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受欢迎的三角函数 >

8sin((3.14)/(4*x))=7

解答

8 sin (\frac{3.14}{4 \cdot x}) = 7

解答

x = \frac{3.14}{4 ( 1.06543 \dots + 2 πn )}, x = \frac{3.14}{4 ( π - 1.06543 \dots + 2 πn )}

+1

度数

x = 0^{\circ} + 6.12049 \dots^{\circ} n, x = 0^{\circ} + 5.38046 \dots^{\circ} n

求解步骤

8 sin (\frac{3.14}{4 x}) = 7

两边除以

8

8 sin (\frac{3.14}{4 x}) = 7

两边除以

8

\frac{8 sin ( \frac{3.14}{4 x} )}{8} = \frac{7}{8}

化简

sin (\frac{3.14}{4 x}) = \frac{7}{8}

sin (\frac{3.14}{4 x}) = \frac{7}{8}

使用反三角函数性质

sin (\frac{3.14}{4 x}) = \frac{7}{8}

sin (\frac{3.14}{4 x}) = \frac{7}{8}

的通解

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

\frac{3.14}{4 x} = arcsin (\frac{7}{8}) + 2 πn, \frac{3.14}{4 x} = π - arcsin (\frac{7}{8}) + 2 πn

\frac{3.14}{4 x} = arcsin (\frac{7}{8}) + 2 πn, \frac{3.14}{4 x} = π - arcsin (\frac{7}{8}) + 2 πn

解

\frac{3.14}{4 x} = arcsin (\frac{7}{8}) + 2 πn : x = \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

\frac{3.14}{4 x} = arcsin (\frac{7}{8}) + 2 πn

在两边乘以

x

\frac{3.14}{4 x} = arcsin (\frac{7}{8}) + 2 πn

在两边乘以

x

\frac{3.14}{4 x} x = arcsin (\frac{7}{8}) x + 2 πn x

化简

\frac{3.14}{4} = arcsin (\frac{7}{8}) x + 2 πn x

\frac{3.14}{4} = arcsin (\frac{7}{8}) x + 2 πn x

交换两边

arcsin (\frac{7}{8}) x + 2 πn x = \frac{3.14}{4}

分解

arcsin (\frac{7}{8}) x + 2 πn x : x (arcsin (\frac{7}{8}) + 2 πn)

arcsin (\frac{7}{8}) x + 2 πn x

因式分解出通项

x

= x (arcsin (\frac{7}{8}) + 2 πn)

x (arcsin (\frac{7}{8}) + 2 πn) = \frac{3.14}{4}

两边除以

arcsin (\frac{7}{8}) + 2 πn; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

x (arcsin (\frac{7}{8}) + 2 πn) = \frac{3.14}{4}

两边除以

arcsin (\frac{7}{8}) + 2 πn; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

\frac{x ( arcsin ( \frac{7}{8} ) + 2 πn )}{arcsin ( \frac{7}{8} ) + 2 πn} = \frac{\frac{3.14}{4}}{arcsin ( \frac{7}{8} ) + 2 πn}; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

化简

\frac{x ( arcsin ( \frac{7}{8} ) + 2 πn )}{arcsin ( \frac{7}{8} ) + 2 πn} = \frac{\frac{3.14}{4}}{arcsin ( \frac{7}{8} ) + 2 πn}

化简

\frac{x ( arcsin ( \frac{7}{8} ) + 2 πn )}{arcsin ( \frac{7}{8} ) + 2 πn} : x

\frac{x ( arcsin ( \frac{7}{8} ) + 2 πn )}{arcsin ( \frac{7}{8} ) + 2 πn}

约分:

arcsin (\frac{7}{8}) + 2 πn

= x

化简

\frac{\frac{3.14}{4}}{arcsin ( \frac{7}{8} ) + 2 πn} : \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}

\frac{\frac{3.14}{4}}{arcsin ( \frac{7}{8} ) + 2 πn}

使用分式法则:

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

= \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}

x = \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

x = \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

x = \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

解

\frac{3.14}{4 x} = π - arcsin (\frac{7}{8}) + 2 πn : x = \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

\frac{3.14}{4 x} = π - arcsin (\frac{7}{8}) + 2 πn

在两边乘以

x

\frac{3.14}{4 x} = π - arcsin (\frac{7}{8}) + 2 πn

在两边乘以

x

\frac{3.14}{4 x} x = π x - arcsin (\frac{7}{8}) x + 2 πn x

化简

\frac{3.14}{4} = π x - arcsin (\frac{7}{8}) x + 2 πn x

\frac{3.14}{4} = π x - arcsin (\frac{7}{8}) x + 2 πn x

交换两边

π x - arcsin (\frac{7}{8}) x + 2 πn x = \frac{3.14}{4}

分解

π x - arcsin (\frac{7}{8}) x + 2 πn x : x (π - arcsin (\frac{7}{8}) + 2 πn)

π x - arcsin (\frac{7}{8}) x + 2 πn x

因式分解出通项

x

= x (π - arcsin (\frac{7}{8}) + 2 πn)

x (π - arcsin (\frac{7}{8}) + 2 πn) = \frac{3.14}{4}

两边除以

π - arcsin (\frac{7}{8}) + 2 πn; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

x (π - arcsin (\frac{7}{8}) + 2 πn) = \frac{3.14}{4}

两边除以

π - arcsin (\frac{7}{8}) + 2 πn; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

\frac{x ( π - arcsin ( \frac{7}{8} ) + 2 πn )}{π - arcsin ( \frac{7}{8} ) + 2 πn} = \frac{\frac{3.14}{4}}{π - arcsin ( \frac{7}{8} ) + 2 πn}; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

化简

\frac{x ( π - arcsin ( \frac{7}{8} ) + 2 πn )}{π - arcsin ( \frac{7}{8} ) + 2 πn} = \frac{\frac{3.14}{4}}{π - arcsin ( \frac{7}{8} ) + 2 πn}

化简

\frac{x ( π - arcsin ( \frac{7}{8} ) + 2 πn )}{π - arcsin ( \frac{7}{8} ) + 2 πn} : x

\frac{x ( π - arcsin ( \frac{7}{8} ) + 2 πn )}{π - arcsin ( \frac{7}{8} ) + 2 πn}

约分:

π - arcsin (\frac{7}{8}) + 2 πn

= x

化简

\frac{\frac{3.14}{4}}{π - arcsin ( \frac{7}{8} ) + 2 πn} : \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}

\frac{\frac{3.14}{4}}{π - arcsin ( \frac{7}{8} ) + 2 πn}

使用分式法则:

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

= \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}

x = \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

x = \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

x = \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

x = \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}, x = \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}

以小数形式表示解

x = \frac{3.14}{4 ( 1.06543 \dots + 2 πn )}, x = \frac{3.14}{4 ( π - 1.06543 \dots + 2 πn )}

作图

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