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受欢迎的三角函数 >

4sin(pi/2 x)=3

解答

4 sin (\frac{π}{2} x) = 3

解答

x = \frac{2 \cdot 0.84806 \dots}{π} + 4 n, x = 2 - \frac{2 \cdot 0.84806 \dots}{π} + 4 n

+1

度数

x = 30.93359 \dots^{\circ} + 229.18311 \dots^{\circ} n, x = 83.65796 \dots^{\circ} + 229.18311 \dots^{\circ} n

求解步骤

4 sin (\frac{π}{2} x) = 3

两边除以

4

4 sin (\frac{π}{2} x) = 3

两边除以

4

\frac{4 sin ( \frac{π}{2} x )}{4} = \frac{3}{4}

化简

sin (\frac{π}{2} x) = \frac{3}{4}

sin (\frac{π}{2} x) = \frac{3}{4}

使用反三角函数性质

sin (\frac{π}{2} x) = \frac{3}{4}

sin (\frac{π}{2} x) = \frac{3}{4}

的通解

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

\frac{π}{2} x = arcsin (\frac{3}{4}) + 2 πn, \frac{π}{2} x = π - arcsin (\frac{3}{4}) + 2 πn

\frac{π}{2} x = arcsin (\frac{3}{4}) + 2 πn, \frac{π}{2} x = π - arcsin (\frac{3}{4}) + 2 πn

解

\frac{π}{2} x = arcsin (\frac{3}{4}) + 2 πn : x = \frac{2 arcsin ( \frac{3}{4} )}{π} + 4 n

\frac{π}{2} x = arcsin (\frac{3}{4}) + 2 πn

在两边乘以

2

\frac{π}{2} x = arcsin (\frac{3}{4}) + 2 πn

在两边乘以

2

2 \cdot \frac{π}{2} x = 2 arcsin (\frac{3}{4}) + 2 \cdot 2 πn

化简

2 \cdot \frac{π}{2} x = 2 arcsin (\frac{3}{4}) + 2 \cdot 2 πn

化简

2 \cdot \frac{π}{2} x : π x

2 \cdot \frac{π}{2} x

分式相乘:

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

= \frac{2 π}{2} x

约分:

2

= x π

化简

2 arcsin (\frac{3}{4}) + 2 \cdot 2 πn : 2 arcsin (\frac{3}{4}) + 4 πn

2 arcsin (\frac{3}{4}) + 2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= 2 arcsin (\frac{3}{4}) + 4 πn

π x = 2 arcsin (\frac{3}{4}) + 4 πn

π x = 2 arcsin (\frac{3}{4}) + 4 πn

π x = 2 arcsin (\frac{3}{4}) + 4 πn

两边除以

π

π x = 2 arcsin (\frac{3}{4}) + 4 πn

两边除以

π

\frac{π x}{π} = \frac{2 arcsin ( \frac{3}{4} )}{π} + \frac{4 πn}{π}

化简

x = \frac{2 arcsin ( \frac{3}{4} )}{π} + 4 n

x = \frac{2 arcsin ( \frac{3}{4} )}{π} + 4 n

解

\frac{π}{2} x = π - arcsin (\frac{3}{4}) + 2 πn : x = 2 - \frac{2 arcsin ( \frac{3}{4} )}{π} + 4 n

\frac{π}{2} x = π - arcsin (\frac{3}{4}) + 2 πn

在两边乘以

2

\frac{π}{2} x = π - arcsin (\frac{3}{4}) + 2 πn

在两边乘以

2

2 \cdot \frac{π}{2} x = 2 π - 2 arcsin (\frac{3}{4}) + 2 \cdot 2 πn

化简

2 \cdot \frac{π}{2} x = 2 π - 2 arcsin (\frac{3}{4}) + 2 \cdot 2 πn

化简

2 \cdot \frac{π}{2} x : π x

2 \cdot \frac{π}{2} x

分式相乘:

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

= \frac{2 π}{2} x

约分:

2

= x π

化简

2 π - 2 arcsin (\frac{3}{4}) + 2 \cdot 2 πn : 2 π - 2 arcsin (\frac{3}{4}) + 4 πn

2 π - 2 arcsin (\frac{3}{4}) + 2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= 2 π - 2 arcsin (\frac{3}{4}) + 4 πn

π x = 2 π - 2 arcsin (\frac{3}{4}) + 4 πn

π x = 2 π - 2 arcsin (\frac{3}{4}) + 4 πn

π x = 2 π - 2 arcsin (\frac{3}{4}) + 4 πn

两边除以

π

π x = 2 π - 2 arcsin (\frac{3}{4}) + 4 πn

两边除以

π

\frac{π x}{π} = \frac{2 π}{π} - \frac{2 arcsin ( \frac{3}{4} )}{π} + \frac{4 πn}{π}

化简

\frac{π x}{π} = \frac{2 π}{π} - \frac{2 arcsin ( \frac{3}{4} )}{π} + \frac{4 πn}{π}

化简

\frac{π x}{π} : x

\frac{π x}{π}

约分:

π

= x

化简

\frac{2 π}{π} - \frac{2 arcsin ( \frac{3}{4} )}{π} + \frac{4 πn}{π} : 2 - \frac{2 arcsin ( \frac{3}{4} )}{π} + 4 n

\frac{2 π}{π} - \frac{2 arcsin ( \frac{3}{4} )}{π} + \frac{4 πn}{π}

消掉

\frac{2 π}{π} : 2

\frac{2 π}{π}

约分:

π

= 2

= 2 - \frac{2 arcsin ( \frac{3}{4} )}{π} + \frac{4 πn}{π}

消掉

\frac{4 πn}{π} : 4 n

\frac{4 πn}{π}

约分:

π

= 4 n

= 2 - \frac{2 arcsin ( \frac{3}{4} )}{π} + 4 n

x = 2 - \frac{2 arcsin ( \frac{3}{4} )}{π} + 4 n

x = 2 - \frac{2 arcsin ( \frac{3}{4} )}{π} + 4 n

x = 2 - \frac{2 arcsin ( \frac{3}{4} )}{π} + 4 n

x = \frac{2 arcsin ( \frac{3}{4} )}{π} + 4 n, x = 2 - \frac{2 arcsin ( \frac{3}{4} )}{π} + 4 n

以小数形式表示解

x = \frac{2 \cdot 0.84806 \dots}{π} + 4 n, x = 2 - \frac{2 \cdot 0.84806 \dots}{π} + 4 n

作图

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