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受欢迎的三角函数 >

solvefor x,r^2=9cos(2x)

解答

求解

x, r^{2} = 9 cos (2 x)

解答

x = \frac{arccos ( \frac{r ^{2}}{9} )}{2} + πn, x = - \frac{arccos ( \frac{r ^{2}}{9} )}{2} + πn

求解步骤

r^{2} = 9 cos (2 x)

交换两边

9 cos (2 x) = r^{2}

两边除以

9

9 cos (2 x) = r^{2}

两边除以

9

\frac{9 cos ( 2 x )}{9} = \frac{r ^{2}}{9}

化简

cos (2 x) = \frac{r ^{2}}{9}

cos (2 x) = \frac{r ^{2}}{9}

使用反三角函数性质

cos (2 x) = \frac{r ^{2}}{9}

cos (2 x) = \frac{r ^{2}}{9}

的通解

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

2 x = arccos (\frac{r ^{2}}{9}) + 2 πn, 2 x = - arccos (\frac{r ^{2}}{9}) + 2 πn

2 x = arccos (\frac{r ^{2}}{9}) + 2 πn, 2 x = - arccos (\frac{r ^{2}}{9}) + 2 πn

解

2 x = arccos (\frac{r ^{2}}{9}) + 2 πn : x = \frac{arccos ( \frac{r ^{2}}{9} )}{2} + πn

2 x = arccos (\frac{r ^{2}}{9}) + 2 πn

两边除以

2

2 x = arccos (\frac{r ^{2}}{9}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{arccos ( \frac{r ^{2}}{9} )}{2} + \frac{2 πn}{2}

化简

x = \frac{arccos ( \frac{r ^{2}}{9} )}{2} + πn

x = \frac{arccos ( \frac{r ^{2}}{9} )}{2} + πn

解

2 x = - arccos (\frac{r ^{2}}{9}) + 2 πn : x = - \frac{arccos ( \frac{r ^{2}}{9} )}{2} + πn

2 x = - arccos (\frac{r ^{2}}{9}) + 2 πn

两边除以

2

2 x = - arccos (\frac{r ^{2}}{9}) + 2 πn

两边除以

2

\frac{2 x}{2} = - \frac{arccos ( \frac{r ^{2}}{9} )}{2} + \frac{2 πn}{2}

化简

x = - \frac{arccos ( \frac{r ^{2}}{9} )}{2} + πn

x = - \frac{arccos ( \frac{r ^{2}}{9} )}{2} + πn

x = \frac{arccos ( \frac{r ^{2}}{9} )}{2} + πn, x = - \frac{arccos ( \frac{r ^{2}}{9} )}{2} + πn

作图

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