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受欢迎的三角函数 >

5cos(5x)=2

解答

5 cos (5 x) = 2

解答

x = \frac{1.15927 \dots}{5} + \frac{2 πn}{5}, x = \frac{2 π}{5} - \frac{1.15927 \dots}{5} + \frac{2 πn}{5}

+1

度数

x = 13.28436 \dots^{\circ} + 7 2^{\circ} n, x = 58.71563 \dots^{\circ} + 7 2^{\circ} n

求解步骤

5 cos (5 x) = 2

两边除以

5

5 cos (5 x) = 2

两边除以

5

\frac{5 cos ( 5 x )}{5} = \frac{2}{5}

化简

cos (5 x) = \frac{2}{5}

cos (5 x) = \frac{2}{5}

使用反三角函数性质

cos (5 x) = \frac{2}{5}

cos (5 x) = \frac{2}{5}

的通解

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

5 x = arccos (\frac{2}{5}) + 2 πn, 5 x = 2 π - arccos (\frac{2}{5}) + 2 πn

5 x = arccos (\frac{2}{5}) + 2 πn, 5 x = 2 π - arccos (\frac{2}{5}) + 2 πn

解

5 x = arccos (\frac{2}{5}) + 2 πn : x = \frac{arccos ( \frac{2}{5} )}{5} + \frac{2 πn}{5}

5 x = arccos (\frac{2}{5}) + 2 πn

两边除以

5

5 x = arccos (\frac{2}{5}) + 2 πn

两边除以

5

\frac{5 x}{5} = \frac{arccos ( \frac{2}{5} )}{5} + \frac{2 πn}{5}

化简

x = \frac{arccos ( \frac{2}{5} )}{5} + \frac{2 πn}{5}

x = \frac{arccos ( \frac{2}{5} )}{5} + \frac{2 πn}{5}

解

5 x = 2 π - arccos (\frac{2}{5}) + 2 πn : x = \frac{2 π}{5} - \frac{arccos ( \frac{2}{5} )}{5} + \frac{2 πn}{5}

5 x = 2 π - arccos (\frac{2}{5}) + 2 πn

两边除以

5

5 x = 2 π - arccos (\frac{2}{5}) + 2 πn

两边除以

5

\frac{5 x}{5} = \frac{2 π}{5} - \frac{arccos ( \frac{2}{5} )}{5} + \frac{2 πn}{5}

化简

x = \frac{2 π}{5} - \frac{arccos ( \frac{2}{5} )}{5} + \frac{2 πn}{5}

x = \frac{2 π}{5} - \frac{arccos ( \frac{2}{5} )}{5} + \frac{2 πn}{5}

x = \frac{arccos ( \frac{2}{5} )}{5} + \frac{2 πn}{5}, x = \frac{2 π}{5} - \frac{arccos ( \frac{2}{5} )}{5} + \frac{2 πn}{5}

以小数形式表示解

x = \frac{1.15927 \dots}{5} + \frac{2 πn}{5}, x = \frac{2 π}{5} - \frac{1.15927 \dots}{5} + \frac{2 πn}{5}

作图

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