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受欢迎的三角函数 >

3sin(pi/5 x)=2

解答

3 sin (\frac{π}{5} x) = 2

解答

x = \frac{5 \cdot 0.72972 \dots}{π} + 10 n, x = 5 - \frac{5 \cdot 0.72972 \dots}{π} + 10 n

+1

度数

x = 66.54318 \dots^{\circ} + 572.95779 \dots^{\circ} n, x = 219.93571 \dots^{\circ} + 572.95779 \dots^{\circ} n

求解步骤

3 sin (\frac{π}{5} x) = 2

两边除以

3

3 sin (\frac{π}{5} x) = 2

两边除以

3

\frac{3 sin ( \frac{π}{5} x )}{3} = \frac{2}{3}

化简

sin (\frac{π}{5} x) = \frac{2}{3}

sin (\frac{π}{5} x) = \frac{2}{3}

使用反三角函数性质

sin (\frac{π}{5} x) = \frac{2}{3}

sin (\frac{π}{5} x) = \frac{2}{3}

的通解

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

\frac{π}{5} x = arcsin (\frac{2}{3}) + 2 πn, \frac{π}{5} x = π - arcsin (\frac{2}{3}) + 2 πn

\frac{π}{5} x = arcsin (\frac{2}{3}) + 2 πn, \frac{π}{5} x = π - arcsin (\frac{2}{3}) + 2 πn

解

\frac{π}{5} x = arcsin (\frac{2}{3}) + 2 πn : x = \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

\frac{π}{5} x = arcsin (\frac{2}{3}) + 2 πn

在两边乘以

5

\frac{π}{5} x = arcsin (\frac{2}{3}) + 2 πn

在两边乘以

5

5 \cdot \frac{π}{5} x = 5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn

化简

5 \cdot \frac{π}{5} x = 5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn

化简

5 \cdot \frac{π}{5} x : π x

5 \cdot \frac{π}{5} x

分式相乘:

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

= \frac{5 π}{5} x

约分:

5

= x π

化简

5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn : 5 arcsin (\frac{2}{3}) + 10 πn

5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn

数字相乘:

5 \cdot 2 = 10

= 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 arcsin (\frac{2}{3}) + 10 πn

两边除以

π

π x = 5 arcsin (\frac{2}{3}) + 10 πn

两边除以

π

\frac{π x}{π} = \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π}

化简

x = \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

x = \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

解

\frac{π}{5} x = π - arcsin (\frac{2}{3}) + 2 πn : x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

\frac{π}{5} x = π - arcsin (\frac{2}{3}) + 2 πn

在两边乘以

5

\frac{π}{5} x = π - arcsin (\frac{2}{3}) + 2 πn

在两边乘以

5

5 \cdot \frac{π}{5} x = 5 π - 5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn

化简

5 \cdot \frac{π}{5} x = 5 π - 5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn

化简

5 \cdot \frac{π}{5} x : π x

5 \cdot \frac{π}{5} x

分式相乘:

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

= \frac{5 π}{5} x

约分:

5

= x π

化简

5 π - 5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn : 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

5 π - 5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn

数字相乘:

5 \cdot 2 = 10

= 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

两边除以

π

π x = 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

两边除以

π

\frac{π x}{π} = \frac{5 π}{π} - \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π}

化简

\frac{π x}{π} = \frac{5 π}{π} - \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π}

化简

\frac{π x}{π} : x

\frac{π x}{π}

约分:

π

= x

化简

\frac{5 π}{π} - \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π} : 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

\frac{5 π}{π} - \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π}

消掉

\frac{5 π}{π} : 5

\frac{5 π}{π}

约分:

π

= 5

= 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π}

消掉

\frac{10 πn}{π} : 10 n

\frac{10 πn}{π}

约分:

π

= 10 n

= 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

x = \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n, x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

以小数形式表示解

x = \frac{5 \cdot 0.72972 \dots}{π} + 10 n, x = 5 - \frac{5 \cdot 0.72972 \dots}{π} + 10 n

作图

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