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受欢迎的三角函数 >

21cos((2pi)/(687)t)+228=220

解答

21 cos (\frac{2 π}{687} t) + 228 = 220

解答

t = \frac{687 \cdot 1.96162 \dots}{2 π} + 687 n, t = - \frac{687 \cdot 1.96162 \dots}{2 π} + 687 n

+1

度数

t = 12288.95420 \dots^{\circ} + 39362.20052 \dots^{\circ} n, t = - 12288.95420 \dots^{\circ} + 39362.20052 \dots^{\circ} n

求解步骤

21 cos (\frac{2 π}{687} t) + 228 = 220

将

228

到右边

21 cos (\frac{2 π}{687} t) + 228 = 220

两边减去

228

21 cos (\frac{2 π}{687} t) + 228 - 228 = 220 - 228

化简

21 cos (\frac{2 π}{687} t) = - 8

21 cos (\frac{2 π}{687} t) = - 8

两边除以

21

21 cos (\frac{2 π}{687} t) = - 8

两边除以

21

\frac{21 cos ( \frac{2 π}{687} t )}{21} = \frac{- 8}{21}

化简

cos (\frac{2 π}{687} t) = - \frac{8}{21}

cos (\frac{2 π}{687} t) = - \frac{8}{21}

使用反三角函数性质

cos (\frac{2 π}{687} t) = - \frac{8}{21}

cos (\frac{2 π}{687} t) = - \frac{8}{21}

的通解

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

\frac{2 π}{687} t = arccos (- \frac{8}{21}) + 2 πn, \frac{2 π}{687} t = - arccos (- \frac{8}{21}) + 2 πn

\frac{2 π}{687} t = arccos (- \frac{8}{21}) + 2 πn, \frac{2 π}{687} t = - arccos (- \frac{8}{21}) + 2 πn

解

\frac{2 π}{687} t = arccos (- \frac{8}{21}) + 2 πn : t = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

\frac{2 π}{687} t = arccos (- \frac{8}{21}) + 2 πn

在两边乘以

687

\frac{2 π}{687} t = arccos (- \frac{8}{21}) + 2 πn

在两边乘以

687

687 \cdot \frac{2 π}{687} t = 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

化简

687 \cdot \frac{2 π}{687} t = 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

化简

687 \cdot \frac{2 π}{687} t : 2 π t

687 \cdot \frac{2 π}{687} t

分式相乘:

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

= \frac{2 \cdot 687 π}{687} t

约分:

687

= t \cdot 2 π

化简

687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn : 687 arccos (- \frac{8}{21}) + 1374 πn

687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

数字相乘:

687 \cdot 2 = 1374

= 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = 687 arccos (- \frac{8}{21}) + 1374 πn

两边除以

2 π

2 π t = 687 arccos (- \frac{8}{21}) + 1374 πn

两边除以

2 π

\frac{2 π t}{2 π} = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π}

化简

\frac{2 π t}{2 π} = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π}

化简

\frac{2 π t}{2 π} : t

\frac{2 π t}{2 π}

数字相除:

\frac{2}{2} = 1

= \frac{π t}{π}

约分:

π

= t

化简

\frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π} : \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

\frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π}

消掉

\frac{1374 πn}{2 π} : 687 n

\frac{1374 πn}{2 π}

消掉

\frac{1374 πn}{2 π} : 687 n

\frac{1374 πn}{2 π}

数字相除:

\frac{1374}{2} = 687

= \frac{687 πn}{π}

约分:

π

= 687 n

= 687 n

= \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

解

\frac{2 π}{687} t = - arccos (- \frac{8}{21}) + 2 πn : t = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

\frac{2 π}{687} t = - arccos (- \frac{8}{21}) + 2 πn

在两边乘以

687

\frac{2 π}{687} t = - arccos (- \frac{8}{21}) + 2 πn

在两边乘以

687

687 \cdot \frac{2 π}{687} t = - 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

化简

687 \cdot \frac{2 π}{687} t = - 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

化简

687 \cdot \frac{2 π}{687} t : 2 π t

687 \cdot \frac{2 π}{687} t

分式相乘:

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

= \frac{2 \cdot 687 π}{687} t

约分:

687

= t \cdot 2 π

化简

- 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn : - 687 arccos (- \frac{8}{21}) + 1374 πn

- 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

数字相乘:

687 \cdot 2 = 1374

= - 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = - 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = - 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = - 687 arccos (- \frac{8}{21}) + 1374 πn

两边除以

2 π

2 π t = - 687 arccos (- \frac{8}{21}) + 1374 πn

两边除以

2 π

\frac{2 π t}{2 π} = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π}

化简

\frac{2 π t}{2 π} = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π}

化简

\frac{2 π t}{2 π} : t

\frac{2 π t}{2 π}

数字相除:

\frac{2}{2} = 1

= \frac{π t}{π}

约分:

π

= t

化简

- \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π} : - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

- \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π}

消掉

\frac{1374 πn}{2 π} : 687 n

\frac{1374 πn}{2 π}

消掉

\frac{1374 πn}{2 π} : 687 n

\frac{1374 πn}{2 π}

数字相除:

\frac{1374}{2} = 687

= \frac{687 πn}{π}

约分:

π

= 687 n

= 687 n

= - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n, t = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

以小数形式表示解

t = \frac{687 \cdot 1.96162 \dots}{2 π} + 687 n, t = - \frac{687 \cdot 1.96162 \dots}{2 π} + 687 n

作图

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