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受欢迎的三角函数 >

cos(2x)=((5k-8))/5

解答

cos (2 x) = \frac{( 5 k - 8 )}{5}

解答

x = \frac{arccos ( \frac{5 k - 8}{5} )}{2} + πn, x = - \frac{arccos ( \frac{5 k - 8}{5} )}{2} + πn

求解步骤

cos (2 x) = \frac{( 5 k - 8 )}{5}

使用反三角函数性质

cos (2 x) = \frac{5 k - 8}{5}

cos (2 x) = \frac{5 k - 8}{5}

的通解

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

2 x = arccos (\frac{5 k - 8}{5}) + 2 πn, 2 x = - arccos (\frac{5 k - 8}{5}) + 2 πn

2 x = arccos (\frac{5 k - 8}{5}) + 2 πn, 2 x = - arccos (\frac{5 k - 8}{5}) + 2 πn

解

2 x = arccos (\frac{5 k - 8}{5}) + 2 πn : x = \frac{arccos ( \frac{5 k - 8}{5} )}{2} + πn

2 x = arccos (\frac{5 k - 8}{5}) + 2 πn

两边除以

2

2 x = arccos (\frac{5 k - 8}{5}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{arccos ( \frac{5 k - 8}{5} )}{2} + \frac{2 πn}{2}

化简

x = \frac{arccos ( \frac{5 k - 8}{5} )}{2} + πn

x = \frac{arccos ( \frac{5 k - 8}{5} )}{2} + πn

解

2 x = - arccos (\frac{5 k - 8}{5}) + 2 πn : x = - \frac{arccos ( \frac{5 k - 8}{5} )}{2} + πn

2 x = - arccos (\frac{5 k - 8}{5}) + 2 πn

两边除以

2

2 x = - arccos (\frac{5 k - 8}{5}) + 2 πn

两边除以

2

\frac{2 x}{2} = - \frac{arccos ( \frac{5 k - 8}{5} )}{2} + \frac{2 πn}{2}

化简

x = - \frac{arccos ( \frac{5 k - 8}{5} )}{2} + πn

x = - \frac{arccos ( \frac{5 k - 8}{5} )}{2} + πn

x = \frac{arccos ( \frac{5 k - 8}{5} )}{2} + πn, x = - \frac{arccos ( \frac{5 k - 8}{5} )}{2} + πn

作图

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