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受欢迎的三角函数 >

1/3 =cos((pix)/(12))

解答

\frac{1}{3} = cos (\frac{π x}{12})

解答

x = \frac{12 \cdot 1.23095 \dots}{π} + 24 n, x = 24 - \frac{12 \cdot 1.23095 \dots}{π} + 24 n

+1

度数

x = 269.40009 \dots^{\circ} + 1375.09870 \dots^{\circ} n, x = 1105.69861 \dots^{\circ} + 1375.09870 \dots^{\circ} n

求解步骤

\frac{1}{3} = cos (\frac{π x}{12})

交换两边

cos (\frac{π x}{12}) = \frac{1}{3}

使用反三角函数性质

cos (\frac{π x}{12}) = \frac{1}{3}

cos (\frac{π x}{12}) = \frac{1}{3}

的通解

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

\frac{π x}{12} = arccos (\frac{1}{3}) + 2 πn, \frac{π x}{12} = 2 π - arccos (\frac{1}{3}) + 2 πn

\frac{π x}{12} = arccos (\frac{1}{3}) + 2 πn, \frac{π x}{12} = 2 π - arccos (\frac{1}{3}) + 2 πn

解

\frac{π x}{12} = arccos (\frac{1}{3}) + 2 πn : x = \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

\frac{π x}{12} = arccos (\frac{1}{3}) + 2 πn

在两边乘以

12

\frac{π x}{12} = arccos (\frac{1}{3}) + 2 πn

在两边乘以

12

\frac{12 π x}{12} = 12 arccos (\frac{1}{3}) + 12 \cdot 2 πn

化简

\frac{12 π x}{12} = 12 arccos (\frac{1}{3}) + 12 \cdot 2 πn

化简

\frac{12 π x}{12} : π x

\frac{12 π x}{12}

数字相除:

\frac{12}{12} = 1

= π x

化简

12 arccos (\frac{1}{3}) + 12 \cdot 2 πn : 12 arccos (\frac{1}{3}) + 24 πn

12 arccos (\frac{1}{3}) + 12 \cdot 2 πn

数字相乘:

12 \cdot 2 = 24

= 12 arccos (\frac{1}{3}) + 24 πn

π x = 12 arccos (\frac{1}{3}) + 24 πn

π x = 12 arccos (\frac{1}{3}) + 24 πn

π x = 12 arccos (\frac{1}{3}) + 24 πn

两边除以

π

π x = 12 arccos (\frac{1}{3}) + 24 πn

两边除以

π

\frac{π x}{π} = \frac{12 arccos ( \frac{1}{3} )}{π} + \frac{24 πn}{π}

化简

x = \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

x = \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

解

\frac{π x}{12} = 2 π - arccos (\frac{1}{3}) + 2 πn : x = 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

\frac{π x}{12} = 2 π - arccos (\frac{1}{3}) + 2 πn

在两边乘以

12

\frac{π x}{12} = 2 π - arccos (\frac{1}{3}) + 2 πn

在两边乘以

12

\frac{12 π x}{12} = 12 \cdot 2 π - 12 arccos (\frac{1}{3}) + 12 \cdot 2 πn

化简

\frac{12 π x}{12} = 12 \cdot 2 π - 12 arccos (\frac{1}{3}) + 12 \cdot 2 πn

化简

\frac{12 π x}{12} : π x

\frac{12 π x}{12}

数字相除:

\frac{12}{12} = 1

= π x

化简

12 \cdot 2 π - 12 arccos (\frac{1}{3}) + 12 \cdot 2 πn : 24 π - 12 arccos (\frac{1}{3}) + 24 πn

12 \cdot 2 π - 12 arccos (\frac{1}{3}) + 12 \cdot 2 πn

数字相乘:

12 \cdot 2 = 24

= 24 π - 12 arccos (\frac{1}{3}) + 24 πn

π x = 24 π - 12 arccos (\frac{1}{3}) + 24 πn

π x = 24 π - 12 arccos (\frac{1}{3}) + 24 πn

π x = 24 π - 12 arccos (\frac{1}{3}) + 24 πn

两边除以

π

π x = 24 π - 12 arccos (\frac{1}{3}) + 24 πn

两边除以

π

\frac{π x}{π} = \frac{24 π}{π} - \frac{12 arccos ( \frac{1}{3} )}{π} + \frac{24 πn}{π}

化简

\frac{π x}{π} = \frac{24 π}{π} - \frac{12 arccos ( \frac{1}{3} )}{π} + \frac{24 πn}{π}

化简

\frac{π x}{π} : x

\frac{π x}{π}

约分:

π

= x

化简

\frac{24 π}{π} - \frac{12 arccos ( \frac{1}{3} )}{π} + \frac{24 πn}{π} : 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

\frac{24 π}{π} - \frac{12 arccos ( \frac{1}{3} )}{π} + \frac{24 πn}{π}

消掉

\frac{24 π}{π} : 24

\frac{24 π}{π}

约分:

π

= 24

= 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + \frac{24 πn}{π}

消掉

\frac{24 πn}{π} : 24 n

\frac{24 πn}{π}

约分:

π

= 24 n

= 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

x = 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

x = 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

x = 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

x = \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n, x = 24 - \frac{12 arccos ( \frac{1}{3} )}{π} + 24 n

以小数形式表示解

x = \frac{12 \cdot 1.23095 \dots}{π} + 24 n, x = 24 - \frac{12 \cdot 1.23095 \dots}{π} + 24 n

作图

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