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受欢迎的三角函数 >

50=36sin((2pi)/(365)(t-101))+14

解答

50 = 36 sin (\frac{2 π}{365} (t - 101)) + 14

解答

t = 365 n + \frac{769}{4}

+1

度数

t = 11015.11361 \dots^{\circ} + 20912.95952 \dots^{\circ} n

求解步骤

50 = 36 sin (\frac{2 π}{365} (t - 101)) + 14

交换两边

36 sin (\frac{2 π}{365} (t - 101)) + 14 = 50

将

14

到右边

36 sin (\frac{2 π}{365} (t - 101)) + 14 = 50

两边减去

14

36 sin (\frac{2 π}{365} (t - 101)) + 14 - 14 = 50 - 14

化简

36 sin (\frac{2 π}{365} (t - 101)) = 36

36 sin (\frac{2 π}{365} (t - 101)) = 36

两边除以

36

36 sin (\frac{2 π}{365} (t - 101)) = 36

两边除以

36

\frac{36 sin ( \frac{2 π}{365} ( t - 101 ) )}{36} = \frac{36}{36}

化简

sin (\frac{2 π}{365} (t - 101)) = 1

sin (\frac{2 π}{365} (t - 101)) = 1

sin (\frac{2 π}{365} (t - 101)) = 1

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{2 π}{365} (t - 101) = \frac{π}{2} + 2 πn

\frac{2 π}{365} (t - 101) = \frac{π}{2} + 2 πn

解

\frac{2 π}{365} (t - 101) = \frac{π}{2} + 2 πn : t = 365 n + \frac{769}{4}

\frac{2 π}{365} (t - 101) = \frac{π}{2} + 2 πn

在两边乘以

365

\frac{2 π}{365} (t - 101) = \frac{π}{2} + 2 πn

在两边乘以

365

365 \cdot \frac{2 π}{365} (t - 101) = 365 \cdot \frac{π}{2} + 365 \cdot 2 πn

化简

365 \cdot \frac{2 π}{365} (t - 101) = 365 \cdot \frac{π}{2} + 365 \cdot 2 πn

化简

365 \cdot \frac{2 π}{365} (t - 101) : 2 π (t - 101)

365 \cdot \frac{2 π}{365} (t - 101)

分式相乘:

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

= \frac{2 \cdot 365 π}{365} (t - 101)

约分:

365

= (t - 101) \cdot 2 π

化简

365 \cdot \frac{π}{2} + 365 \cdot 2 πn : \frac{365 π}{2} + 730 πn

365 \cdot \frac{π}{2} + 365 \cdot 2 πn

乘

365 \cdot \frac{π}{2} : \frac{365 π}{2}

365 \cdot \frac{π}{2}

分式相乘:

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

= \frac{π 365}{2}

= \frac{365 π}{2} + 365 \cdot 2 πn

数字相乘:

365 \cdot 2 = 730

= \frac{365 π}{2} + 730 πn

2 π (t - 101) = \frac{365 π}{2} + 730 πn

2 π (t - 101) = \frac{365 π}{2} + 730 πn

2 π (t - 101) = \frac{365 π}{2} + 730 πn

两边除以

2 π

2 π (t - 101) = \frac{365 π}{2} + 730 πn

两边除以

2 π

\frac{2 π ( t - 101 )}{2 π} = \frac{\frac{365 π}{2}}{2 π} + \frac{730 πn}{2 π}

化简

\frac{2 π ( t - 101 )}{2 π} = \frac{\frac{365 π}{2}}{2 π} + \frac{730 πn}{2 π}

化简

\frac{2 π ( t - 101 )}{2 π} : t - 101

\frac{2 π ( t - 101 )}{2 π}

数字相除:

\frac{2}{2} = 1

= \frac{π ( t - 101 )}{π}

约分:

π

= t - 101

化简

\frac{\frac{365 π}{2}}{2 π} + \frac{730 πn}{2 π} : \frac{365}{4} + 365 n

\frac{\frac{365 π}{2}}{2 π} + \frac{730 πn}{2 π}

\frac{\frac{365 π}{2}}{2 π} = \frac{365}{4}

\frac{\frac{365 π}{2}}{2 π}

使用分式法则:

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

= \frac{365 π}{2 \cdot 2 π}

数字相乘:

2 \cdot 2 = 4

= \frac{365 π}{4 π}

约分:

π

= \frac{365}{4}

\frac{730 πn}{2 π} = 365 n

\frac{730 πn}{2 π}

消掉

\frac{730 πn}{2 π} : 365 n

\frac{730 πn}{2 π}

数字相除:

\frac{730}{2} = 365

= \frac{365 πn}{π}

约分:

π

= 365 n

= 365 n

= \frac{365}{4} + 365 n

t - 101 = \frac{365}{4} + 365 n

t - 101 = \frac{365}{4} + 365 n

t - 101 = \frac{365}{4} + 365 n

将

101

到右边

t - 101 = \frac{365}{4} + 365 n

两边加上

101

t - 101 + 101 = \frac{365}{4} + 365 n + 101

化简

t - 101 + 101 = \frac{365}{4} + 365 n + 101

化简

t - 101 + 101 : t

t - 101 + 101

同类项相加:

- 101 + 101 = 0

= t

化简

\frac{365}{4} + 365 n + 101 : 365 n + \frac{769}{4}

\frac{365}{4} + 365 n + 101

合并分式

101 + \frac{365}{4} : \frac{769}{4}

101 + \frac{365}{4}

将项转换为分式:

101 = \frac{101 \cdot 4}{4}

= \frac{101 \cdot 4}{4} + \frac{365}{4}

因为分母相等，所以合并分式:

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

= \frac{101 \cdot 4 + 365}{4}

101 \cdot 4 + 365 = 769

101 \cdot 4 + 365

数字相乘:

101 \cdot 4 = 404

= 404 + 365

数字相加:

404 + 365 = 769

= 769

= \frac{769}{4}

= 365 n + \frac{769}{4}

t = 365 n + \frac{769}{4}

t = 365 n + \frac{769}{4}

t = 365 n + \frac{769}{4}

t = 365 n + \frac{769}{4}

作图

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