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受欢迎的三角函数 >

sin(pi/6 x)= 1/2

解答

sin (\frac{π}{6} x) = \frac{1}{2}

解答

x = 1 + 12 n, x = 5 + 12 n

+1

度数

x = 57.29577 \dots^{\circ} + 687.54935 \dots^{\circ} n, x = 286.47889 \dots^{\circ} + 687.54935 \dots^{\circ} n

求解步骤

sin (\frac{π}{6} x) = \frac{1}{2}

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

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

解

\frac{π}{6} x = \frac{π}{6} + 2 πn : x = 1 + 12 n

\frac{π}{6} x = \frac{π}{6} + 2 πn

在两边乘以

6

\frac{π}{6} x = \frac{π}{6} + 2 πn

在两边乘以

6

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

化简

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

化简

6 \cdot \frac{π}{6} x : π x

6 \cdot \frac{π}{6} x

分式相乘:

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

= \frac{6 π}{6} x

约分:

6

= x π

化简

6 \cdot \frac{π}{6} + 6 \cdot 2 πn : π + 12 πn

6 \cdot \frac{π}{6} + 6 \cdot 2 πn

6 \cdot \frac{π}{6} = π

6 \cdot \frac{π}{6}

分式相乘:

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

= \frac{π 6}{6}

约分:

6

= π

6 \cdot 2 πn = 12 πn

6 \cdot 2 πn

数字相乘:

6 \cdot 2 = 12

= 12 πn

= π + 12 πn

π x = π + 12 πn

π x = π + 12 πn

π x = π + 12 πn

两边除以

π

π x = π + 12 πn

两边除以

π

\frac{π x}{π} = \frac{π}{π} + \frac{12 πn}{π}

化简

\frac{π x}{π} = \frac{π}{π} + \frac{12 πn}{π}

化简

\frac{π x}{π} : x

\frac{π x}{π}

约分:

π

= x

化简

\frac{π}{π} + \frac{12 πn}{π} : 1 + 12 n

\frac{π}{π} + \frac{12 πn}{π}

使用法则

\frac{a}{a} = 1

\frac{π}{π} = 1

= 1 + \frac{12 πn}{π}

消掉

\frac{12 πn}{π} : 12 n

\frac{12 πn}{π}

约分:

π

= 12 n

= 1 + 12 n

x = 1 + 12 n

x = 1 + 12 n

x = 1 + 12 n

解

\frac{π}{6} x = \frac{5 π}{6} + 2 πn : x = 5 + 12 n

\frac{π}{6} x = \frac{5 π}{6} + 2 πn

在两边乘以

6

\frac{π}{6} x = \frac{5 π}{6} + 2 πn

在两边乘以

6

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

化简

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

化简

6 \cdot \frac{π}{6} x : π x

6 \cdot \frac{π}{6} x

分式相乘:

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

= \frac{6 π}{6} x

约分:

6

= x π

化简

6 \cdot \frac{5 π}{6} + 6 \cdot 2 πn : 5 π + 12 πn

6 \cdot \frac{5 π}{6} + 6 \cdot 2 πn

6 \cdot \frac{5 π}{6} = 5 π

6 \cdot \frac{5 π}{6}

分式相乘:

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

= \frac{5 π 6}{6}

约分:

6

= 5 π

6 \cdot 2 πn = 12 πn

6 \cdot 2 πn

数字相乘:

6 \cdot 2 = 12

= 12 πn

= 5 π + 12 πn

π x = 5 π + 12 πn

π x = 5 π + 12 πn

π x = 5 π + 12 πn

两边除以

π

π x = 5 π + 12 πn

两边除以

π

\frac{π x}{π} = \frac{5 π}{π} + \frac{12 πn}{π}

化简

\frac{π x}{π} = \frac{5 π}{π} + \frac{12 πn}{π}

化简

\frac{π x}{π} : x

\frac{π x}{π}

约分:

π

= x

化简

\frac{5 π}{π} + \frac{12 πn}{π} : 5 + 12 n

\frac{5 π}{π} + \frac{12 πn}{π}

消掉

\frac{5 π}{π} : 5

\frac{5 π}{π}

约分:

π

= 5

= 5 + \frac{12 πn}{π}

消掉

\frac{12 πn}{π} : 12 n

\frac{12 πn}{π}

约分:

π

= 12 n

= 5 + 12 n

x = 5 + 12 n

x = 5 + 12 n

x = 5 + 12 n

x = 1 + 12 n, x = 5 + 12 n

作图

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