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受欢迎的三角函数 >

8cos(6x)=2

解答

8 cos (6 x) = 2

解答

x = \frac{1.31811 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{1.31811 \dots}{6} + \frac{πn}{3}

+1

度数

x = 12.58708 \dots^{\circ} + 6 0^{\circ} n, x = 47.41291 \dots^{\circ} + 6 0^{\circ} n

求解步骤

8 cos (6 x) = 2

两边除以

8

8 cos (6 x) = 2

两边除以

8

\frac{8 cos ( 6 x )}{8} = \frac{2}{8}

化简

cos (6 x) = \frac{1}{4}

cos (6 x) = \frac{1}{4}

使用反三角函数性质

cos (6 x) = \frac{1}{4}

cos (6 x) = \frac{1}{4}

的通解

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

6 x = arccos (\frac{1}{4}) + 2 πn, 6 x = 2 π - arccos (\frac{1}{4}) + 2 πn

6 x = arccos (\frac{1}{4}) + 2 πn, 6 x = 2 π - arccos (\frac{1}{4}) + 2 πn

解

6 x = arccos (\frac{1}{4}) + 2 πn : x = \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

6 x = arccos (\frac{1}{4}) + 2 πn

两边除以

6

6 x = arccos (\frac{1}{4}) + 2 πn

两边除以

6

\frac{6 x}{6} = \frac{arccos ( \frac{1}{4} )}{6} + \frac{2 πn}{6}

化简

x = \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

x = \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

解

6 x = 2 π - arccos (\frac{1}{4}) + 2 πn : x = \frac{π}{3} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

6 x = 2 π - arccos (\frac{1}{4}) + 2 πn

两边除以

6

6 x = 2 π - arccos (\frac{1}{4}) + 2 πn

两边除以

6

\frac{6 x}{6} = \frac{2 π}{6} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{2 πn}{6}

化简

\frac{6 x}{6} = \frac{2 π}{6} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{2 πn}{6}

化简

\frac{6 x}{6} : x

\frac{6 x}{6}

数字相除:

\frac{6}{6} = 1

= x

化简

\frac{2 π}{6} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{2 πn}{6} : \frac{π}{3} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

\frac{2 π}{6} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{2 πn}{6}

消掉

\frac{2 π}{6} : \frac{π}{3}

\frac{2 π}{6}

约分:

2

= \frac{π}{3}

= \frac{π}{3} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{2 πn}{6}

消掉

\frac{2 πn}{6} : \frac{πn}{3}

\frac{2 πn}{6}

约分:

2

= \frac{πn}{3}

= \frac{π}{3} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

x = \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

以小数形式表示解

x = \frac{1.31811 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{1.31811 \dots}{6} + \frac{πn}{3}

作图

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