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受欢迎的三角函数 >

8cos(2x)-1=2

解答

8 cos (2 x) - 1 = 2

解答

x = \frac{1.18639 \dots}{2} + πn, x = π - \frac{1.18639 \dots}{2} + πn

+1

度数

x = 33.98784 \dots^{\circ} + 18 0^{\circ} n, x = 146.01215 \dots^{\circ} + 18 0^{\circ} n

求解步骤

8 cos (2 x) - 1 = 2

将

1

到右边

8 cos (2 x) - 1 = 2

两边加上

1

8 cos (2 x) - 1 + 1 = 2 + 1

化简

8 cos (2 x) = 3

8 cos (2 x) = 3

两边除以

8

8 cos (2 x) = 3

两边除以

8

\frac{8 cos ( 2 x )}{8} = \frac{3}{8}

化简

cos (2 x) = \frac{3}{8}

cos (2 x) = \frac{3}{8}

使用反三角函数性质

cos (2 x) = \frac{3}{8}

cos (2 x) = \frac{3}{8}

的通解

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

2 x = arccos (\frac{3}{8}) + 2 πn, 2 x = 2 π - arccos (\frac{3}{8}) + 2 πn

2 x = arccos (\frac{3}{8}) + 2 πn, 2 x = 2 π - arccos (\frac{3}{8}) + 2 πn

解

2 x = arccos (\frac{3}{8}) + 2 πn : x = \frac{arccos ( \frac{3}{8} )}{2} + πn

2 x = arccos (\frac{3}{8}) + 2 πn

两边除以

2

2 x = arccos (\frac{3}{8}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2}

化简

x = \frac{arccos ( \frac{3}{8} )}{2} + πn

x = \frac{arccos ( \frac{3}{8} )}{2} + πn

解

2 x = 2 π - arccos (\frac{3}{8}) + 2 πn : x = π - \frac{arccos ( \frac{3}{8} )}{2} + πn

2 x = 2 π - arccos (\frac{3}{8}) + 2 πn

两边除以

2

2 x = 2 π - arccos (\frac{3}{8}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2}

化简

x = π - \frac{arccos ( \frac{3}{8} )}{2} + πn

x = π - \frac{arccos ( \frac{3}{8} )}{2} + πn

x = \frac{arccos ( \frac{3}{8} )}{2} + πn, x = π - \frac{arccos ( \frac{3}{8} )}{2} + πn

以小数形式表示解

x = \frac{1.18639 \dots}{2} + πn, x = π - \frac{1.18639 \dots}{2} + πn

作图

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