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受欢迎的三角函数 >

sin(4x)cos(7x)-cos(4x)sin(7x)=-0.6

解答

sin (4 x) cos (7 x) - cos (4 x) sin (7 x) = - 0.6

解答

x = \frac{0.64350 \dots}{3} - \frac{2 πn}{3}, x = - \frac{π}{3} - \frac{0.64350 \dots}{3} - \frac{2 πn}{3}

+1

度数

x = 12.28996 \dots^{\circ} - 12 0^{\circ} n, x = - 72.28996 \dots^{\circ} - 12 0^{\circ} n

求解步骤

sin (4 x) cos (7 x) - cos (4 x) sin (7 x) = - 0.6

使用三角恒等式改写

sin (4 x) cos (7 x) - cos (4 x) sin (7 x)

使用角差恒等式:

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

= sin (4 x - 7 x)

sin (4 x - 7 x) = - 0.6

使用反三角函数性质

sin (4 x - 7 x) = - 0.6

sin (4 x - 7 x) = - 0.6

的通解

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

4 x - 7 x = arcsin (- 0.6) + 2 πn, 4 x - 7 x = π + arcsin (0.6) + 2 πn

4 x - 7 x = arcsin (- 0.6) + 2 πn, 4 x - 7 x = π + arcsin (0.6) + 2 πn

解

4 x - 7 x = arcsin (- 0.6) + 2 πn : x = \frac{arcsin ( \frac{3}{5} )}{3} - \frac{2 πn}{3}

4 x - 7 x = arcsin (- 0.6) + 2 πn

化简

4 x - 7 x : - 3 x

4 x - 7 x

同类项相加:

4 x - 7 x = - 3 x

= - 3 x

化简

arcsin (- 0.6) + 2 πn : - arcsin (\frac{3}{5}) + 2 πn

arcsin (- 0.6) + 2 πn

arcsin (- 0.6) = - arcsin (\frac{3}{5})

arcsin (- 0.6)

= arcsin (- \frac{3}{5})

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{3}{5}) = - arcsin (\frac{3}{5})

= - arcsin (\frac{3}{5})

= - arcsin (\frac{3}{5}) + 2 πn

- 3 x = - arcsin (\frac{3}{5}) + 2 πn

两边除以

- 3

- 3 x = - arcsin (\frac{3}{5}) + 2 πn

两边除以

- 3

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

化简

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

化简

\frac{- 3 x}{- 3} : x

\frac{- 3 x}{- 3}

使用分式法则:

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

= \frac{3 x}{3}

数字相除:

\frac{3}{3} = 1

= x

化简

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

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

使用分式法则:

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

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

使用分式法则:

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

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

使用法则

- (- a) = a

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

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

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

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

解

4 x - 7 x = π + arcsin (0.6) + 2 πn : x = - \frac{π}{3} - \frac{arcsin ( 0.6 )}{3} - \frac{2 πn}{3}

4 x - 7 x = π + arcsin (0.6) + 2 πn

同类项相加:

4 x - 7 x = - 3 x

- 3 x = π + arcsin (0.6) + 2 πn

两边除以

- 3

- 3 x = π + arcsin (0.6) + 2 πn

两边除以

- 3

\frac{- 3 x}{- 3} = \frac{π}{- 3} + \frac{arcsin ( 0.6 )}{- 3} + \frac{2 πn}{- 3}

化简

\frac{- 3 x}{- 3} = \frac{π}{- 3} + \frac{arcsin ( 0.6 )}{- 3} + \frac{2 πn}{- 3}

化简

\frac{- 3 x}{- 3} : x

\frac{- 3 x}{- 3}

使用分式法则:

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

= \frac{3 x}{3}

数字相除:

\frac{3}{3} = 1

= x

化简

\frac{π}{- 3} + \frac{arcsin ( 0.6 )}{- 3} + \frac{2 πn}{- 3} : - \frac{π}{3} - \frac{arcsin ( 0.6 )}{3} - \frac{2 πn}{3}

\frac{π}{- 3} + \frac{arcsin ( 0.6 )}{- 3} + \frac{2 πn}{- 3}

使用分式法则:

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

= - \frac{π}{3} + \frac{arcsin ( 0.6 )}{- 3} + \frac{2 πn}{- 3}

使用分式法则:

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

= - \frac{π}{3} - \frac{arcsin ( 0.6 )}{3} + \frac{2 πn}{- 3}

使用分式法则:

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

= - \frac{π}{3} - \frac{arcsin ( 0.6 )}{3} - \frac{2 πn}{3}

x = - \frac{π}{3} - \frac{arcsin ( 0.6 )}{3} - \frac{2 πn}{3}

x = - \frac{π}{3} - \frac{arcsin ( 0.6 )}{3} - \frac{2 πn}{3}

x = - \frac{π}{3} - \frac{arcsin ( 0.6 )}{3} - \frac{2 πn}{3}

x = \frac{arcsin ( \frac{3}{5} )}{3} - \frac{2 πn}{3}, x = - \frac{π}{3} - \frac{arcsin ( 0.6 )}{3} - \frac{2 πn}{3}

以小数形式表示解

x = \frac{0.64350 \dots}{3} - \frac{2 πn}{3}, x = - \frac{π}{3} - \frac{0.64350 \dots}{3} - \frac{2 πn}{3}

作图

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