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受欢迎的三角函数 >

11.75=5sin((pit)/6-(7pi)/6)+8

解答

11.75 = 5 sin (\frac{π t}{6} - \frac{7 π}{6}) + 8

解答

t = 7 + 12 n + \frac{6 \cdot 0.84806 \dots}{π}, t = 13 + 12 n - \frac{6 \cdot 0.84806 \dots}{π}

+1

度数

t = 493.87124 \dots^{\circ} + 687.54935 \dots^{\circ} n, t = 652.04434 \dots^{\circ} + 687.54935 \dots^{\circ} n

求解步骤

11.75 = 5 sin (\frac{π t}{6} - \frac{7 π}{6}) + 8

交换两边

5 sin (\frac{π t}{6} - \frac{7 π}{6}) + 8 = 11.75

将

8

到右边

5 sin (\frac{π t}{6} - \frac{7 π}{6}) + 8 = 11.75

两边减去

8

5 sin (\frac{π t}{6} - \frac{7 π}{6}) + 8 - 8 = 11.75 - 8

化简

5 sin (\frac{π t}{6} - \frac{7 π}{6}) = 3.75

5 sin (\frac{π t}{6} - \frac{7 π}{6}) = 3.75

两边除以

5

5 sin (\frac{π t}{6} - \frac{7 π}{6}) = 3.75

两边除以

5

\frac{5 sin ( \frac{π t}{6} - \frac{7 π}{6} )}{5} = \frac{3.75}{5}

化简

sin (\frac{π t}{6} - \frac{7 π}{6}) = 0.75

sin (\frac{π t}{6} - \frac{7 π}{6}) = 0.75

使用反三角函数性质

sin (\frac{π t}{6} - \frac{7 π}{6}) = 0.75

sin (\frac{π t}{6} - \frac{7 π}{6}) = 0.75

的通解

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

\frac{π t}{6} - \frac{7 π}{6} = arcsin (0.75) + 2 πn, \frac{π t}{6} - \frac{7 π}{6} = π - arcsin (0.75) + 2 πn

\frac{π t}{6} - \frac{7 π}{6} = arcsin (0.75) + 2 πn, \frac{π t}{6} - \frac{7 π}{6} = π - arcsin (0.75) + 2 πn

解

\frac{π t}{6} - \frac{7 π}{6} = arcsin (0.75) + 2 πn : t = 7 + 12 n + \frac{6 arcsin ( 0.75 )}{π}

\frac{π t}{6} - \frac{7 π}{6} = arcsin (0.75) + 2 πn

将

\frac{7 π}{6}

到右边

\frac{π t}{6} - \frac{7 π}{6} = arcsin (0.75) + 2 πn

两边加上

\frac{7 π}{6}

\frac{π t}{6} - \frac{7 π}{6} + \frac{7 π}{6} = arcsin (0.75) + 2 πn + \frac{7 π}{6}

化简

\frac{π t}{6} = arcsin (0.75) + 2 πn + \frac{7 π}{6}

\frac{π t}{6} = arcsin (0.75) + 2 πn + \frac{7 π}{6}

在两边乘以

6

\frac{π t}{6} = arcsin (0.75) + 2 πn + \frac{7 π}{6}

在两边乘以

6

\frac{6 π t}{6} = 6 arcsin (0.75) + 6 \cdot 2 πn + 6 \cdot \frac{7 π}{6}

化简

\frac{6 π t}{6} = 6 arcsin (0.75) + 6 \cdot 2 πn + 6 \cdot \frac{7 π}{6}

化简

\frac{6 π t}{6} : π t

\frac{6 π t}{6}

数字相除:

\frac{6}{6} = 1

= π t

化简

6 arcsin (0.75) + 6 \cdot 2 πn + 6 \cdot \frac{7 π}{6} : 6 arcsin (0.75) + 12 πn + 7 π

6 arcsin (0.75) + 6 \cdot 2 πn + 6 \cdot \frac{7 π}{6}

6 \cdot 2 πn = 12 πn

6 \cdot 2 πn

数字相乘:

6 \cdot 2 = 12

= 12 πn

6 \cdot \frac{7 π}{6} = 7 π

6 \cdot \frac{7 π}{6}

分式相乘:

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

= \frac{7 π 6}{6}

约分:

6

= 7 π

= 6 arcsin (0.75) + 12 πn + 7 π

π t = 6 arcsin (0.75) + 12 πn + 7 π

π t = 6 arcsin (0.75) + 12 πn + 7 π

π t = 6 arcsin (0.75) + 12 πn + 7 π

两边除以

π

π t = 6 arcsin (0.75) + 12 πn + 7 π

两边除以

π

\frac{π t}{π} = \frac{6 arcsin ( 0.75 )}{π} + \frac{12 πn}{π} + \frac{7 π}{π}

化简

\frac{π t}{π} = \frac{6 arcsin ( 0.75 )}{π} + \frac{12 πn}{π} + \frac{7 π}{π}

化简

\frac{π t}{π} : t

\frac{π t}{π}

约分:

π

= t

化简

\frac{6 arcsin ( 0.75 )}{π} + \frac{12 πn}{π} + \frac{7 π}{π} : 7 + 12 n + \frac{6 arcsin ( 0.75 )}{π}

\frac{6 arcsin ( 0.75 )}{π} + \frac{12 πn}{π} + \frac{7 π}{π}

对同类项分组

= \frac{7 π}{π} + \frac{12 πn}{π} + \frac{6 arcsin ( 0.75 )}{π}

消掉

\frac{7 π}{π} : 7

\frac{7 π}{π}

约分:

π

= 7

= 7 + \frac{12 πn}{π} + \frac{6 arcsin ( 0.75 )}{π}

消掉

\frac{12 πn}{π} : 12 n

\frac{12 πn}{π}

约分:

π

= 12 n

= 7 + 12 n + \frac{6 arcsin ( 0.75 )}{π}

t = 7 + 12 n + \frac{6 arcsin ( 0.75 )}{π}

t = 7 + 12 n + \frac{6 arcsin ( 0.75 )}{π}

t = 7 + 12 n + \frac{6 arcsin ( 0.75 )}{π}

解

\frac{π t}{6} - \frac{7 π}{6} = π - arcsin (0.75) + 2 πn : t = 13 + 12 n - \frac{6 arcsin ( 0.75 )}{π}

\frac{π t}{6} - \frac{7 π}{6} = π - arcsin (0.75) + 2 πn

将

\frac{7 π}{6}

到右边

\frac{π t}{6} - \frac{7 π}{6} = π - arcsin (0.75) + 2 πn

两边加上

\frac{7 π}{6}

\frac{π t}{6} - \frac{7 π}{6} + \frac{7 π}{6} = π - arcsin (0.75) + 2 πn + \frac{7 π}{6}

化简

\frac{π t}{6} = π - arcsin (0.75) + 2 πn + \frac{7 π}{6}

\frac{π t}{6} = π - arcsin (0.75) + 2 πn + \frac{7 π}{6}

在两边乘以

6

\frac{π t}{6} = π - arcsin (0.75) + 2 πn + \frac{7 π}{6}

在两边乘以

6

\frac{6 π t}{6} = 6 π - 6 arcsin (0.75) + 6 \cdot 2 πn + 6 \cdot \frac{7 π}{6}

化简

\frac{6 π t}{6} = 6 π - 6 arcsin (0.75) + 6 \cdot 2 πn + 6 \cdot \frac{7 π}{6}

化简

\frac{6 π t}{6} : π t

\frac{6 π t}{6}

数字相除:

\frac{6}{6} = 1

= π t

化简

6 π - 6 arcsin (0.75) + 6 \cdot 2 πn + 6 \cdot \frac{7 π}{6} : 13 π + 12 πn - 6 arcsin (0.75)

6 π - 6 arcsin (0.75) + 6 \cdot 2 πn + 6 \cdot \frac{7 π}{6}

6 \cdot 2 πn = 12 πn

6 \cdot 2 πn

数字相乘:

6 \cdot 2 = 12

= 12 πn

6 \cdot \frac{7 π}{6} = 7 π

6 \cdot \frac{7 π}{6}

分式相乘:

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

= \frac{7 π 6}{6}

约分:

6

= 7 π

= 6 π - 6 arcsin (0.75) + 12 πn + 7 π

对同类项分组

= 6 π + 7 π + 12 πn - 6 arcsin (0.75)

同类项相加:

6 π + 7 π = 13 π

= 13 π + 12 πn - 6 arcsin (0.75)

π t = 13 π + 12 πn - 6 arcsin (0.75)

π t = 13 π + 12 πn - 6 arcsin (0.75)

π t = 13 π + 12 πn - 6 arcsin (0.75)

两边除以

π

π t = 13 π + 12 πn - 6 arcsin (0.75)

两边除以

π

\frac{π t}{π} = \frac{13 π}{π} + \frac{12 πn}{π} - \frac{6 arcsin ( 0.75 )}{π}

化简

\frac{π t}{π} = \frac{13 π}{π} + \frac{12 πn}{π} - \frac{6 arcsin ( 0.75 )}{π}

化简

\frac{π t}{π} : t

\frac{π t}{π}

约分:

π

= t

化简

\frac{13 π}{π} + \frac{12 πn}{π} - \frac{6 arcsin ( 0.75 )}{π} : 13 + 12 n - \frac{6 arcsin ( 0.75 )}{π}

\frac{13 π}{π} + \frac{12 πn}{π} - \frac{6 arcsin ( 0.75 )}{π}

消掉

\frac{13 π}{π} : 13

\frac{13 π}{π}

约分:

π

= 13

= 13 + \frac{12 πn}{π} - \frac{6 arcsin ( 0.75 )}{π}

消掉

\frac{12 πn}{π} : 12 n

\frac{12 πn}{π}

约分:

π

= 12 n

= 13 + 12 n - \frac{6 arcsin ( 0.75 )}{π}

t = 13 + 12 n - \frac{6 arcsin ( 0.75 )}{π}

t = 13 + 12 n - \frac{6 arcsin ( 0.75 )}{π}

t = 13 + 12 n - \frac{6 arcsin ( 0.75 )}{π}

t = 7 + 12 n + \frac{6 arcsin ( 0.75 )}{π}, t = 13 + 12 n - \frac{6 arcsin ( 0.75 )}{π}

以小数形式表示解

t = 7 + 12 n + \frac{6 \cdot 0.84806 \dots}{π}, t = 13 + 12 n - \frac{6 \cdot 0.84806 \dots}{π}

作图

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