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受欢迎的三角函数 >

9-10cos(2x)=0

解答

9 - 10 cos (2 x) = 0

解答

x = \frac{0.45102 \dots}{2} + πn, x = π - \frac{0.45102 \dots}{2} + πn

+1

度数

x = 12.92096 \dots^{\circ} + 18 0^{\circ} n, x = 167.07903 \dots^{\circ} + 18 0^{\circ} n

求解步骤

9 - 10 cos (2 x) = 0

将

9

到右边

9 - 10 cos (2 x) = 0

两边减去

9

9 - 10 cos (2 x) - 9 = 0 - 9

化简

- 10 cos (2 x) = - 9

- 10 cos (2 x) = - 9

两边除以

- 10

- 10 cos (2 x) = - 9

两边除以

- 10

\frac{- 10 cos ( 2 x )}{- 10} = \frac{- 9}{- 10}

化简

cos (2 x) = \frac{9}{10}

cos (2 x) = \frac{9}{10}

使用反三角函数性质

cos (2 x) = \frac{9}{10}

cos (2 x) = \frac{9}{10}

的通解

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

2 x = arccos (\frac{9}{10}) + 2 πn, 2 x = 2 π - arccos (\frac{9}{10}) + 2 πn

2 x = arccos (\frac{9}{10}) + 2 πn, 2 x = 2 π - arccos (\frac{9}{10}) + 2 πn

解

2 x = arccos (\frac{9}{10}) + 2 πn : x = \frac{arccos ( \frac{9}{10} )}{2} + πn

2 x = arccos (\frac{9}{10}) + 2 πn

两边除以

2

2 x = arccos (\frac{9}{10}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{arccos ( \frac{9}{10} )}{2} + \frac{2 πn}{2}

化简

x = \frac{arccos ( \frac{9}{10} )}{2} + πn

x = \frac{arccos ( \frac{9}{10} )}{2} + πn

解

2 x = 2 π - arccos (\frac{9}{10}) + 2 πn : x = π - \frac{arccos ( \frac{9}{10} )}{2} + πn

2 x = 2 π - arccos (\frac{9}{10}) + 2 πn

两边除以

2

2 x = 2 π - arccos (\frac{9}{10}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{9}{10} )}{2} + \frac{2 πn}{2}

化简

x = π - \frac{arccos ( \frac{9}{10} )}{2} + πn

x = π - \frac{arccos ( \frac{9}{10} )}{2} + πn

x = \frac{arccos ( \frac{9}{10} )}{2} + πn, x = π - \frac{arccos ( \frac{9}{10} )}{2} + πn

以小数形式表示解

x = \frac{0.45102 \dots}{2} + πn, x = π - \frac{0.45102 \dots}{2} + πn

作图

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