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受欢迎的三角函数 >

solvefor t,10=14+8sin((pit)/(12))

解答

求解

t, 10 = 14 + 8 sin (\frac{π t}{12})

解答

t = 14 + 24 n, t = 22 + 24 n

+1

度数

t = 802.14091 \dots^{\circ} + 1375.09870 \dots^{\circ} n, t = 1260.50714 \dots^{\circ} + 1375.09870 \dots^{\circ} n

求解步骤

10 = 14 + 8 sin (\frac{π t}{12})

交换两边

14 + 8 sin (\frac{π t}{12}) = 10

将

14

到右边

14 + 8 sin (\frac{π t}{12}) = 10

两边减去

14

14 + 8 sin (\frac{π t}{12}) - 14 = 10 - 14

化简

8 sin (\frac{π t}{12}) = - 4

8 sin (\frac{π t}{12}) = - 4

两边除以

8

8 sin (\frac{π t}{12}) = - 4

两边除以

8

\frac{8 sin ( \frac{π t}{12} )}{8} = \frac{- 4}{8}

化简

\frac{8 sin ( \frac{π t}{12} )}{8} = \frac{- 4}{8}

化简

\frac{8 sin ( \frac{π t}{12} )}{8} : sin (\frac{π t}{12})

\frac{8 sin ( \frac{π t}{12} )}{8}

数字相除:

\frac{8}{8} = 1

= sin (\frac{π t}{12})

化简

\frac{- 4}{8} : - \frac{1}{2}

\frac{- 4}{8}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{4}{8}

约分:

4

= - \frac{1}{2}

sin (\frac{π t}{12}) = - \frac{1}{2}

sin (\frac{π t}{12}) = - \frac{1}{2}

sin (\frac{π t}{12}) = - \frac{1}{2}

sin (\frac{π t}{12}) = - \frac{1}{2}

的通解

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{π t}{12} = \frac{7 π}{6} + 2 πn, \frac{π t}{12} = \frac{11 π}{6} + 2 πn

\frac{π t}{12} = \frac{7 π}{6} + 2 πn, \frac{π t}{12} = \frac{11 π}{6} + 2 πn

解

\frac{π t}{12} = \frac{7 π}{6} + 2 πn : t = 14 + 24 n

\frac{π t}{12} = \frac{7 π}{6} + 2 πn

在两边乘以

12

\frac{π t}{12} = \frac{7 π}{6} + 2 πn

在两边乘以

12

\frac{12 π t}{12} = 12 \cdot \frac{7 π}{6} + 12 \cdot 2 πn

化简

\frac{12 π t}{12} = 12 \cdot \frac{7 π}{6} + 12 \cdot 2 πn

化简

\frac{12 π t}{12} : π t

\frac{12 π t}{12}

数字相除:

\frac{12}{12} = 1

= π t

化简

12 \cdot \frac{7 π}{6} + 12 \cdot 2 πn : 14 π + 24 πn

12 \cdot \frac{7 π}{6} + 12 \cdot 2 πn

12 \cdot \frac{7 π}{6} = 14 π

12 \cdot \frac{7 π}{6}

分式相乘:

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

= \frac{7 π 12}{6}

数字相乘:

7 \cdot 12 = 84

= \frac{84 π}{6}

数字相除:

\frac{84}{6} = 14

= 14 π

12 \cdot 2 πn = 24 πn

12 \cdot 2 πn

数字相乘:

12 \cdot 2 = 24

= 24 πn

= 14 π + 24 πn

π t = 14 π + 24 πn

π t = 14 π + 24 πn

π t = 14 π + 24 πn

两边除以

π

π t = 14 π + 24 πn

两边除以

π

\frac{π t}{π} = \frac{14 π}{π} + \frac{24 πn}{π}

化简

\frac{π t}{π} = \frac{14 π}{π} + \frac{24 πn}{π}

化简

\frac{π t}{π} : t

\frac{π t}{π}

约分:

π

= t

化简

\frac{14 π}{π} + \frac{24 πn}{π} : 14 + 24 n

\frac{14 π}{π} + \frac{24 πn}{π}

消掉

\frac{14 π}{π} : 14

\frac{14 π}{π}

约分:

π

= 14

= 14 + \frac{24 πn}{π}

消掉

\frac{24 πn}{π} : 24 n

\frac{24 πn}{π}

约分:

π

= 24 n

= 14 + 24 n

t = 14 + 24 n

t = 14 + 24 n

t = 14 + 24 n

解

\frac{π t}{12} = \frac{11 π}{6} + 2 πn : t = 22 + 24 n

\frac{π t}{12} = \frac{11 π}{6} + 2 πn

在两边乘以

12

\frac{π t}{12} = \frac{11 π}{6} + 2 πn

在两边乘以

12

\frac{12 π t}{12} = 12 \cdot \frac{11 π}{6} + 12 \cdot 2 πn

化简

\frac{12 π t}{12} = 12 \cdot \frac{11 π}{6} + 12 \cdot 2 πn

化简

\frac{12 π t}{12} : π t

\frac{12 π t}{12}

数字相除:

\frac{12}{12} = 1

= π t

化简

12 \cdot \frac{11 π}{6} + 12 \cdot 2 πn : 22 π + 24 πn

12 \cdot \frac{11 π}{6} + 12 \cdot 2 πn

12 \cdot \frac{11 π}{6} = 22 π

12 \cdot \frac{11 π}{6}

分式相乘:

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

= \frac{11 π 12}{6}

数字相乘:

11 \cdot 12 = 132

= \frac{132 π}{6}

数字相除:

\frac{132}{6} = 22

= 22 π

12 \cdot 2 πn = 24 πn

12 \cdot 2 πn

数字相乘:

12 \cdot 2 = 24

= 24 πn

= 22 π + 24 πn

π t = 22 π + 24 πn

π t = 22 π + 24 πn

π t = 22 π + 24 πn

两边除以

π

π t = 22 π + 24 πn

两边除以

π

\frac{π t}{π} = \frac{22 π}{π} + \frac{24 πn}{π}

化简

\frac{π t}{π} = \frac{22 π}{π} + \frac{24 πn}{π}

化简

\frac{π t}{π} : t

\frac{π t}{π}

约分:

π

= t

化简

\frac{22 π}{π} + \frac{24 πn}{π} : 22 + 24 n

\frac{22 π}{π} + \frac{24 πn}{π}

消掉

\frac{22 π}{π} : 22

\frac{22 π}{π}

约分:

π

= 22

= 22 + \frac{24 πn}{π}

消掉

\frac{24 πn}{π} : 24 n

\frac{24 πn}{π}

约分:

π

= 24 n

= 22 + 24 n

t = 22 + 24 n

t = 22 + 24 n

t = 22 + 24 n

t = 14 + 24 n, t = 22 + 24 n

作图

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