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受欢迎的三角函数 >

sin(4x)cos(6x)-cos(4x)sin(6x)=-0.75

解答

sin (4 x) cos (6 x) - cos (4 x) sin (6 x) = - 0.75

解答

x = \frac{0.84806 \dots}{2} - πn, x = - \frac{π}{2} - \frac{0.84806 \dots}{2} - πn

+1

度数

x = 24.29518 \dots^{\circ} - 18 0^{\circ} n, x = - 114.29518 \dots^{\circ} - 18 0^{\circ} n

求解步骤

sin (4 x) cos (6 x) - cos (4 x) sin (6 x) = - 0.75

使用三角恒等式改写

sin (4 x) cos (6 x) - cos (4 x) sin (6 x)

使用角差恒等式:

sin (s) cos (t) - cos (s) sin (t) = sin (s - t)

= sin (4 x - 6 x)

sin (4 x - 6 x) = - 0.75

使用反三角函数性质

sin (4 x - 6 x) = - 0.75

sin (4 x - 6 x) = - 0.75

的通解

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

4 x - 6 x = arcsin (- 0.75) + 2 πn, 4 x - 6 x = π + arcsin (0.75) + 2 πn

4 x - 6 x = arcsin (- 0.75) + 2 πn, 4 x - 6 x = π + arcsin (0.75) + 2 πn

解

4 x - 6 x = arcsin (- 0.75) + 2 πn : x = \frac{arcsin ( \frac{3}{4} )}{2} - πn

4 x - 6 x = arcsin (- 0.75) + 2 πn

化简

4 x - 6 x : - 2 x

4 x - 6 x

同类项相加:

4 x - 6 x = - 2 x

= - 2 x

化简

arcsin (- 0.75) + 2 πn : - arcsin (\frac{3}{4}) + 2 πn

arcsin (- 0.75) + 2 πn

arcsin (- 0.75) = - arcsin (\frac{3}{4})

arcsin (- 0.75)

= arcsin (- \frac{3}{4})

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{3}{4}) = - arcsin (\frac{3}{4})

= - arcsin (\frac{3}{4})

= - arcsin (\frac{3}{4}) + 2 πn

- 2 x = - arcsin (\frac{3}{4}) + 2 πn

两边除以

- 2

- 2 x = - arcsin (\frac{3}{4}) + 2 πn

两边除以

- 2

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

化简

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

化简

\frac{- 2 x}{- 2} : x

\frac{- 2 x}{- 2}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

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

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

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

\frac{arcsin ( \frac{3}{4} )}{- 2}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

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

\frac{2 πn}{- 2} = - πn

\frac{2 πn}{- 2}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= - πn

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

使用法则

- (- a) = a

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

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

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

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

解

4 x - 6 x = π + arcsin (0.75) + 2 πn : x = - \frac{π}{2} - \frac{arcsin ( 0.75 )}{2} - πn

4 x - 6 x = π + arcsin (0.75) + 2 πn

同类项相加:

4 x - 6 x = - 2 x

- 2 x = π + arcsin (0.75) + 2 πn

两边除以

- 2

- 2 x = π + arcsin (0.75) + 2 πn

两边除以

- 2

\frac{- 2 x}{- 2} = \frac{π}{- 2} + \frac{arcsin ( 0.75 )}{- 2} + \frac{2 πn}{- 2}

化简

\frac{- 2 x}{- 2} = \frac{π}{- 2} + \frac{arcsin ( 0.75 )}{- 2} + \frac{2 πn}{- 2}

化简

\frac{- 2 x}{- 2} : x

\frac{- 2 x}{- 2}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{π}{- 2} + \frac{arcsin ( 0.75 )}{- 2} + \frac{2 πn}{- 2} : - \frac{π}{2} - \frac{arcsin ( 0.75 )}{2} - πn

\frac{π}{- 2} + \frac{arcsin ( 0.75 )}{- 2} + \frac{2 πn}{- 2}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{π}{2} + \frac{arcsin ( 0.75 )}{- 2} + \frac{2 πn}{- 2}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{π}{2} - \frac{arcsin ( 0.75 )}{2} + \frac{2 πn}{- 2}

\frac{2 πn}{- 2} = - πn

\frac{2 πn}{- 2}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= - πn

= - \frac{π}{2} - \frac{arcsin ( 0.75 )}{2} - πn

x = - \frac{π}{2} - \frac{arcsin ( 0.75 )}{2} - πn

x = - \frac{π}{2} - \frac{arcsin ( 0.75 )}{2} - πn

x = - \frac{π}{2} - \frac{arcsin ( 0.75 )}{2} - πn

x = \frac{arcsin ( \frac{3}{4} )}{2} - πn, x = - \frac{π}{2} - \frac{arcsin ( 0.75 )}{2} - πn

以小数形式表示解

x = \frac{0.84806 \dots}{2} - πn, x = - \frac{π}{2} - \frac{0.84806 \dots}{2} - πn

作图

流行的例子

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