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受欢迎的三角函数 >

5sin(pi/4 x)=4

解答

5 sin (\frac{π}{4} x) = 4

解答

x = \frac{4 \cdot 0.92729 \dots}{π} + 8 n, x = 4 - \frac{4 \cdot 0.92729 \dots}{π} + 8 n

+1

度数

x = 67.64734 \dots^{\circ} + 458.36623 \dots^{\circ} n, x = 161.53577 \dots^{\circ} + 458.36623 \dots^{\circ} n

求解步骤

5 sin (\frac{π}{4} x) = 4

两边除以

5

5 sin (\frac{π}{4} x) = 4

两边除以

5

\frac{5 sin ( \frac{π}{4} x )}{5} = \frac{4}{5}

化简

sin (\frac{π}{4} x) = \frac{4}{5}

sin (\frac{π}{4} x) = \frac{4}{5}

使用反三角函数性质

sin (\frac{π}{4} x) = \frac{4}{5}

sin (\frac{π}{4} x) = \frac{4}{5}

的通解

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

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

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

解

\frac{π}{4} x = arcsin (\frac{4}{5}) + 2 πn : x = \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

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

在两边乘以

4

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

在两边乘以

4

4 \cdot \frac{π}{4} x = 4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn

化简

4 \cdot \frac{π}{4} x = 4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn

化简

4 \cdot \frac{π}{4} x : π x

4 \cdot \frac{π}{4} x

分式相乘:

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

= \frac{4 π}{4} x

约分:

4

= x π

化简

4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn : 4 arcsin (\frac{4}{5}) + 8 πn

4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn

数字相乘:

4 \cdot 2 = 8

= 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 arcsin (\frac{4}{5}) + 8 πn

两边除以

π

π x = 4 arcsin (\frac{4}{5}) + 8 πn

两边除以

π

\frac{π x}{π} = \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π}

化简

x = \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

x = \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

解

\frac{π}{4} x = π - arcsin (\frac{4}{5}) + 2 πn : x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

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

在两边乘以

4

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

在两边乘以

4

4 \cdot \frac{π}{4} x = 4 π - 4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn

化简

4 \cdot \frac{π}{4} x = 4 π - 4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn

化简

4 \cdot \frac{π}{4} x : π x

4 \cdot \frac{π}{4} x

分式相乘:

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

= \frac{4 π}{4} x

约分:

4

= x π

化简

4 π - 4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn : 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

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

数字相乘:

4 \cdot 2 = 8

= 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

两边除以

π

π x = 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

两边除以

π

\frac{π x}{π} = \frac{4 π}{π} - \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π}

化简

\frac{π x}{π} = \frac{4 π}{π} - \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π}

化简

\frac{π x}{π} : x

\frac{π x}{π}

约分:

π

= x

化简

\frac{4 π}{π} - \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π} : 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

\frac{4 π}{π} - \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π}

消掉

\frac{4 π}{π} : 4

\frac{4 π}{π}

约分:

π

= 4

= 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π}

消掉

\frac{8 πn}{π} : 8 n

\frac{8 πn}{π}

约分:

π

= 8 n

= 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

x = \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n, x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

以小数形式表示解

x = \frac{4 \cdot 0.92729 \dots}{π} + 8 n, x = 4 - \frac{4 \cdot 0.92729 \dots}{π} + 8 n

作图

流行的例子

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