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受欢迎的三角函数 >

cos(3x)= 1/3

解答

cos (3 x) = \frac{1}{3}

解答

x = \frac{1.23095 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{1.23095 \dots}{3} + \frac{2 πn}{3}

+1

度数

x = 23.50959 \dots^{\circ} + 12 0^{\circ} n, x = 96.49040 \dots^{\circ} + 12 0^{\circ} n

求解步骤

cos (3 x) = \frac{1}{3}

使用反三角函数性质

cos (3 x) = \frac{1}{3}

cos (3 x) = \frac{1}{3}

的通解

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

3 x = arccos (\frac{1}{3}) + 2 πn, 3 x = 2 π - arccos (\frac{1}{3}) + 2 πn

3 x = arccos (\frac{1}{3}) + 2 πn, 3 x = 2 π - arccos (\frac{1}{3}) + 2 πn

解

3 x = arccos (\frac{1}{3}) + 2 πn : x = \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

3 x = arccos (\frac{1}{3}) + 2 πn

两边除以

3

3 x = arccos (\frac{1}{3}) + 2 πn

两边除以

3

\frac{3 x}{3} = \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

化简

x = \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

解

3 x = 2 π - arccos (\frac{1}{3}) + 2 πn : x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

3 x = 2 π - arccos (\frac{1}{3}) + 2 πn

两边除以

3

3 x = 2 π - arccos (\frac{1}{3}) + 2 πn

两边除以

3

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

化简

x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

以小数形式表示解

x = \frac{1.23095 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{1.23095 \dots}{3} + \frac{2 πn}{3}

作图

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