 x

3 x - \frac{π}{4} + \frac{π}{4}

同类项相加:

- \frac{π}{4} + \frac{π}{4} = 0

= 3 x

化简

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

\frac{π}{4} + 2 πn + \frac{π}{4}

对同类项分组

= \frac{π}{4} + \frac{π}{4} + 2 πn

合并分式

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

使用法则

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

= \frac{π + π}{4}

同类项相加:

π + π = 2 π

= \frac{2 π}{4}

约分:

2

= \frac{π}{2}

= \frac{π}{2} + 2 πn

3 x = \frac{π}{2} + 2 πn

3 x = \frac{π}{2} + 2 πn

3 x = \frac{π}{2} + 2 πn

两边除以

3

3 x = \frac{π}{2} + 2 πn

两边除以

3

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

化简

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

化简

\frac{3 x}{3} : x

\frac{3 x}{3}

数字相除:

\frac{3}{3} = 1

= x

化简

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

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

\frac{\frac{π}{2}}{3} = \frac{π}{6}

\frac{\frac{π}{2}}{3}

使用分式法则:

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

= \frac{π}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{π}{6}

= \frac{π}{6} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}

解

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

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

将

\frac{π}{4}

到右边

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

两边加上

\frac{π}{4}

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

化简

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

化简

3 x - \frac{π}{4} + \frac{π}{4} : 3 x

3 x - \frac{π}{4} + \frac{π}{4}

同类项相加:

- \frac{π}{4} + \frac{π}{4} = 0

= 3 x

化简

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

\frac{3 π}{4} + 2 πn + \frac{π}{4}

对同类项分组

= 2 πn + \frac{π}{4} + \frac{3 π}{4}

合并分式

\frac{π}{4} + \frac{3 π}{4} : π

使用法则

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

= \frac{π + 3 π}{4}

同类项相加:

π + 3 π = 4 π

= \frac{4 π}{4}

数字相除:

\frac{4}{4} = 1

= π

= 2 πn + π

3 x = 2 πn + π

3 x = 2 πn + π

3 x = 2 πn + π

两边除以

3

3 x = 2 πn + π

两边除以

3

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

化简

x = \frac{2 πn}{3} + \frac{π}{3}

x = \frac{2 πn}{3} + \frac{π}{3}

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

作图

流行的例子

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3 cot (x - 1 0^{\circ}) = 4

2.4638cos(x)=2.5843

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solvefor t,cos(wt+k)=(20)/((2*pi*f)^2)

so l v e f or t, cos (wt + k) = \frac{20}{( 2 \cdot π \cdot f ) ^{2}}