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受欢迎的三角函数 >

sin(120pit)=0.06141

解答

sin (120 \cdot π \cdot t) = 0.06141

解答

t = \frac{0.06144 \dots}{120 π} + \frac{n}{60}, t = \frac{1}{120} - \frac{0.06144 \dots}{120 π} + \frac{n}{60}

+1

度数

t = 0.00933 \dots^{\circ} + 0.95492 \dots^{\circ} n, t = 0.46812 \dots^{\circ} + 0.95492 \dots^{\circ} n

求解步骤

sin (120 π t) = 0.06141

使用反三角函数性质

sin (120 π t) = 0.06141

sin (120 π t) = 0.06141

的通解

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

120 π t = arcsin (0.06141) + 2 πn, 120 π t = π - arcsin (0.06141) + 2 πn

120 π t = arcsin (0.06141) + 2 πn, 120 π t = π - arcsin (0.06141) + 2 πn

解

120 π t = arcsin (0.06141) + 2 πn : t = \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

120 π t = arcsin (0.06141) + 2 πn

两边除以

120 π

120 π t = arcsin (0.06141) + 2 πn

两边除以

120 π

\frac{120 π t}{120 π} = \frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π}

化简

\frac{120 π t}{120 π} = \frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π}

化简

\frac{120 π t}{120 π} : t

\frac{120 π t}{120 π}

数字相除:

\frac{120}{120} = 1

= \frac{π t}{π}

约分:

π

= t

化简

\frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π} : \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

\frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π}

消掉

\frac{2 πn}{120 π} : \frac{n}{60}

\frac{2 πn}{120 π}

消掉

\frac{2 πn}{120 π} : \frac{n}{60}

\frac{2 πn}{120 π}

约分:

2

= \frac{πn}{60 π}

约分:

π

= \frac{n}{60}

= \frac{n}{60}

= \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

t = \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

t = \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

t = \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

解

120 π t = π - arcsin (0.06141) + 2 πn : t = \frac{1}{120} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

120 π t = π - arcsin (0.06141) + 2 πn

两边除以

120 π

120 π t = π - arcsin (0.06141) + 2 πn

两边除以

120 π

\frac{120 π t}{120 π} = \frac{π}{120 π} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π}

化简

\frac{120 π t}{120 π} = \frac{π}{120 π} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π}

化简

\frac{120 π t}{120 π} : t

\frac{120 π t}{120 π}

数字相除:

\frac{120}{120} = 1

= \frac{π t}{π}

约分:

π

= t

化简

\frac{π}{120 π} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π} : \frac{1}{120} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

\frac{π}{120 π} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π}

消掉

\frac{π}{120 π} : \frac{1}{120}

\frac{π}{120 π}

约分:

π

= \frac{1}{120}

= \frac{1}{120} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π}

消掉

\frac{2 πn}{120 π} : \frac{n}{60}

\frac{2 πn}{120 π}

消掉

\frac{2 πn}{120 π} : \frac{n}{60}

\frac{2 πn}{120 π}

约分:

2

= \frac{πn}{60 π}

约分:

π

= \frac{n}{60}

= \frac{n}{60}

= \frac{1}{120} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

t = \frac{1}{120} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

t = \frac{1}{120} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

t = \frac{1}{120} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

t = \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}, t = \frac{1}{120} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

以小数形式表示解

t = \frac{0.06144 \dots}{120 π} + \frac{n}{60}, t = \frac{1}{120} - \frac{0.06144 \dots}{120 π} + \frac{n}{60}

作图

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