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受欢迎的三角函数 >

6/pi =3cos(2x)

解答

\frac{6}{π} = 3 cos (2 x)

解答

x = \frac{0.88068 \dots}{2} + πn, x = π - \frac{0.88068 \dots}{2} + πn

+1

度数

x = 25.22988 \dots^{\circ} + 18 0^{\circ} n, x = 154.77011 \dots^{\circ} + 18 0^{\circ} n

求解步骤

\frac{6}{π} = 3 cos (2 x)

交换两边

3 cos (2 x) = \frac{6}{π}

两边除以

3

3 cos (2 x) = \frac{6}{π}

两边除以

3

\frac{3 cos ( 2 x )}{3} = \frac{\frac{6}{π}}{3}

化简

\frac{3 cos ( 2 x )}{3} = \frac{\frac{6}{π}}{3}

化简

\frac{3 cos ( 2 x )}{3} : cos (2 x)

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

数字相除:

\frac{3}{3} = 1

= cos (2 x)

化简

\frac{\frac{6}{π}}{3} : \frac{2}{π}

\frac{\frac{6}{π}}{3}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{6}{π 3}

数字相除:

\frac{6}{3} = 2

= \frac{2}{π}

cos (2 x) = \frac{2}{π}

cos (2 x) = \frac{2}{π}

cos (2 x) = \frac{2}{π}

使用反三角函数性质

cos (2 x) = \frac{2}{π}

cos (2 x) = \frac{2}{π}

的通解

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

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

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

解

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

2 x = arccos (\frac{2}{π}) + 2 πn

两边除以

2

2 x = arccos (\frac{2}{π}) + 2 πn

两边除以

2

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

化简

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

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

解

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

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

两边除以

2

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

两边除以

2

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

化简

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

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

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

以小数形式表示解

x = \frac{0.88068 \dots}{2} + πn, x = π - \frac{0.88068 \dots}{2} + πn

作图

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