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受欢迎的三角函数 >

6sin(pi/4 x)=3

解答

6 sin (\frac{π}{4} x) = 3

解答

x = \frac{2}{3} + 8 n, x = \frac{10}{3} + 8 n

+1

度数

x = 38.19718 \dots^{\circ} + 458.36623 \dots^{\circ} n, x = 190.98593 \dots^{\circ} + 458.36623 \dots^{\circ} n

求解步骤

6 sin (\frac{π}{4} x) = 3

两边除以

6

6 sin (\frac{π}{4} x) = 3

两边除以

6

\frac{6 sin ( \frac{π}{4} x )}{6} = \frac{3}{6}

化简

sin (\frac{π}{4} x) = \frac{1}{2}

sin (\frac{π}{4} x) = \frac{1}{2}

sin (\frac{π}{4} x) = \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}

\frac{π}{4} x = \frac{π}{6} + 2 πn, \frac{π}{4} x = \frac{5 π}{6} + 2 πn

\frac{π}{4} x = \frac{π}{6} + 2 πn, \frac{π}{4} x = \frac{5 π}{6} + 2 πn

解

\frac{π}{4} x = \frac{π}{6} + 2 πn : x = \frac{2}{3} + 8 n

\frac{π}{4} x = \frac{π}{6} + 2 πn

在两边乘以

4

\frac{π}{4} x = \frac{π}{6} + 2 πn

在两边乘以

4

4 \cdot \frac{π}{4} x = 4 \cdot \frac{π}{6} + 4 \cdot 2 πn

化简

4 \cdot \frac{π}{4} x = 4 \cdot \frac{π}{6} + 4 \cdot 2 πn

化简

4 \cdot \frac{π}{4} x : π x

4 \cdot \frac{π}{4} x

分式相乘:

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

= \frac{4 π}{4} x

约分:

4

= x π

化简

4 \cdot \frac{π}{6} + 4 \cdot 2 πn : \frac{2 π}{3} + 8 πn

4 \cdot \frac{π}{6} + 4 \cdot 2 πn

4 \cdot \frac{π}{6} = \frac{2 π}{3}

4 \cdot \frac{π}{6}

分式相乘:

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

= \frac{π 4}{6}

约分:

2

= \frac{2 π}{3}

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

数字相乘:

4 \cdot 2 = 8

= 8 πn

= \frac{2 π}{3} + 8 πn

π x = \frac{2 π}{3} + 8 πn

π x = \frac{2 π}{3} + 8 πn

π x = \frac{2 π}{3} + 8 πn

两边除以

π

π x = \frac{2 π}{3} + 8 πn

两边除以

π

\frac{π x}{π} = \frac{\frac{2 π}{3}}{π} + \frac{8 πn}{π}

化简

\frac{π x}{π} = \frac{\frac{2 π}{3}}{π} + \frac{8 πn}{π}

化简

\frac{π x}{π} : x

\frac{π x}{π}

约分:

π

= x

化简

\frac{\frac{2 π}{3}}{π} + \frac{8 πn}{π} : \frac{2}{3} + 8 n

\frac{\frac{2 π}{3}}{π} + \frac{8 πn}{π}

\frac{\frac{2 π}{3}}{π} = \frac{2}{3}

\frac{\frac{2 π}{3}}{π}

使用分式法则:

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

= \frac{2 π}{3 π}

约分:

π

= \frac{2}{3}

\frac{8 πn}{π} = 8 n

\frac{8 πn}{π}

约分:

π

= 8 n

= \frac{2}{3} + 8 n

x = \frac{2}{3} + 8 n

x = \frac{2}{3} + 8 n

x = \frac{2}{3} + 8 n

解

\frac{π}{4} x = \frac{5 π}{6} + 2 πn : x = \frac{10}{3} + 8 n

\frac{π}{4} x = \frac{5 π}{6} + 2 πn

在两边乘以

4

\frac{π}{4} x = \frac{5 π}{6} + 2 πn

在两边乘以

4

4 \cdot \frac{π}{4} x = 4 \cdot \frac{5 π}{6} + 4 \cdot 2 πn

化简

4 \cdot \frac{π}{4} x = 4 \cdot \frac{5 π}{6} + 4 \cdot 2 πn

化简

4 \cdot \frac{π}{4} x : π x

4 \cdot \frac{π}{4} x

分式相乘:

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

= \frac{4 π}{4} x

约分:

4

= x π

化简

4 \cdot \frac{5 π}{6} + 4 \cdot 2 πn : \frac{10 π}{3} + 8 πn

4 \cdot \frac{5 π}{6} + 4 \cdot 2 πn

4 \cdot \frac{5 π}{6} = \frac{10 π}{3}

4 \cdot \frac{5 π}{6}

分式相乘:

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

= \frac{5 π 4}{6}

数字相乘:

5 \cdot 4 = 20

= \frac{20 π}{6}

约分:

2

= \frac{10 π}{3}

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

数字相乘:

4 \cdot 2 = 8

= 8 πn

= \frac{10 π}{3} + 8 πn

π x = \frac{10 π}{3} + 8 πn

π x = \frac{10 π}{3} + 8 πn

π x = \frac{10 π}{3} + 8 πn

两边除以

π

π x = \frac{10 π}{3} + 8 πn

两边除以

π

\frac{π x}{π} = \frac{\frac{10 π}{3}}{π} + \frac{8 πn}{π}

化简

\frac{π x}{π} = \frac{\frac{10 π}{3}}{π} + \frac{8 πn}{π}

化简

\frac{π x}{π} : x

\frac{π x}{π}

约分:

π

= x

化简

\frac{\frac{10 π}{3}}{π} + \frac{8 πn}{π} : \frac{10}{3} + 8 n

\frac{\frac{10 π}{3}}{π} + \frac{8 πn}{π}

\frac{\frac{10 π}{3}}{π} = \frac{10}{3}

\frac{\frac{10 π}{3}}{π}

使用分式法则:

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

= \frac{10 π}{3 π}

约分:

π

= \frac{10}{3}

\frac{8 πn}{π} = 8 n

\frac{8 πn}{π}

约分:

π

= 8 n

= \frac{10}{3} + 8 n

x = \frac{10}{3} + 8 n

x = \frac{10}{3} + 8 n

x = \frac{10}{3} + 8 n

x = \frac{2}{3} + 8 n, x = \frac{10}{3} + 8 n

作图

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