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受欢迎的三角函数 >

solvefor t,fw=2+cos(10pit)

解答

求解

t, f w = 2 + cos (10 π t)

解答

t = \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}, t = - \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

求解步骤

f w = 2 + cos (10 π t)

交换两边

2 + cos (10 π t) = f w

将

2

到右边

2 + cos (10 π t) = f w

两边减去

2

2 + cos (10 π t) - 2 = f w - 2

化简

cos (10 π t) = f w - 2

cos (10 π t) = f w - 2

使用反三角函数性质

cos (10 π t) = f w - 2

cos (10 π t) = f w - 2

的通解

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

10 π t = arccos (f w - 2) + 2 πn, 10 π t = - arccos (f w - 2) + 2 πn

10 π t = arccos (f w - 2) + 2 πn, 10 π t = - arccos (f w - 2) + 2 πn

解

10 π t = arccos (f w - 2) + 2 πn : t = \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

10 π t = arccos (f w - 2) + 2 πn

两边除以

10 π

10 π t = arccos (f w - 2) + 2 πn

两边除以

10 π

\frac{10 π t}{10 π} = \frac{arccos ( f w - 2 )}{10 π} + \frac{2 πn}{10 π}

化简

\frac{10 π t}{10 π} = \frac{arccos ( f w - 2 )}{10 π} + \frac{2 πn}{10 π}

化简

\frac{10 π t}{10 π} : t

\frac{10 π t}{10 π}

数字相除:

\frac{10}{10} = 1

= \frac{π t}{π}

约分:

π

= t

化简

\frac{arccos ( f w - 2 )}{10 π} + \frac{2 πn}{10 π} : \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

\frac{arccos ( f w - 2 )}{10 π} + \frac{2 πn}{10 π}

消掉

\frac{2 πn}{10 π} : \frac{n}{5}

\frac{2 πn}{10 π}

消掉

\frac{2 πn}{10 π} : \frac{n}{5}

\frac{2 πn}{10 π}

约分:

2

= \frac{πn}{5 π}

约分:

π

= \frac{n}{5}

= \frac{n}{5}

= \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

t = \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

t = \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

t = \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

解

10 π t = - arccos (f w - 2) + 2 πn : t = - \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

10 π t = - arccos (f w - 2) + 2 πn

两边除以

10 π

10 π t = - arccos (f w - 2) + 2 πn

两边除以

10 π

\frac{10 π t}{10 π} = - \frac{arccos ( f w - 2 )}{10 π} + \frac{2 πn}{10 π}

化简

\frac{10 π t}{10 π} = - \frac{arccos ( f w - 2 )}{10 π} + \frac{2 πn}{10 π}

化简

\frac{10 π t}{10 π} : t

\frac{10 π t}{10 π}

数字相除:

\frac{10}{10} = 1

= \frac{π t}{π}

约分:

π

= t

化简

- \frac{arccos ( f w - 2 )}{10 π} + \frac{2 πn}{10 π} : - \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

- \frac{arccos ( f w - 2 )}{10 π} + \frac{2 πn}{10 π}

消掉

\frac{2 πn}{10 π} : \frac{n}{5}

\frac{2 πn}{10 π}

消掉

\frac{2 πn}{10 π} : \frac{n}{5}

\frac{2 πn}{10 π}

约分:

2

= \frac{πn}{5 π}

约分:

π

= \frac{n}{5}

= \frac{n}{5}

= - \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

t = - \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

t = - \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

t = - \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

t = \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}, t = - \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

作图

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