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受欢迎的三角函数 >

4cos(2x)-1=0

解答

4 cos (2 x) - 1 = 0

解答

x = \frac{1.31811 \dots}{2} + πn, x = π - \frac{1.31811 \dots}{2} + πn

+1

度数

x = 37.76124 \dots^{\circ} + 18 0^{\circ} n, x = 142.23875 \dots^{\circ} + 18 0^{\circ} n

求解步骤

4 cos (2 x) - 1 = 0

将

1

到右边

4 cos (2 x) - 1 = 0

两边加上

1

4 cos (2 x) - 1 + 1 = 0 + 1

化简

4 cos (2 x) = 1

4 cos (2 x) = 1

两边除以

4

4 cos (2 x) = 1

两边除以

4

\frac{4 cos ( 2 x )}{4} = \frac{1}{4}

化简

cos (2 x) = \frac{1}{4}

cos (2 x) = \frac{1}{4}

使用反三角函数性质

cos (2 x) = \frac{1}{4}

cos (2 x) = \frac{1}{4}

的通解

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

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

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

解

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

2 x = arccos (\frac{1}{4}) + 2 πn

两边除以

2

2 x = arccos (\frac{1}{4}) + 2 πn

两边除以

2

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

化简

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

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

解

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

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

两边除以

2

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

两边除以

2

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

化简

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

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

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

以小数形式表示解

x = \frac{1.31811 \dots}{2} + πn, x = π - \frac{1.31811 \dots}{2} + πn

作图

流行的例子

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3 tan^{2} (θ) = 1

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3 cos (x) = 2 sin^{2} (x)

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