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受欢迎的三角函数 >

5cos(3x+60)=4

解答

5 cos (3 x + 60) = 4

解答

x = - 20 + \frac{2 πn}{3} + \frac{0.64350 \dots}{3}, x = \frac{2 π}{3} + \frac{2 πn}{3} - \frac{0.64350 \dots}{3} - 20

+1

度数

x = - 1133.62562 \dots^{\circ} + 12 0^{\circ} n, x = - 1038.20555 \dots^{\circ} + 12 0^{\circ} n

求解步骤

5 cos (3 x + 60) = 4

两边除以

5

5 cos (3 x + 60) = 4

两边除以

5

\frac{5 cos ( 3 x + 60 )}{5} = \frac{4}{5}

化简

cos (3 x + 60) = \frac{4}{5}

cos (3 x + 60) = \frac{4}{5}

使用反三角函数性质

cos (3 x + 60) = \frac{4}{5}

cos (3 x + 60) = \frac{4}{5}

的通解

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

3 x + 60 = arccos (\frac{4}{5}) + 2 πn, 3 x + 60 = 2 π - arccos (\frac{4}{5}) + 2 πn

3 x + 60 = arccos (\frac{4}{5}) + 2 πn, 3 x + 60 = 2 π - arccos (\frac{4}{5}) + 2 πn

解

3 x + 60 = arccos (\frac{4}{5}) + 2 πn : x = - 20 + \frac{2 πn}{3} + \frac{arccos ( \frac{4}{5} )}{3}

3 x + 60 = arccos (\frac{4}{5}) + 2 πn

将

60

到右边

3 x + 60 = arccos (\frac{4}{5}) + 2 πn

两边减去

60

3 x + 60 - 60 = arccos (\frac{4}{5}) + 2 πn - 60

化简

3 x = arccos (\frac{4}{5}) + 2 πn - 60

3 x = arccos (\frac{4}{5}) + 2 πn - 60

两边除以

3

3 x = arccos (\frac{4}{5}) + 2 πn - 60

两边除以

3

\frac{3 x}{3} = \frac{arccos ( \frac{4}{5} )}{3} + \frac{2 πn}{3} - \frac{60}{3}

化简

\frac{3 x}{3} = \frac{arccos ( \frac{4}{5} )}{3} + \frac{2 πn}{3} - \frac{60}{3}

化简

\frac{3 x}{3} : x

\frac{3 x}{3}

数字相除:

\frac{3}{3} = 1

= x

化简

\frac{arccos ( \frac{4}{5} )}{3} + \frac{2 πn}{3} - \frac{60}{3} : - 20 + \frac{2 πn}{3} + \frac{arccos ( \frac{4}{5} )}{3}

\frac{arccos ( \frac{4}{5} )}{3} + \frac{2 πn}{3} - \frac{60}{3}

对同类项分组

= - \frac{60}{3} + \frac{2 πn}{3} + \frac{arccos ( \frac{4}{5} )}{3}

数字相除:

\frac{60}{3} = 20

= - 20 + \frac{2 πn}{3} + \frac{arccos ( \frac{4}{5} )}{3}

x = - 20 + \frac{2 πn}{3} + \frac{arccos ( \frac{4}{5} )}{3}

x = - 20 + \frac{2 πn}{3} + \frac{arccos ( \frac{4}{5} )}{3}

x = - 20 + \frac{2 πn}{3} + \frac{arccos ( \frac{4}{5} )}{3}

解

3 x + 60 = 2 π - arccos (\frac{4}{5}) + 2 πn : x = \frac{2 π}{3} + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3} - 20

3 x + 60 = 2 π - arccos (\frac{4}{5}) + 2 πn

将

60

到右边

3 x + 60 = 2 π - arccos (\frac{4}{5}) + 2 πn

两边减去

60

3 x + 60 - 60 = 2 π - arccos (\frac{4}{5}) + 2 πn - 60

化简

3 x = 2 π - arccos (\frac{4}{5}) + 2 πn - 60

3 x = 2 π - arccos (\frac{4}{5}) + 2 πn - 60

两边除以

3

3 x = 2 π - arccos (\frac{4}{5}) + 2 πn - 60

两边除以

3

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{4}{5} )}{3} + \frac{2 πn}{3} - \frac{60}{3}

化简

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{4}{5} )}{3} + \frac{2 πn}{3} - \frac{60}{3}

化简

\frac{3 x}{3} : x

\frac{3 x}{3}

数字相除:

\frac{3}{3} = 1

= x

化简

\frac{2 π}{3} - \frac{arccos ( \frac{4}{5} )}{3} + \frac{2 πn}{3} - \frac{60}{3} : \frac{2 π}{3} + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3} - 20

\frac{2 π}{3} - \frac{arccos ( \frac{4}{5} )}{3} + \frac{2 πn}{3} - \frac{60}{3}

对同类项分组

= \frac{2 π}{3} - \frac{60}{3} + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3}

数字相除:

\frac{60}{3} = 20

= \frac{2 π}{3} - 20 + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3}

对同类项分组

= \frac{2 π}{3} + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3} - 20

x = \frac{2 π}{3} + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3} - 20

x = \frac{2 π}{3} + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3} - 20

x = \frac{2 π}{3} + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3} - 20

x = - 20 + \frac{2 πn}{3} + \frac{arccos ( \frac{4}{5} )}{3}, x = \frac{2 π}{3} + \frac{2 πn}{3} - \frac{arccos ( \frac{4}{5} )}{3} - 20

以小数形式表示解

x = - 20 + \frac{2 πn}{3} + \frac{0.64350 \dots}{3}, x = \frac{2 π}{3} + \frac{2 πn}{3} - \frac{0.64350 \dots}{3} - 20

作图

流行的例子

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