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受欢迎的三角函数 >

105=100+30sin((12pi)/5 t)

解答

105 = 100 + 30 sin (\frac{12 π}{5} t)

解答

t = \frac{5 \cdot 0.16744 \dots}{12 π} + \frac{5 n}{6}, t = \frac{5}{12} - \frac{5 \cdot 0.16744 \dots}{12 π} + \frac{5 n}{6}

+1

度数

t = 1.27245 \dots^{\circ} + 47.74648 \dots^{\circ} n, t = 22.60078 \dots^{\circ} + 47.74648 \dots^{\circ} n

求解步骤

105 = 100 + 30 sin (\frac{12 π}{5} t)

交换两边

100 + 30 sin (\frac{12 π}{5} t) = 105

将

100

到右边

100 + 30 sin (\frac{12 π}{5} t) = 105

两边减去

100

100 + 30 sin (\frac{12 π}{5} t) - 100 = 105 - 100

化简

30 sin (\frac{12 π}{5} t) = 5

30 sin (\frac{12 π}{5} t) = 5

两边除以

30

30 sin (\frac{12 π}{5} t) = 5

两边除以

30

\frac{30 sin ( \frac{12 π}{5} t )}{30} = \frac{5}{30}

化简

sin (\frac{12 π}{5} t) = \frac{1}{6}

sin (\frac{12 π}{5} t) = \frac{1}{6}

使用反三角函数性质

sin (\frac{12 π}{5} t) = \frac{1}{6}

sin (\frac{12 π}{5} t) = \frac{1}{6}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

\frac{12 π}{5} t = arcsin (\frac{1}{6}) + 2 πn, \frac{12 π}{5} t = π - arcsin (\frac{1}{6}) + 2 πn

\frac{12 π}{5} t = arcsin (\frac{1}{6}) + 2 πn, \frac{12 π}{5} t = π - arcsin (\frac{1}{6}) + 2 πn

解

\frac{12 π}{5} t = arcsin (\frac{1}{6}) + 2 πn : t = \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

\frac{12 π}{5} t = arcsin (\frac{1}{6}) + 2 πn

在两边乘以

5

\frac{12 π}{5} t = arcsin (\frac{1}{6}) + 2 πn

在两边乘以

5

5 \cdot \frac{12 π}{5} t = 5 arcsin (\frac{1}{6}) + 5 \cdot 2 πn

化简

5 \cdot \frac{12 π}{5} t = 5 arcsin (\frac{1}{6}) + 5 \cdot 2 πn

化简

5 \cdot \frac{12 π}{5} t : 12 π t

5 \cdot \frac{12 π}{5} t

分式相乘:

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

= \frac{12 \cdot 5 π}{5} t

约分:

5

= t \cdot 12 π

化简

5 arcsin (\frac{1}{6}) + 5 \cdot 2 πn : 5 arcsin (\frac{1}{6}) + 10 πn

5 arcsin (\frac{1}{6}) + 5 \cdot 2 πn

数字相乘:

5 \cdot 2 = 10

= 5 arcsin (\frac{1}{6}) + 10 πn

12 π t = 5 arcsin (\frac{1}{6}) + 10 πn

12 π t = 5 arcsin (\frac{1}{6}) + 10 πn

12 π t = 5 arcsin (\frac{1}{6}) + 10 πn

两边除以

12 π

12 π t = 5 arcsin (\frac{1}{6}) + 10 πn

两边除以

12 π

\frac{12 π t}{12 π} = \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π}

化简

\frac{12 π t}{12 π} = \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π}

化简

\frac{12 π t}{12 π} : t

\frac{12 π t}{12 π}

数字相除:

\frac{12}{12} = 1

= \frac{π t}{π}

约分:

π

= t

化简

\frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π} : \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

\frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π}

消掉

\frac{10 πn}{12 π} : \frac{5 n}{6}

\frac{10 πn}{12 π}

消掉

\frac{10 πn}{12 π} : \frac{5 n}{6}

\frac{10 πn}{12 π}

约分:

2

= \frac{5 πn}{6 π}

约分:

π

= \frac{5 n}{6}

= \frac{5 n}{6}

= \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

t = \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

t = \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

t = \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

解

\frac{12 π}{5} t = π - arcsin (\frac{1}{6}) + 2 πn : t = \frac{5}{12} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

\frac{12 π}{5} t = π - arcsin (\frac{1}{6}) + 2 πn

在两边乘以

5

\frac{12 π}{5} t = π - arcsin (\frac{1}{6}) + 2 πn

在两边乘以

5

5 \cdot \frac{12 π}{5} t = 5 π - 5 arcsin (\frac{1}{6}) + 5 \cdot 2 πn

化简

5 \cdot \frac{12 π}{5} t = 5 π - 5 arcsin (\frac{1}{6}) + 5 \cdot 2 πn

化简

5 \cdot \frac{12 π}{5} t : 12 π t

5 \cdot \frac{12 π}{5} t

分式相乘:

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

= \frac{12 \cdot 5 π}{5} t

约分:

5

= t \cdot 12 π

化简

5 π - 5 arcsin (\frac{1}{6}) + 5 \cdot 2 πn : 5 π - 5 arcsin (\frac{1}{6}) + 10 πn

5 π - 5 arcsin (\frac{1}{6}) + 5 \cdot 2 πn

数字相乘:

5 \cdot 2 = 10

= 5 π - 5 arcsin (\frac{1}{6}) + 10 πn

12 π t = 5 π - 5 arcsin (\frac{1}{6}) + 10 πn

12 π t = 5 π - 5 arcsin (\frac{1}{6}) + 10 πn

12 π t = 5 π - 5 arcsin (\frac{1}{6}) + 10 πn

两边除以

12 π

12 π t = 5 π - 5 arcsin (\frac{1}{6}) + 10 πn

两边除以

12 π

\frac{12 π t}{12 π} = \frac{5 π}{12 π} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π}

化简

\frac{12 π t}{12 π} = \frac{5 π}{12 π} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π}

化简

\frac{12 π t}{12 π} : t

\frac{12 π t}{12 π}

数字相除:

\frac{12}{12} = 1

= \frac{π t}{π}

约分:

π

= t

化简

\frac{5 π}{12 π} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π} : \frac{5}{12} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

\frac{5 π}{12 π} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π}

消掉

\frac{5 π}{12 π} : \frac{5}{12}

\frac{5 π}{12 π}

约分:

π

= \frac{5}{12}

= \frac{5}{12} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π}

消掉

\frac{10 πn}{12 π} : \frac{5 n}{6}

\frac{10 πn}{12 π}

消掉

\frac{10 πn}{12 π} : \frac{5 n}{6}

\frac{10 πn}{12 π}

约分:

2

= \frac{5 πn}{6 π}

约分:

π

= \frac{5 n}{6}

= \frac{5 n}{6}

= \frac{5}{12} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

t = \frac{5}{12} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

t = \frac{5}{12} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

t = \frac{5}{12} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

t = \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}, t = \frac{5}{12} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

以小数形式表示解

t = \frac{5 \cdot 0.16744 \dots}{12 π} + \frac{5 n}{6}, t = \frac{5}{12} - \frac{5 \cdot 0.16744 \dots}{12 π} + \frac{5 n}{6}

作图

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