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受欢迎的三角函数 >

sin(135-x)=sin(x)

解答

sin (135 - x) = sin (x)

解答

x = - 2 πn + \frac{135}{2}, x = - π + \frac{135}{2} - 2 πn

+1

度数

x = 3867.46511 \dots^{\circ} - 36 0^{\circ} n, x = 3687.46511 \dots^{\circ} - 36 0^{\circ} n

求解步骤

sin (135 - x) = sin (x)

两边减去

sin (x)

sin (135 - x) - sin (x) = 0

使用三角恒等式改写

sin (135 - x) - sin (x)

使用和差化积恒等式:

sin (s) - sin (t) = 2 sin (\frac{s - t}{2}) cos (\frac{s + t}{2})

= 2 sin (\frac{135 - x - x}{2}) cos (\frac{135 - x + x}{2})

化简

2 sin (\frac{135 - x - x}{2}) cos (\frac{135 - x + x}{2}) : 2 cos (\frac{135}{2}) sin (\frac{135 - 2 x}{2})

2 sin (\frac{135 - x - x}{2}) cos (\frac{135 - x + x}{2})

同类项相加:

- x - x = - 2 x

= 2 sin (\frac{- 2 x + 135}{2}) cos (\frac{x - x + 135}{2})

同类项相加:

- x + x = 0

= 2 cos (\frac{135}{2}) sin (\frac{- 2 x + 135}{2})

= 2 cos (\frac{135}{2}) sin (\frac{135 - 2 x}{2})

2 cos (\frac{135}{2}) sin (\frac{135 - 2 x}{2}) = 0

两边除以

2 cos (\frac{135}{2})

2 cos (\frac{135}{2}) sin (\frac{135 - 2 x}{2}) = 0

两边除以

2 cos (\frac{135}{2})

\frac{2 cos ( \frac{135}{2} ) sin ( \frac{135 - 2 x}{2} )}{2 cos ( \frac{135}{2} )} = \frac{0}{2 cos ( \frac{135}{2} )}

化简

sin (\frac{135 - 2 x}{2}) = 0

sin (\frac{135 - 2 x}{2}) = 0

sin (\frac{135 - 2 x}{2}) = 0

的通解

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{135 - 2 x}{2} = 0 + 2 πn, \frac{135 - 2 x}{2} = π + 2 πn

\frac{135 - 2 x}{2} = 0 + 2 πn, \frac{135 - 2 x}{2} = π + 2 πn

解

\frac{135 - 2 x}{2} = 0 + 2 πn : x = - 2 πn + \frac{135}{2}

\frac{135 - 2 x}{2} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{135 - 2 x}{2} = 2 πn

在两边乘以

2

\frac{135 - 2 x}{2} = 2 πn

在两边乘以

2

\frac{2 ( 135 - 2 x )}{2} = 2 \cdot 2 πn

化简

135 - 2 x = 4 πn

135 - 2 x = 4 πn

将

135

到右边

135 - 2 x = 4 πn

两边减去

135

135 - 2 x - 135 = 4 πn - 135

化简

- 2 x = 4 πn - 135

- 2 x = 4 πn - 135

两边除以

- 2

- 2 x = 4 πn - 135

两边除以

- 2

\frac{- 2 x}{- 2} = \frac{4 πn}{- 2} - \frac{135}{- 2}

化简

\frac{- 2 x}{- 2} = \frac{4 πn}{- 2} - \frac{135}{- 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{4 πn}{- 2} - \frac{135}{- 2} : - 2 πn + \frac{135}{2}

\frac{4 πn}{- 2} - \frac{135}{- 2}

\frac{4 πn}{- 2} = - 2 πn

\frac{4 πn}{- 2}

使用分式法则:

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

= - \frac{4 πn}{2}

数字相除:

\frac{4}{2} = 2

= - 2 πn

= - 2 πn - \frac{135}{- 2}

使用分式法则:

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

= - 2 πn - (- \frac{135}{2})

使用法则

- (- a) = a

= - 2 πn + \frac{135}{2}

x = - 2 πn + \frac{135}{2}

x = - 2 πn + \frac{135}{2}

x = - 2 πn + \frac{135}{2}

解

\frac{135 - 2 x}{2} = π + 2 πn : x = - π + \frac{135}{2} - 2 πn

\frac{135 - 2 x}{2} = π + 2 πn

在两边乘以

2

\frac{135 - 2 x}{2} = π + 2 πn

在两边乘以

2

\frac{2 ( 135 - 2 x )}{2} = 2 π + 2 \cdot 2 πn

化简

135 - 2 x = 2 π + 4 πn

135 - 2 x = 2 π + 4 πn

将

135

到右边

135 - 2 x = 2 π + 4 πn

两边减去

135

135 - 2 x - 135 = 2 π + 4 πn - 135

化简

- 2 x = 2 π + 4 πn - 135

- 2 x = 2 π + 4 πn - 135

两边除以

- 2

- 2 x = 2 π + 4 πn - 135

两边除以

- 2

\frac{- 2 x}{- 2} = \frac{2 π}{- 2} + \frac{4 πn}{- 2} - \frac{135}{- 2}

化简

\frac{- 2 x}{- 2} = \frac{2 π}{- 2} + \frac{4 πn}{- 2} - \frac{135}{- 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{2 π}{- 2} + \frac{4 πn}{- 2} - \frac{135}{- 2} : - π + \frac{135}{2} - 2 πn

\frac{2 π}{- 2} + \frac{4 πn}{- 2} - \frac{135}{- 2}

对同类项分组

= \frac{2 π}{- 2} - \frac{135}{- 2} + \frac{4 πn}{- 2}

\frac{2 π}{- 2} = - π

\frac{2 π}{- 2}

使用分式法则:

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

= - \frac{2 π}{2}

数字相除:

\frac{2}{2} = 1

= - π

= - π - \frac{135}{- 2} + \frac{4 πn}{- 2}

\frac{135}{- 2} = - \frac{135}{2}

\frac{135}{- 2}

使用分式法则:

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

= - \frac{135}{2}

\frac{4 πn}{- 2} = - 2 πn

\frac{4 πn}{- 2}

使用分式法则:

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

= - \frac{4 πn}{2}

数字相除:

\frac{4}{2} = 2

= - 2 πn

= - π - (- \frac{135}{2}) - 2 πn

使用法则

- (- a) = a

= - π + \frac{135}{2} - 2 πn

x = - π + \frac{135}{2} - 2 πn

x = - π + \frac{135}{2} - 2 πn

x = - π + \frac{135}{2} - 2 πn

x = - 2 πn + \frac{135}{2}, x = - π + \frac{135}{2} - 2 πn

作图

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