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受欢迎的三角函数 >

10sin(20t-pi/6)=8

解答

10 sin (20 t - \frac{π}{6}) = 8

解答

t = \frac{πn}{10} + \frac{π}{120} + \frac{0.92729 \dots}{20}, t = \frac{π}{20} + \frac{π}{120} + \frac{πn}{10} - \frac{0.92729 \dots}{20}

+1

度数

t = 4.15650 \dots^{\circ} + 1 8^{\circ} n, t = 7.84349 \dots^{\circ} + 1 8^{\circ} n

求解步骤

10 sin (20 t - \frac{π}{6}) = 8

两边除以

10

10 sin (20 t - \frac{π}{6}) = 8

两边除以

10

\frac{10 sin ( 20 t - \frac{π}{6} )}{10} = \frac{8}{10}

化简

sin (20 t - \frac{π}{6}) = \frac{4}{5}

sin (20 t - \frac{π}{6}) = \frac{4}{5}

使用反三角函数性质

sin (20 t - \frac{π}{6}) = \frac{4}{5}

sin (20 t - \frac{π}{6}) = \frac{4}{5}

的通解

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

20 t - \frac{π}{6} = arcsin (\frac{4}{5}) + 2 πn, 20 t - \frac{π}{6} = π - arcsin (\frac{4}{5}) + 2 πn

20 t - \frac{π}{6} = arcsin (\frac{4}{5}) + 2 πn, 20 t - \frac{π}{6} = π - arcsin (\frac{4}{5}) + 2 πn

解

20 t - \frac{π}{6} = arcsin (\frac{4}{5}) + 2 πn : t = \frac{πn}{10} + \frac{π}{120} + \frac{arcsin ( \frac{4}{5} )}{20}

20 t - \frac{π}{6} = arcsin (\frac{4}{5}) + 2 πn

将

\frac{π}{6}

到右边

20 t - \frac{π}{6} = arcsin (\frac{4}{5}) + 2 πn

两边加上

\frac{π}{6}

20 t - \frac{π}{6} + \frac{π}{6} = arcsin (\frac{4}{5}) + 2 πn + \frac{π}{6}

化简

20 t = arcsin (\frac{4}{5}) + 2 πn + \frac{π}{6}

20 t = arcsin (\frac{4}{5}) + 2 πn + \frac{π}{6}

两边除以

20

20 t = arcsin (\frac{4}{5}) + 2 πn + \frac{π}{6}

两边除以

20

\frac{20 t}{20} = \frac{arcsin ( \frac{4}{5} )}{20} + \frac{2 πn}{20} + \frac{\frac{π}{6}}{20}

化简

\frac{20 t}{20} = \frac{arcsin ( \frac{4}{5} )}{20} + \frac{2 πn}{20} + \frac{\frac{π}{6}}{20}

化简

\frac{20 t}{20} : t

\frac{20 t}{20}

数字相除:

\frac{20}{20} = 1

= t

化简

\frac{arcsin ( \frac{4}{5} )}{20} + \frac{2 πn}{20} + \frac{\frac{π}{6}}{20} : \frac{πn}{10} + \frac{π}{120} + \frac{arcsin ( \frac{4}{5} )}{20}

\frac{arcsin ( \frac{4}{5} )}{20} + \frac{2 πn}{20} + \frac{\frac{π}{6}}{20}

对同类项分组

= \frac{2 πn}{20} + \frac{\frac{π}{6}}{20} + \frac{arcsin ( \frac{4}{5} )}{20}

\frac{2 πn}{20} = \frac{πn}{10}

\frac{2 πn}{20}

约分:

2

= \frac{πn}{10}

\frac{\frac{π}{6}}{20} = \frac{π}{120}

\frac{\frac{π}{6}}{20}

使用分式法则:

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

= \frac{π}{6 \cdot 20}

数字相乘:

6 \cdot 20 = 120

= \frac{π}{120}

= \frac{πn}{10} + \frac{π}{120} + \frac{arcsin ( \frac{4}{5} )}{20}

t = \frac{πn}{10} + \frac{π}{120} + \frac{arcsin ( \frac{4}{5} )}{20}

t = \frac{πn}{10} + \frac{π}{120} + \frac{arcsin ( \frac{4}{5} )}{20}

t = \frac{πn}{10} + \frac{π}{120} + \frac{arcsin ( \frac{4}{5} )}{20}

解

20 t - \frac{π}{6} = π - arcsin (\frac{4}{5}) + 2 πn : t = \frac{π}{20} + \frac{π}{120} + \frac{πn}{10} - \frac{arcsin ( \frac{4}{5} )}{20}

20 t - \frac{π}{6} = π - arcsin (\frac{4}{5}) + 2 πn

将

\frac{π}{6}

到右边

20 t - \frac{π}{6} = π - arcsin (\frac{4}{5}) + 2 πn

两边加上

\frac{π}{6}

20 t - \frac{π}{6} + \frac{π}{6} = π - arcsin (\frac{4}{5}) + 2 πn + \frac{π}{6}

化简

20 t = π - arcsin (\frac{4}{5}) + 2 πn + \frac{π}{6}

20 t = π - arcsin (\frac{4}{5}) + 2 πn + \frac{π}{6}

两边除以

20

20 t = π - arcsin (\frac{4}{5}) + 2 πn + \frac{π}{6}

两边除以

20

\frac{20 t}{20} = \frac{π}{20} - \frac{arcsin ( \frac{4}{5} )}{20} + \frac{2 πn}{20} + \frac{\frac{π}{6}}{20}

化简

\frac{20 t}{20} = \frac{π}{20} - \frac{arcsin ( \frac{4}{5} )}{20} + \frac{2 πn}{20} + \frac{\frac{π}{6}}{20}

化简

\frac{20 t}{20} : t

\frac{20 t}{20}

数字相除:

\frac{20}{20} = 1

= t

化简

\frac{π}{20} - \frac{arcsin ( \frac{4}{5} )}{20} + \frac{2 πn}{20} + \frac{\frac{π}{6}}{20} : \frac{π}{20} + \frac{π}{120} + \frac{πn}{10} - \frac{arcsin ( \frac{4}{5} )}{20}

\frac{π}{20} - \frac{arcsin ( \frac{4}{5} )}{20} + \frac{2 πn}{20} + \frac{\frac{π}{6}}{20}

对同类项分组

= \frac{π}{20} + \frac{2 πn}{20} + \frac{\frac{π}{6}}{20} - \frac{arcsin ( \frac{4}{5} )}{20}

\frac{2 πn}{20} = \frac{πn}{10}

\frac{2 πn}{20}

约分:

2

= \frac{πn}{10}

\frac{\frac{π}{6}}{20} = \frac{π}{120}

\frac{\frac{π}{6}}{20}

使用分式法则:

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

= \frac{π}{6 \cdot 20}

数字相乘:

6 \cdot 20 = 120

= \frac{π}{120}

= \frac{π}{20} + \frac{πn}{10} + \frac{π}{120} - \frac{arcsin ( \frac{4}{5} )}{20}

对同类项分组

= \frac{π}{20} + \frac{π}{120} + \frac{πn}{10} - \frac{arcsin ( \frac{4}{5} )}{20}

t = \frac{π}{20} + \frac{π}{120} + \frac{πn}{10} - \frac{arcsin ( \frac{4}{5} )}{20}

t = \frac{π}{20} + \frac{π}{120} + \frac{πn}{10} - \frac{arcsin ( \frac{4}{5} )}{20}

t = \frac{π}{20} + \frac{π}{120} + \frac{πn}{10} - \frac{arcsin ( \frac{4}{5} )}{20}

t = \frac{πn}{10} + \frac{π}{120} + \frac{arcsin ( \frac{4}{5} )}{20}, t = \frac{π}{20} + \frac{π}{120} + \frac{πn}{10} - \frac{arcsin ( \frac{4}{5} )}{20}

以小数形式表示解

t = \frac{πn}{10} + \frac{π}{120} + \frac{0.92729 \dots}{20}, t = \frac{π}{20} + \frac{π}{120} + \frac{πn}{10} - \frac{0.92729 \dots}{20}

作图

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